Proton Therapy Physics

PROTON THERAPY PHYSICS

Edited by

Harald Paganetti

A TAY L O R & F R A N C I S B O O K

Proton Therapy Physics

Series in Medical Physics and Biomedical Engineering Series Editors: John G Webster, Slavik Tabakov, Kwan-Hoong Ng Other recent books in the series: Practical Biomedical Signal Analysis Using MATLAB® K J Blinowska and J Zygierewicz Physics for Diagnostic Radiology, Third Edition P P Dendy and B Heaton (Eds.) Nuclear Medicine Physics J J Pedroso de Lima (Ed) Handbook of Photonics for Biomedical Science Valery V Tuchin (Ed) Handbook of Anatomical Models for Radiation Dosimetry Xie George Xu and Keith F Eckerman (Eds) Fundamentals of MRI: An Interactive Learning Approach Elizabeth Berry and Andrew J Bulpitt Handbook of Optical Sensing of Glucose in Biological Fluids and Tissues Valery V Tuchin (Ed) Intelligent and Adaptive Systems in Medicine Oliver C L Haas and Keith J Burnham A Introduction to Radiation Protection in Medicine Jamie V Trapp and Tomas Kron (Eds) A Practical Approach to Medical Image Processing Elizabeth Berry Biomolecular Action of Ionizing Radiation Shirley Lehnert An Introduction to Rehabilitation Engineering R A Cooper, H Ohnabe, and D A Hobson The Physics of Modern Brachytherapy for Oncology D Baltas, N Zamboglou, and L Sakelliou Electrical Impedance Tomography D Holder (Ed)

Series in Medical Physics and Biomedical Engineering

Proton Therapy Physics

Edited by

Harald Paganetti

Massachusetts General Hospital and Harvard Medical School, Boston, USA

Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

A TA Y L O R & F R A N C I S B O O K

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2012 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 2011912 International Standard Book Number-13: 978-1-4398-3645-3 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

Contents About the Series.................................................................................................... vii The International Organization for Medical Physics........................................ix Introduction.............................................................................................................xi Editor.................................................................................................................... xvii Contributors.......................................................................................................... xix 1. Proton Therapy: History and Rationale......................................................1 Harald Paganetti 2. Physics of Proton Interactions in Matter.................................................. 19 Bernard Gottschalk 3. Proton Accelerators....................................................................................... 61 Marco Schippers 4. Characteristics of Clinical Proton Beams............................................... 103 Hsiao-Ming Lu and Jacob Flanz 5. Beam Delivery Using Passive Scattering................................................ 125 Roelf Slopsema 6. Particle Beam Scanning............................................................................. 157 Jacob Flanz 7. Dosimetry...................................................................................................... 191 Hugo Palmans 8. Quality Assurance and Commissioning................................................ 221 Zuofeng Li, Roelf Slopsema, Stella Flampouri, and Daniel K. Yeung 9. Monte Carlo Simulations........................................................................... 265 Harald Paganetti 10. Physics of Treatment Planning for Single-Field Uniform Dose........305 Martijn Engelsman 11. Physics of Treatment Planning Using Scanned Beams....................... 335 Antony Lomax

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12. Dose Calculation Algorithms................................................................... 381 Benjamin Clasie, Harald Paganetti, and Hanne M. Kooy 13. Precision and Uncertainties in Proton Therapy for Nonmoving Targets..................................................................................... 413 Jatinder R. Palta and Daniel K. Yeung 14. Precision and Uncertainties in Proton Therapy for Moving Targets............................................................................................435 Martijn Engelsman and Christoph Bert 15. Treatment-Planning Optimization.......................................................... 461 Alexei V. Trofimov, Jan H. Unkelbach, and David Craft 16. In Vivo Dose Verification.......................................................................... 489 Katia Parodi 17. Basic Aspects of Shielding........................................................................ 525 Nisy Elizabeth Ipe 18. Late Effects from Scattered and Secondary Radiation........................ 555 Harald Paganetti 19. The Physics of Proton Biology.................................................................. 593 Harald Paganetti 20. Fully Exploiting the Benefits of Protons: Using Risk Models for Normal Tissue Complications in Treatment Optimization................ 627 Peter van Luijk and Marco Schippers

About the Series The Series in Medical Physics and Biomedical Engineering describes the applications of physical sciences, engineering, and mathematics in medicine and clinical research. The series seeks (but is not restricted to) publications in the following topics: • • • • • • • • • • • • • • • • • • • • • • •

Artificial organs Assistive technology Bioinformatics Bioinstrumentation Biomaterials Biomechanics Biomedical engineering Clinical engineering Imaging Implants Medical computing and mathematics Medical/surgical devices Patient monitoring Physiological measurement Prosthetics Radiation protection, health physics, and dosimetry Regulatory issues Rehabilitation engineering Sports medicine Systems physiology Telemedicine Tissue engineering Treatment

The Series in Medical Physics and Biomedical Engineering is an international series that meets the need for up-to-date texts in this rapidly developing field. Books in the series range in level from introductory graduate textbooks and practical handbooks to more advanced expositions of current research. The Series in Medical Physics and Biomedical Engineering is the official book series of the International Organization for Medical Physics. vii

The International Organization for Medical Physics The International Organization for Medical Physics (IOMP), founded in 1963, is a scientific, educational, and professional organization of 76 national adhering organizations, more than 16,500 individual members, several corporate members, and four international regional organizations. IOMP is administered by the Council, which includes delegates from each of the Adhering National Organizations. Regular meetings of the Council are held electronically as well as every three years at the World Congress on Medical Physics and Biomedical Engineering. The president and other officers form the Executive Committee, and there are also committees covering the main areas of activity, including education and training, scientific, professional relations, and publications.

Objectives • To contribute to the advancement of medical physics in all its aspects • To organize international cooperation in medical physics, especially in developing countries • To encourage and advise on the formation of national organizations of medical physics in those countries that lack such organizations

Activities Official journals of the IOMP are Physics in Medicine and Biology, Medical Physics, and Physiological Measurement. The IOMP publishes a bulletin Medical Physics World twice a year that is distributed to all members. A World Congress on Medical Physics and Biomedical Engineering is held every three years in cooperation with IFMBE through the International Union for Physics and Engineering Sciences in Medicine. A regionally based International Conference on Medical Physics is held between World Congresses. IOMP also sponsors international conferences, workshops, and courses. IOMP representatives contribute to various international committees and working groups. ix

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The International Organization for Medical Physics

The IOMP has several programs to assist medical physicists in developing countries. The joint IOMP Library Programme supports 69 active libraries in 42 developing countries, and the Used Equipment Programme coordinates equipment donations. The Travel Assistance Programme provides a limited number of grants to enable physicists to attend the World Congresses. The IOMP website is being developed to include a scientific database of international standards in medical physics and a virtual education and resource center. Information on the activities of the IOMP can be found on its website at http://www.iomp.org.

Introduction According to the World Health Organization, cancer is the leading cause of death worldwide. A large portion of cancer patients (e.g., more than half of all cancer patients in the United States) receive radiation therapy during the course of treatment. Radiation therapy is used either as the sole treatment or, more typically, in combination with other therapies, including surgery and chemotherapy. Radiation interacts with tissue via atomic and nuclear interactions. The energy transferred to and deposited in the tissue in such interactions is quantified as “absorbed dose” and expressed in energy (Joules) absorbed per unit mass (kg), which has the units of Gray (Gy). Depending on the number and spatial correlation of such interactions, mainly with cellular DNA, they can result in mutations or complete functional disruption (i.e., cell death). Assessing radiation damage is a complex problem because the cell typically does have the limited ability to repair certain types of lesions. There are many degrees of freedom when administering radiation, for example, different radiation modalities, doses, and beam directions. The main focus in research and development of radiation therapy is on eradicating cancerous tissue while minimizing the irradiation of healthy tissue. The ideal scenario would be to treat the designated target without damaging any healthy structures. This is not possible for various reasons such as uncertainties in defining the target volume as well as delivering the therapeutic dose as planned. Furthermore, applying external beam radiation therapy typically requires the beam to penetrate healthy tissue in order to reach the target. Treatment planning in radiation therapy uses mathematical and physical formalisms to optimize the trade-off between delivering a high and conformal dose to the target and limiting the doses to critical structures. The dose tolerance levels for critical structures, as well as the required doses for various tumor types, are typically defined on the basis of decades of clinical experience. When considering the trade-off between administering the prescribed target dose and the dose to healthy tissue, the term “therapeutic ratio” is often used. The therapeutic ratio can be defined as the ratio of the probabilities for tumor eradication and normal tissue complication. Technological advances in beam delivery and treatment modality focus mainly on increasing the therapeutic ratio. Improvements can be achieved, for example, by applying advanced imaging techniques leading to improved patient setup or tumor localization. A gain in the therapeutic ratio can also be expected when using proton therapy instead of conventional photon or electron therapy. The rationale for using proton beams instead of photon beams is the feasibility of delivering xi

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Introduction

higher doses to the tumor while maintaining the total dose to critical structures or maintaining the target dose while reducing the total dose to critical structures. The most prominent difference between photon and proton beams is the finite range of a proton beam. After a short build-up region, photon beams show an exponentially decreasing energy deposition with increasing depth in tissue. Except for superficial lesions, a higher dose to the tumor compared with the organ at risk can only be achieved by using multiple beam directions. Furthermore, a homogenous dose distribution can only be achieved by utilizing various different beam angles, not by delivering a single field. In contrast, the energy transferred to tissue by protons is inversely proportional to the proton velocity as protons lose their energy mainly in electromagnetic interactions with orbital electrons of atoms. The more the protons slow down, the higher the energy they transfer to tissue per track length, causing the maximum dose deposition at a certain depth in tissue. For a single proton, the peak is very sharp. For a proton beam, it is broadened into a peak of typically a few millimeters width because of the statistical distribution of the proton tracks. The peak is called the Bragg peak (Figure 1). This feature allows pointing a beam toward a critical structure. The depth and width of the Bragg peak is a function of the beam energy and the material (tissue) heterogeneity in the beam path. The peak depth can be influenced by changing the beam energy and can thus be positioned within the target for each beam direction. Although protons from a single beam direction are able to deliver a homogeneous dose throughout the target (by varying the beam energy), multiple beam angles are also used in proton therapy to even further optimize the dose distribution with respect to organs at risk. Note that there is also a slight difference between photon and proton beams when considering the lateral penumbra. For large depths (more than ~16 cm), the penumbra for proton beams is slightly wider than the one for photon beams by typically a few millimeters. Depending on the site, this can be a slight disadvantage of proton beams. Dose

Bragg peak

Depth in tissue FIGURE 1 Energy deposition as a function of depth for a proton beam leading to the Bragg peak.

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The physical characteristic of proton beams—their finite range—can be used in radiation therapy for increasing the dose to the target or decreasing the dose to organs at risk. Treatment plan comparisons show that protons offer potential gains for many sites. In some cases, the dose conformity that can be reached with intensity-modulated photon therapy might be comparable to one that can be achieved with proton techniques. However, because of the difference in physics between photon beams and proton beams as outlined above, the total energy deposited in the patient for any treatment will always be higher with photons than with protons. The use of protons leads to a reduction of the total energy when treating a given target by a factor of about three compared to standard photon techniques and by a factor of about two compared to intensity-­modulated photon plans. The irradiation of a smaller volume of normal tissues compared to conventional modalities allows higher doses to the tumor, leading to an increased tumor control probability. Furthermore, proton therapy allows a smaller dose to critical structures while maintaining the target dose compared to photon techniques. Benefits can thus be expected particularly for pediatric patients where the irradiation of large volumes are particularly critical in terms of long-term side effects. The share of patients treated with proton therapy compared with photon therapy is currently still low but is expected to increase significantly in the near future, as evidenced by the number of facilities currently planned or under construction. With the increasing use of protons as radiation therapy modality comes the need for a better understanding of the characteristics of protons. Protons are not just heavy photons when it comes to treatment planning, quality assurance, delivery uncertainties, radiation monitoring, and biological considerations. To fully utilize the advantages of proton therapy and, just as importantly, to understand the uncertainties and limitations of precisely shaped dose distribution, proton therapy physics needs to be understood. Furthermore, the clinical impact and the evidence for improved outcomes need to be studied. Proton therapy research has increased significantly in the last few years. Figure 2 shows how the number of proton therapy–related publications in most relevant scientific journals has increased over the years. This book starts with an overview about the history of proton therapy in Chapter 1. The pioneering work done at a few institutions in the early days of proton therapy is acknowledged, and the main developments up to the first hospital-based facilities are outlined. The chapter concludes with comments about the original and current clinical rationale for proton therapy. The atomic and nuclear physics background necessary for understanding proton interactions with tissue is summarized in Chapter 2. The chapter covers the basic physics of protons slowing down in matter independent of their medical use. The ways in which protons can interact with materials/tissue is described from both macroscopic (e.g., dose) and microscopic (energy loss

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Introduction

160

Number of publications

140

Proton therapy research publications

120 100 80 60 40 20 0 1970

1980

1990 Year

2000

2010

FIGURE 2 The number of publications listed in PubMed (a free database of citations on life sciences and biomedical topics) per year with the phrase equal or similar to “proton radiation therapy” in the title or abstract (). Also shown is an exponential fit of the form Publications = a × eb[year-1970] (solid line).

kinematics) points of view. Furthermore, Chapter 2 presents equations that can be used for estimating many characteristics of proton beams. Chapter 3 describes the physics of proton accelerators, including currently used techniques (cyclotrons and synchrotrons) and a brief discussion of new developments. The chapter goes beyond simply summarizing the characteristics of such machines for proton therapy and also describes some of the main principles of particle accelerator physics. Chapter 4 outlines the characteristics of clinical proton beams and how the clinical parameters are connected to the design features and the operational settings of the beam delivery system. Parameters such as dose rate, beam intensity, beam energy, beam range, distal falloff, and lateral penumbra are introduced. The next two chapters describe in detail how to generate a conformal dose distribution in the patient. Passive scattered beam delivery systems are discussed in Chapter 5. Scattering techniques to create a broad beam as well as range modulation techniques to generate a clinically desired depth–dose distribution are outlined in detail. Next, Chapter 6 focuses on magnetic beam scanning systems. Scanning hardware as well as parameters that determine the scanning beam characteristics (e.g., its time structure and performance) are discussed. The chapter closes with a discussion of safety and quality assurance aspects. Chapter 7 focuses on dosimetry and covers the main detector systems and measuring techniques for reference dosimetry as well as beam profile measurements. The underlying dosimetry formalism is reviewed as well as the basic aspects of microdosimetry. Chapter 8 expands on this topic by

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outlining the basic quality assurance and commissioning guidelines, including acceptance testing. The quality assurance guidelines focus on dosimetry as well as mechanical and safety issues. One aspect of increasing importance in the field of medical physics is the use of computer simulations to replace or assist experimental methods. After an introduction to the Monte Carlo particle-tracking method, Chapter  9 demonstrates how Monte Carlo simulations can be used to address various clinical and research aspects in proton therapy. Examples are treatment head design studies as well as the simulation of scattered radiation for radiation protection or dose deposition characteristics for biophysical modeling. Next, treatment planning is outlined. The treatment planning process is largely modality independent. Consequently, Chapter 10 covers only protonspecific aspects of treatment planning for passive scattering and scanning delivery for single-field uniform dose (i.e., homogeneous dose distributions in the target from each beam direction). Proton-specific margin considerations and special treatment techniques are discussed. Chapter 11 describes treatment planning for multiple-field uniform dose and intensity-modulated proton therapy using beam scanning. The challenges and the potential of intensity-modulated treatments are described, including uncertainties and optimization strategies. A few case studies conclude this chapter. One of the key methods used in treatment planning is the dose calculation method. Chapter 12 does focus on dose calculation concepts and algorithms. The formalism for pencil beam algorithms is reviewed from a theoretical and practical implementation point of view. Further, the Monte Carlo dose calculation method and hybrid methods are outlined. One of the advantages of proton therapy is the ability to precisely shape dose distributions, in particular using the distal falloff due to the finite beam range. Uncertainties in the proton beam range limit the use of the finite range of proton beams in the patient because more precise dose distributions are less forgiving in terms of errors and uncertainties. Chapter 13 discusses precision and uncertainties for nonmoving targets. Special emphasis is on the dosimetric consequences of heterogeneities. Chapter 14 deals with precision and uncertainties for moving targets, such as when treating lung cancer with proton beams. The clinical impact of motion as well as methods of motion management for minimizing motion effects are outlined. Computerized treatment planning relies on optimization algorithms to generate a clinically acceptable plan. Chapter 15 reviews some of the main aspects of treatment plan optimization including the consideration of some of the uncertainties discussed in Chapters 13 and 14. Robust and fourdimensional optimization strategies are described. Chapter 16 discusses methods for in vivo dose or beam range verification. These include the detection of photons caused by nuclear excitations and of annihilation photons created after the generation of positron emitters by the primary proton beam.

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Introduction

The safety of patients as well as operating personnel has to be ensured by proper shielding of a treatment beam. In proton therapy the main concerns are secondary neutrons. Shielding considerations and measurement methods are covered in Chapter 17. The consequences of scattered or secondary radiation that a patient receives during treatment of the primary cancer could include long-time side effects such as a second cancer. This aspect is outlined in Chapter 18. Secondary doses are quantified, and methods to estimate the risks for radiation-induced cancers are presented. Although this book is concerned mainly with proton therapy physics, biological implications are discussed briefly as they relate directly to physics aspects. The biological implications of using protons are outlined from a physics perspective in Chapter 19. Finally, outcome modeling is summarized in Chapter 20. This final chapter illustrates the use of risk models for normal tissue complications in treatment optimization. Proton beams allow precise dose shaping, and thus, personalized treatment planning might become particularly important for proton therapy in the future. The goal of this book is to offer a coherent and instructive overview of proton therapy physics. It might serve as a practical guide for physicians, dosimetrists, radiation therapists, and physicists who already have some experience in radiation oncology. Furthermore, it can serve graduate students who are either in a medical physics program or are considering a career in medical physics. Certainly it is also of interest to physicians in their last year of medical school or residency who have a desire to understand proton therapy physics. There are some overlaps between different chapters that could not be avoided because each chapter should be largely independent. Overall, the book covers most, but certainly not all, aspects of proton therapy physics.

Editor Dr. Harald Paganetti is currently Director of Physics Research at the Department of Radiation Oncology at Massachusetts General Hospital in Boston and Associate Professor of Radiation Oncology at Harvard Medical School. He received his PhD in experimental nuclear physics in 1992 from the Rheinische-Friedrich-Wilhelms University in Bonn, Germany, and has been working in radiation therapy research on experimental as well as theoretical projects since 1994. He has authored and coauthored more than 100 peerreviewed publications, mostly on proton therapy. Dr. Paganetti has been awarded various research grants from the National Cancer Institute in the United States. He serves on several editorial boards and is a member of numerous task groups and committees for associations such as the American Association of Physicists in Medicine, the International Organization for Medical Physics, and the National Institutes of Health/National Cancer Institute. Dr. Paganetti teaches regularly worldwide on different aspect of proton therapy physics.

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Contributors Christoph Bert GSI Helmholtzzentrum für Schwerionenforschung GmbH Abteilung Biophysik Darmstadt, Germany

Bernard Gottschalk Laboratory for Particle Physics and Cosmology Harvard University Cambridge, Massachusetts

Benjamin Clasie Department of Radiation Oncology Massachusetts General Hospital and Harvard Medical School Proton Therapy Center Boston, Massachusetts

Nisy Elizabeth Ipe Shielding Design, Dosimetry, and Radiation Protection San Carlos, California

David Craft Department of Radiation Oncology Massachusetts General Hospital and Harvard Medical School Proton Therapy Center Boston, Massachusetts Martijn Engelsman Department of Radiation Oncology Massachusetts General Hospital and Harvard Medical School Proton Therapy Center Boston, Massachusetts Stella Flampouri University of Florida Proton Therapy Institute Jacksonville, Florida Jacob Flanz Department of Radiation Oncology Massachusetts General Hospital and Harvard Medical School Proton Therapy Center Boston, Massachusetts

Hanne M. Kooy Department of Radiation Oncology Massachusetts General Hospital and Harvard Medical School Proton Therapy Center Boston, Massachusetts Zuofeng Li University of Florida Proton Therapy Institute Jacksonville, Florida Antony Lomax Center for Proton Therapy Paul Scherrer Institute Villigen, Switzerland Hsiao-Ming Lu Department of Radiation Oncology Massachusetts General Hospital and Harvard Medical School Proton Therapy Center Boston, Massachusetts

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Harald Paganetti Department of Radiation Oncology Massachusetts General Hospital and Harvard Medical School Proton Therapy Center Boston, Massachusetts Hugo Palmans National Physical Laboratory Acoustics and Ionising Radiation Teddington, United Kingdom Jatinder R. Palta Department of Radiation Oncology University of Florida Gainesville, Florida Katia Parodi Heidelberg Ion Beam Therapy Center and Department of Radiation Oncology Heidelberg University Clinic Heidelberg, Germany Marco Schippers Paul Scherrer Institut Villigen, Switzerland Roelf Slopsema University of Florida Proton Therapy Institute Jacksonville, Florida

Contributors

Alexei V. Trofimov Department of Radiation Oncology Massachusetts General Hospital and Harvard Medical School Proton Therapy Center Boston, Massachusetts Jan H. Unkelbach Department of Radiation Oncology Massachusetts General Hospital and Harvard Medical School Proton Therapy Center Boston, Massachusetts Peter van Luijk Department of Radiation Oncology University Medical Center Groningen University of Groningen Groningen, The Netherlands Daniel K. Yeung University of Florida Proton Therapy Institute Jacksonville, Florida Department of Radiation Oncology University of Florida Gainesville, Florida

1 Proton Therapy: History and Rationale Harald Paganetti CONTENTS 1.1 The Advent of Protons in Cancer Therapy.................................................1 1.2 History of Proton Therapy Facilities............................................................2 1.2.1 Early Days: Lawrence Berkeley Laboratory, Berkeley, California............................................................................................. 2 1.2.2 Early Days: Gustav Werner Institute, Uppsala, Sweden............... 3 1.2.3 Early Days: Harvard Cyclotron Laboratory, Cambridge, Massachusetts��������������������������������������������������������������� 3 1.2.4 Second Generation: Proton Therapy in Russia...............................4 1.2.5 Second Generation: Proton Therapy in Japan................................. 4 1.2.6 Second Generation: Proton Therapy Worldwide...........................5 1.2.7 Hospital-Based Proton Therapy........................................................5 1.2.8 Facilities and Patient Numbers.........................................................5 1.3 History of Proton Therapy Devices.............................................................. 7 1.3.1 Proton Accelerators............................................................................. 7 1.3.2 Mechanically Modulating Proton Beams........................................ 7 1.3.3 Scattering for Broad Beams............................................................... 7 1.3.4 Magnetic Beam Scanning.................................................................. 7 1.3.5 Impact of Proton Technology in Other Areas of Radiation Therapy�����������������������������������������������������������������������������8 1.4 The Clinical Rationale for Using Protons in Cancer Therapy.................. 9 1.4.1 Dose Distributions..............................................................................9 1.4.2 Early Clinical Implications.............................................................. 10 1.4.3 Current Clinical Implications......................................................... 11 1.4.4 Economic Considerations................................................................ 11 Acknowledgments................................................................................................. 12 References................................................................................................................ 12

1.1  The Advent of Protons in Cancer Therapy The first medical application of ionizing radiation, using x-rays, occurred in 1895 (1, 2). In the following decades, radiation therapy became one of the main treatment options in oncology (3). Many improvements have been made with 1

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Proton Therapy Physics

respect to how radiation is administered considering biological effects, for example, the introduction of fractionated radiation therapy in the 1920s and 1930s. Technical advances have been aimed mainly at reducing dose to healthy tissue while maintaining prescribed doses to the target or increasing the dose to target structures with either no change or a reduction of dose to normal tissue. Computerized treatment planning, advanced imaging and patient setup, and the introduction of mega-voltage x-rays are examples of new techniques that have impacted beam delivery precision during the history of radiation therapy. Another way of reducing dose to critical structures is to take advantage of dose deposition characteristics offered by different types of particles. The advantages of proton radiation therapy, compared with “conventional” photon radiation therapy, were first outlined by Wilson in 1946 (4). He presented the idea of utilizing the finite range and the Bragg peak of proton beams for treating targets deep within healthy tissue and was thus the first to describe the potential of proton beams for medical use. Wilson’s suggestion to use protons (in fact he also extended his thoughts to heavy ions) was based on the well-known physics of protons as they slowed down during penetration of tissue.

1.2  History of Proton Therapy Facilities 1.2.1  Early Days: Lawrence Berkeley Laboratory, Berkeley, California The idea of proton therapy was not immediately picked up at Wilson’s home institution, Harvard University, but was adopted a couple of years later by the Lawrence Berkeley Laboratory (LBL) in California. Pioneering the medical use of protons, Tobias, Anger, and Lawrence (5) in 1952 published their work on biological studies on mice using protons, deuterons, and helium beams. Many experiments with mice followed at LBL (6), and the first patient was treated in 1954 (7). The early patients had metastatic breast cancer and received proton irradiation of their pituitary gland for hormone suppression. The bony landmarks made targeting of the beam feasible. The Bragg peak itself was not utilized. Instead, using a 340-MeV proton beam, patients were treated with a crossfiring technique (i.e., using only the plateau region of the depth dose curve). This approximated a rotational treatment technique to concentrate the dose in the target. Protons as well as helium beams were applied. Between 1954 and 1957, 30 patients were treated with protons. Initially large single doses were administered (7), and later fractionated delivery treatment three times a week was applied (8). The first patient using the Bragg peak was treated in 1960 for a metastatic lesion in the deltoid muscle, using a helium beam (9). The LBL program moved to heavier ions entirely in 1975, resulting in several developments that also benefited proton therapy.

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1.2.2  Early Days: Gustav Werner Institute, Uppsala, Sweden In 1955, shortly after the first proton treatments at LBL, radiation oncologists in Uppsala, Sweden, became interested in the medical use of protons. Initially, a series of animal (rabbits and goats) experiments were performed to study the biological effect of proton radiation (10–12). The first patient was treated in 1957 using a 185-MeV cyclotron at the Gustav Werner Institute (12–14). Subsequently, radiosurgery beams were used to treat intracranial lesions, and by 1968, 69 patients had been treated (15, 16). Because of limitations in beam time at the cyclotron, high doses per fraction were administered. Instead of the cross-firing technique, the use of the Bragg peak was adopted early on by using large fields and range-modulated beams (14, 17, 18). In fact, the Gustav Werner Institute was the first to use range modulation using a ridge filter, that is, a spread-out Bragg peak (SOBP) with a homogeneous dose plateau at a certain depth in tissue (14), based on the original idea of Robert Wilson, in which various mono-energetic proton beams resulting in Bragg peaks were combined to achieve a homogeneous dose distribution in the target. The proton therapy program ran from 1957 to 1976 and reopened in 1988 (19). 1.2.3 Early Days: Harvard Cyclotron Laboratory, Cambridge, Massachusetts Preclinical work on proton therapy at Harvard University (Harvard Cyclotron Laboratory [HCL]) started in 1959 (20). The cyclotron at HCL had sufficient energy (160 MeV) to reach the majority of sites in the human body up to a depth of about 16 cm. The relative biological effectiveness (RBE) of proton beams was studied in the 1960s using experiments on chromosome aberrations in bean roots (21), mortality in mice (22), and skin reactions on primates (23). Subsequently, the basis for today’s practice of using a clinical RBE (see Chapter 19) was established (24–27). The clinical program was based on a collaboration between HCL and the neurosurgical department of Massachusetts General Hospital (MGH). The first patients were treated in 1961 (28). Intracranial targets needed only a small beam, which could be delivered using a single scattering technique to broaden the beam. As at LBL, pituitary irradiation was one of the main targets. Because of the maximum beam energy of 160 MeV, it was decided to focus on using the Bragg peak instead of applying a crossfire technique. Until 1975, 732 patients had undergone pituitary irradiation at HCL (29). On the basis of the growing interest in biomedical research and proton therapy, the facility was expanded by constructing a biomedical annex in 1963. This was funded by NASA to examine the medical effects of protons. When the research program funded by the U.S. Office of Naval Research, which originally funded the cyclotron, was shut down in 1967, the proton therapy project was in danger of being terminated. Extensive negotiations between MGH  and HCL, as well as small grants by the National Cancer Institute

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Proton Therapy Physics

(NCI) in 1971 and the National Science Foundation (NSF) in 1972 helped, thus saving the program. In 1973, the radiation oncology department commenced an extensive proton therapy program. The first patient was a four-year-old boy with a posterior pelvic sarcoma. Subsequently, the potential of the HCL proton beam for treatment of skull-base sarcomas, head-and-neck region carcinomas, and uveal melanomas was identified, and several studies on fractionated proton therapy were performed (30). Furthermore, a series of radiobiological experiments was done (25). On the basis of the development of a technique to treat choroidal melanomas at MGH, the Massachusetts Eye and Ear Infirmary, and HCL, melanoma treatments started in 1975 (31) after tests had been done using monkeys (32, 33). The first treatments for prostate patients were in the late 1970s (34). A milestone for the operation at HCL as well as for proton therapy research in general was a large research grant by the NCI awarded in 1976 to MGH Radiation Oncology to allow extensive studies on various aspects of proton therapy. The HCL facility treated a total of 9116 patients until 2002. 1.2.4  Second Generation: Proton Therapy in Russia Proton therapy began early at three centers in Russia. Research on using proton beams in radiation oncology had been started in Dubna (Joint Institute for Nuclear Research [JINR]) and at the Institute of Theoretical and Experimental Physics (ITEP) in Moscow in 1967. The Dubna facility started treatments in April 1967, followed by ITEP in 1968 (35–39). A joint project between the Petersburg Nuclear Physics Institute and the Central Research Institute of Roentgenology and Radiology (CRIRR) in St. Petersburg launched a proton therapy program in 1975 in Gatchina, a nuclear physics research facility near St. Petersburg. The latter treated intracranial diseases using Bragg curve plateau irradiation with a 1-GeV beam (40). The program at ITEP was the largest of these programs and was based on a 7.2-GeV proton synchrotron with a medical beam extraction of up to 200 MeV. Patients were treated with broad beams and a ridge filter to create depth–dose distributions. Starting in 1972, the majority of treatments irradiated the pituitary glands of breast cancer and prostate cancer patients using the plateau of the Bragg curve (35, 41). By the end of 1981, 575 patients with various indications had been treated with Bragg peak dose distributions (35). 1.2.5  Second Generation: Proton Therapy in Japan The history of proton therapy treatments in Japan goes back to 1979 when the National Institute of Radiological Sciences (NIRS) at Chiba started treatments at a 70-MeV facility (42). Of the 29 patients treated between 1979 and 1984, only 11 received proton therapy alone and 18 received a boost irradiation of protons after either photon beam or fast neutron therapy. The effort was followed by the use of a 250-MeV beam at the Particle Radiation Medical

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5

Science Center in Tsukuba in 1983 using a 250-MeV proton beam obtained by degrading a 500-MeV beam from a booster synchrotron of the National Laboratory for High Energy Physics (KEK) (43). Japan has since emerged as one of the main users of proton and heavy ion therapy. 1.2.6  Second Generation: Proton Therapy Worldwide The late 1980s and early 1990s saw a number of initiatives starting proton therapy programs on several continents, for example, at the Paul Scherrer Institute (PSI) (Switzerland) in 1984, Clatterbridge (U.K.) in 1989, Orsay (France) in 1991, and iThemba Laboratory for Acclerator Based Sciences (iThemba LABS) (South Africa) in 1993. In particular the activities at PSI, starting with a 72-MeV beam for ocular melanoma treatments (44) and after 1996 using a 200-MeV beam, have lead to many technical and treatment planning improvements in proton therapy. 1.2.7  Hospital-Based Proton Therapy By the early 1990s, proton therapy was based mainly in research institutions and was used on a modest number of patients, in part because of very restricted beam time availability at some centers. Then, in 1990, the first hospital-based facility was built and started operation at the Loma Linda University Medical Center (LLUMC) in California (45). The accelerator system, based on a synchrotron (46), was developed in collaboration with Fermilab. The gantries were designed by the HCL group (47). By July 1993, 12,914 patients had been treated with protons worldwide—still roughly half of those at HCL and 25% in Russia (48). Roughly 50% were radiosurgery patients treated with small fields. However, the facility at Loma Linda would soon treat the biggest share of proton therapy patients. It took another few years before the first commercially available equipment was installed and in operation at MGH, which transferred the program from the HCL to its main hospital campus in 2001. At the time when the facility was purchased, proton therapy was still considered mainly experimental as part of a research effort. In fact, the construction project was in part funded by the NCI. The commercial equipment sold to MGH started the interest of different companies to offer proton therapy solutions and the interest of major hospitals to buy proton therapy facilities. Many other hospital-based facilities have been opened since then. 1.2.8  Facilities and Patient Numbers Table 1.1 lists the facilities and the number of patients treated with protons as of December 2010. On the basis of the increasing interest in proton therapy and the number of additional facilities under construction, one can assume that roughly 6000 patients will be treated with protons in 2011 in the United States alone.

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TABLE 1.1 Total Years of Operation and Patients Treated with Protons. Worldwide (as of 12/2010)

Facility

Ocular Tumors Only

Berkeley 184, California Uppsala_1, Sweden Cambridge (Harvard), Massachusetts Dubna (JINR_1), Russia Chiba (NIRS), Japan Tsukuba (PMRC_1), Japan Louvain-la-Neuve, Belgium Bloomington (MPRI_1), Indiana Moscow (ITEP), Russia St. Petersburg, Russia Villigen (PSI_1, 72 MeV), Switzerland Uppsala_2, Sweden Clatterbridge, England Loma Linda (LLUMC), California Nice (CAL), France Orsay (CPO), France iThemba LABS, Somerset West, South Africa UCSF – CNL, California Vancouver (TRIUMF), Canada Villigen (PSI_2, 230 MeV), Switzerland Dubna (JINR_2), Russia Kashiwa (NCC), Japan Berlin (HMI), Germany Hyogo (HIBMC), Japan Tsukuba (PMRC_2), Japan Boston (MGH-FHBPTC), Massachusetts Catania (INFN-LNS), Italy Wakasa Bay (WERC), Japan Shizuoka, Japan Wanjie (WPTC), China Bloomington (MPRI_2), Indiana Houston, Texas Jacksonville, Florida Ilsan (NCC), South Korea Munich (RPTC), Germany Oklahoma City (ProCurePTC), Oklahoma Heidelberg (HIT), Germany Facilities in operation: 27

1954 1957 30 1957 1976 73 1961 2002 9116 1967 1996 124 • 1979 2002 145 1983 2000 700 • 1991 1993 21 • 1993 1999 34 1969 4246 1975 1362 • 1984 2010 5458 1989 1000 • 1989 2021 1990 15000 • 1991 4209 1991 5216 1993 511 • 1994 1285 • 1995 152 1996 772 1999 720 1998 772 • 1998 1660 2001 2382 2001 1849 2001 4967 • 2002 174 2002 2009 62 2003 986 2004 1078 2004 1145 2006 2700 2006 2679 2007 648 2009 446 2009 21 2010 40 Total number of patients treated: 73,804

First Patient

Last Patient

Number of Patients

Source: The Particle Therapy Co-Operative Group (PTCOG) (http://ptcog.web.psi.ch).

Proton Therapy: History and Rationale

7

1.3  History of Proton Therapy Devices 1.3.1  Proton Accelerators The concept of accelerating particles in a repetitive way with time-­dependent varying potentials led to the invention of the cyclotron by Lawrence in 1929 (49). Cyclotrons accelerate particles while they are circulating in a magnetic field and pass the same accelerating gap several times (see Chapter 3). Gaining energy, the particles are traveling in spirals and are eventually extracted. To overcome the energy limitation of a cyclotron, the principle of phase stability was invented in 1944 (50). One was now able to accelerate particles of different energy on the same radius, leading to the synchrotron (see Chapter 3). The synchrotron concept was suggested first by Oliphant in 1943 (51). Thus, both accelerator types were available when proton therapy was first envisaged. 1.3.2  Mechanically Modulating Proton Beams In his 1946 paper, Wilson introduced the idea of using a rotating wheel of variable thickness to cover an extended volume with an SOBP (although he did not define this term) (4, 52). This technique to produce an SOBP (see Chapter 5) was adopted by proton facilities such as the HCL (53–55). Others have used a ridge filter design to shape an SOBP (14, 56, 57). 1.3.3  Scattering for Broad Beams For treatment sites other than very small targets (e.g., in radiosurgery) proton beams produced by accelerators result in “pencil” beams that are too small to cover an extended target. Thus, scattering foils had to be used to increase their width. To produce a flat dose distribution in lateral direction, it was inefficient to use a single-scattering foil because only a small area in the center of the beam would suffice beam flatness constraints. The doublescattering system, using two scatterers to achieve a parallel beam producing a flat dose distribution with high efficiency, was developed at the HCL in the late 1970s (58). The idea was based on similar systems previously designed for heavy ion and electron beams (59). The double-scattering concept was later improved using a contoured scatterer system (see Chapter 5) (60). 1.3.4  Magnetic Beam Scanning The development of beam scanning was a major milestone in proton therapy. The clinical implications of beam scanning were analyzed in the late 1970s and early 1980s (61, 62). The advantage of scanning is not only the need for fewer beam shaping absorbers in the treatment head (increasing the

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efficiency) but also the potential of delivering variable modulation and thus sparing structures proximal to the SOBP (61). The concept of using magnets to deflect a proton beam (dynamic beam delivery) is as old as the double-scattering scattering system. The idea to magnetically deflect proton beams for treatment was first published by Larsson in 1961 (14). Continuous scanning using an aperture was done in the 1960s in Uppsala (14). The aim was not to scan the tumor with individual pencil beams but to replace the scattering system using a sweeping magnetic field. A method using rotating dipoles instead of a scattering system in order to produce a uniform dose distribution was considered by Koehler, Schneider, and Sisterton (58). It can be considered as intermediate between double-scattered broad beam delivery and beam scanning. Similarly, a technique called wobbling, using magnetic fields to broaden the beam without a double-scattering system, was developed at Berkeley for heavy ion therapy because here the material in the beam path when using a double scattering system produces too much secondary radiation (63). Full-beam scanning uses small proton beams of variable energy and intensity that are magnetically steered to precisely shape of dose around critical structures (see Chapter 6). This concept of using beam scanning in three dimensions for clinical proton beam delivery was developed by Leemann et al. (64). Many different flavors of beam scanning exist. Typical terms are spot, pixel, voxel, dynamic, and raster scanning. The terminology is not consistent. The main differences between scanning systems are whether the delivery is done in a step-and-shoot mode or continuously. Spot scanning, where the beam spots are delivered one by one with beam off-time in between, covering the target volume instead of delivering a rectangular scanned field that has to be shaped by an aperture, was first introduced at NIRS using a 70-MeV beam. Scanning was mainly done to improve the range of the beam by removing a scattering system. At first, two-dimensional scanning was applied in combination with a range-modulating wheel (42). Later, three-dimensional beam scanning was introduced by using a system with two scanning magnets and an automatic range degrader to change the spot energy (42, 65–68). Many studies on different scanning techniques (spot scanning, continuous scanning) were done in the early 1980s at LBL, and continuous scanning in three dimensions without collimator was first done in the early 1990s (69). Beam scanning can be used in passive scattered proton therapy, but it also allows creating fields delivering inhomogeneous dose distributions where only a combination of several fields yields the desired dose distribution in the target (see Chapter 11). This intensity-modulated proton therapy is currently on the verge of finding its way into the clinical routine. 1.3.5 Impact of Proton Technology in Other Areas of Radiation Therapy Some of the developments in proton therapy have influenced the way radiation therapy is being conducted also in conventional radiation therapy.

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9

External beam radiation therapy requires a geometric description of the internal patient anatomy. Until the advent of computed tomography (CT) this could only be obtained from x-ray images, which project the anatomy on a planar film. Because conventional radiation therapy uses photons, the imaging x-ray modality basically just replaces the treating photons. In the case of protons, which stop in the patient, this method does not suffice for treatment planning. When proton treatment of cancer patients began at the HCL, positioning of the target for each treatment field for each fraction was readily achieved by the simple use of bi-planar radiographs. The information was used to decide on potential beam approaches that covered the target in the lateral dimension for each beam path. Pituitary adenomas and arteriovenous malformation were the initial targets for proton therapy (16, 70). These lesions could be visualized on x-rays using contrast material to visualize the vasculature and thus could be treated without the use of CT imaging. It became clear that in order to utilize the superior dose distribution of proton beams one needed to understand the impact of density variations for each beam path (30, 71, 72). Thus, the treatment of other sites in the very heterogeneous head and neck region (e.g., paranasal sinus or nasopharynx) required additional research on accurate imaging to visualize the patient’s geometry and densities in the beam path (71). When CT imaging became available, proton radiation therapy was the early adaptor, that is, using CT for treatment planning (73–75). The proton therapy program at HCL, the heavy ion program at LBL, and the pi-meson program at the University of New Mexico were the first radiation therapy programs to install dedicated CT scanners. Some were modified to allow imaging in a seated position to mimic the treatment geometry. Proton therapy paved the way for many other advances in radiation therapy. The proton therapy group at MGH developed the first computerized treatment planning program in the early 1980s, which was subsequently used clinically (76–79). Other developments included the innovative concepts of beam’s eye view and dose-volume histograms, features that have become standard in radiation therapy today. Sophisticated patient positioning was developed first in proton therapy because the finite range of proton beams required a more precise setup than in photon therapy (80).

1.4 The Clinical Rationale for Using Protons in Cancer Therapy 1.4.1  Dose Distributions Any new radiation treatment technology has to find acceptance amongst clinicians, for example, by demonstrating improved dose distributions and suggesting a more favorable treatment outcome (30). A more favorable dose

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distribution is a distribution that is more closely confined to the tumor volume. This allows reducing the dose to normal structures (decreasing the normal tissue complication probability) or increasing the dose to the tumor (increasing the tumor control probability) or both. When proton therapy became available, it was of interest mainly because it showed dose conformity far superior to any type of conventional photon radiation therapy at that time (72, 81). Nowadays, it is quite feasible for some tumor shapes to reach dose conformity to the target with photons that is comparable to the one achievable with protons, albeit at the expense of using a larger number of beams. The difference in dose conformity between protons and photons has certainly decreased since the early days of proton therapy (at least for regular shaped targets), mainly due to the development of intensity-­modulated photon therapy. There is a limit to further improving and shaping photon generated dose distributions because the total energy deposited in the patient and thus to critical structures cannot be reduced but only distributed differently. Proton radiation therapy, on the other hand, can achieve significant further physical improvements through the use of scanning-beam technology and intensitymodulated proton therapy. This will increase the advantage of proton therapy due to advanced dose sculpting potential. 1.4.2  Early Clinical Implications Target dose distributions can typically be shaped with proton beams by applying fewer beams than with photons. Proton therapy is of particular interest for tumors located close to serially organized tissues where a small local overdose can cause significant complications. Protons are ideal for many targets, specifically if they are concave-shaped or are close to critical structures. The advantages of proton therapy could not be utilized right from the start because of limitations in patient imaging and beam delivery (e.g., the absence of gantry systems). Proton treatments started with the cross firing technique and the irradiation of pituitary targets. The proton therapy program at the HCL began with single fraction treatments of intracranial lesions (28). In the early 1960s the program of fractionated irradiation was commenced by the radiation oncologists at HCL and was used for a greatly expanded number of anatomic sites such as skull base sarcomas, choroidal melanomas, head and neck carcinomas, and others. Choroidal melanomas quickly became the most commonly treated tumor at HCL (82). Starting in 1973, all treatments for cancer patients was done by fractionated dose delivery (30). By the mid-1980s roughly one-third of the treated patients received intracranial radiosurgery treatments (e.g., arterioveneous maformations) (83, 84). Even with a limited number of indications, the distinct advantages of proton treatments compared to photon treatments were seen early on (85). One was able to demonstrate clinical efficacy of proton radiation therapy in

Proton Therapy: History and Rationale

11

otherwise poorly manageable diseases such as for chordoma and chondrosarcoma of the skull base and the spine (86, 87). These present significant treatment challenges as they are often very close to critical structures (e.g., the brain stem, spinal cord, or optic nerves). 1.4.3  Current Clinical Implications Today proton therapy is a well-established treatment option for many tumor types and sites. Advantages when using protons in favor of photons have been shown in terms of tumor control probability and/or normal tissue complications probability. Various dosimetric studies clearly demonstrate superior normal tissue sparing with protons (88–99). It is well recognized that protons are extremely valuable to treat tumors close to critical structures (e.g., for head-and-neck treatments) (100). However, there are circumstances and treatment sites where the advantage appears to be marginal at best (101). In the pediatric patient population the impact of the decreased total absorbed energy in the patient [by a factor of 2–3 (92)] with protons is most significant. The overall quality-of-life and reduction of secondary effects is of great importance and the reduction in overall normal tissue dose is proven to be relevant (91). Using protons for cranio-spinal cases can reduce the dose to the thyroid glands significantly. One prime example is the treatment of medulloblastoma, a malignant tumor that originates in the medulla and extends into the cerebellum. Treatment with photon radiation therapy invariably causes significant dose to the heart, lung, and abdominal tissues as well as organs at risk in the cranium, something that can largely be avoided using protons. These facts have boosted proton therapy in particular for pediatric patients. For example, at MGH about 90% of the pediatric patient population in radiation oncology is treated with proton therapy. About 60% of those treated have brain tumors. Although the dose distributions achievable with protons are superior to those achievable with photons, it is debatable whether the advantages of proton therapy are clinically significant for all treatment sites. There is an ongoing discussion about the necessity for randomized clinical trials to show a significant advantage in outcome by using protons (102–105). Note that data on late morbidity are still scarce because of the follow-up of less than 20 years for most patients. 1.4.4  Economic Considerations Related to the question of clinical trials mentioned above is the cost of health care, that is, whether the gain in tumor control or reduced tissue complication is substantial enough to warrant the additional cost of proton therapy. This is one of the reasons why the treatment of prostate cancer with protons has been criticized (105, 106), and it has been argued that because of the limited availability of proton beams, proton therapy might be used predominantly

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for such cases where protons are believed to make the biggest difference (e.g., for the pediatric patient population) (107). Goitein and Jerman (108) estimated that the cost of a proton treatment is about double the cost of a photon treatment, considering the initial investment and the operation of a facility. The cost of a proton treatment is expected to decrease with the advent of more and more facilities. A detailed discussion on the economic aspects of proton therapy is beyond the scope of this book, and the reader may be referred to publications on this subject (108–111).

Acknowledgments The author thanks Dr. Herman Suit and Jocelyn Woods for proofreading.

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73. Goitein M. Compensation for inhomogeneities in charged particle radiotherapy using computed tomography. Int J Radiat Oncol Biol Phys. 1978 May-Jun;4(5-6):499–508. 74. Goitein M. Computed tomography in planning radiation therapy. Int J Radiat Oncol Biol Phys. 1979 Mar;5(3):445–447. 75. Munzenrider JE, Pilepich M, Rene-Ferrero JB, Tchakarova I, Carter BL. Use of body scanner in radiotherapy treatment planning. Cancer. 1977 Jul;40(1):170–179. 76. Goitein M, Abrams M, Gentry R, Urie M, Verhey L, Wagner M. Planning treatment with heavy charged particles. Int J Radiat Oncol Biol Phys. 1982;8: 2065–2070. 77. Goitein M, Abrams M. Multi-dimensional treatment planning: I. Delineation of anatomy. Int J Radiat Oncol Biol Phys. 1983 Jun;9(6):777–787. 78. Goitein M, Abrams M, Rowell D, Pollari H, Wiles J. Multi-dimensional treatment planning: II. Beam’s eye-view, back projection, and projection through CT sections. Int J Radiat Oncol Biol Phys. 1983 Jun;9(6):789–797. 79. Goitein M, Miller T. Planning proton therapy of the eye. Med Phys. 1983; 10:275–283. 80. Verhey LJ, Goitein M, McNulty P, Munzenrider JE, Suit HD. Precise positioning of patients for radiation therapy. Int J Radiat Oncol Biol Phys. 1982;8:289–294. 81. Suit HD, Goitein M. Dose-limiting tissues in relation to types and location of tumours: implications for efforts to improve radiation dose distributions. Eur J Cancer. 1974 Apr;10(4):217–224. 82. Gragoudas ES, Seddon JM, Egan K, Glynn R, Munzenrider J, Austin-Seymour M, et al. Long-term results of proton beam irradiated uveal melanomas. Ophthalmology. 1987 Apr;94(4):349–353. 83. Kjellberg RN, Davis KR, Lyons S, Butler W, Adams RD. Bragg peak proton beam therapy for arteriovenous malformation of the brain. Clin Neurosurg. 1983;31:248–290. 84. Kjellberg RN, Hanamura T, Davis KR, Lyons SL, Adams RD. Bragg-peak proton-beam therapy for arteriovenous malformations of the brain. N Engl J Med. 1983 Aug 4;309(5):269–274. 85. Suit H, Goitein M, Munzenrider J, Verhey L, Blitzer P, Gragoudas E, et al. Evaluation of the clinical applicability of proton beams in definitive fractionated radiation therapy. Int J Radiat Oncol Biol Phys. 1982;8:2199–2205. 86. Suit HD, Goitein M, Munzenrider J, Verhey L, Davis KR, Koehler A, et al. Definitive radiation therapy for chordoma and chondrosarcoma of base of skull and cervical spine. J Neurosurg. 1982 Mar;56(3):377–385. 87. Austin-Seymour M, Munzenrieder JE, Goitein M, Gentry R, Gragoudas E, Koehler AM, et al. Progress in low-LET heavy particle therapy: intracranial and paracranial tumors and uveal melanomas. Radiat Res. 1985;104:S219–226. 88. Archambeau JO, Slater JD, Slater JM, Tangeman R. Role for proton beam irradiation in treatment of pediatric CNS malignancies. Int J Radiat Oncol Biol Phys. 1992;22:287–294. 89. Fuss M, Hug EB, Schaefer RA, Nevinny-Stickel M, Miller DW, Slater JM, et al. Proton radiation therapy (PRT) for pediatric optic pathway gliomas: comparison with 3D planned conventional photons and a standard photon technique. Int J Radiat Oncol Biol Phys. 1999;45:1117–1126. 90. Fuss M, Poljanc K, Miller DW, Archambeau JO, Slater JM, Slater JD, et al. Normal tissue complication probability (NTCP) calculations as a means to compare

Proton Therapy: History and Rationale

17

proton and photon plans and evaluation of clinical appropriateness of calculated values. Int J Cancer (Radiat Oncol Invest). 2000;90:351–358. 91. Lin R, Hug EB, Schaefer RA, Miller DW, Slater JM, Slater JD. Conformal proton radiation therapy of the posterior fossa: a study comparing protons with three-dimensional planned photons in limiting dose to auditory structures. Int J Radiat Oncol Biol Phys. 2000;48:1219–1226. 92. Lomax AJ, Bortfeld T, Goitein G, Debus J, Dykstra C, Tercier P-A, et al. A treatment planning inter-comparison of proton and intensity modulated photon radiotherapy. Radiother Oncol. 1999;51:257–271. 93. St. Clair WH, Adams JA, Bues M, Fullerton BC, La Shell S, Kooy HM, et al. Advantage of protons compared to conventional X-ray or IMRT in the treatment of a pediatric patient with medulloblastoma. Int J Radiat Oncol Biol Phys. 2004 Mar 1;58(3):727–734. 94. Suit HD, Goldberg S, Niemierko A, Trofimov A, Adams J, Paganetti H, et al. Proton beams to replace photon beams in radical dose treatments. Acta Oncol. 2003;42:800–808. 95. Yock T, Schneider R, Friedmann A, Adams J, Fullerton B, Tarbell N. Proton radiotherapy for orbital rhabdomyosarcoma: clinical outcome and a dosimetric comparison with photons. Int J Radiat Oncol Biol Phys. 2005 Nov 15;63(4):1161–1168. 96. Isacsson U, Hagberg H, Johansson K-A, Montelius A, Jung B, Glimelius B. Potential advantages of protons over conventional radiation beams for paraspinal tumours. Radiother Oncol. 1997;45:63–70. 97. Isacsson U, Montelius A, Jung B, Glimelius B. Comparative treatment planning between proton and X-ray therapy in locally advanced rectal cancer. Radiother Oncol. 1996;41:263–272. 98. Miralbell R, Lomax A, Russo M. Potential role of proton therapy in the treatment of pediatric medulloblastoma/primitive neuro-ectodermal tumors: spinal theca irradiation. Int J Radiat Oncol Biol Phys. 1997;38: 805–811. 99. Weber DC, Trofimov AV, Delaney TF, Bortfeld T. A treatment plan comparison of intensity modulated photon and proton therapy for paraspinal sarcomas. Int J Radiat Oncol Biol Phys. 2004;58:1596–1606. 100. Chan AW, Liebsch NJ. Proton radiation therapy for head and neck cancer. J Surg Oncol. 2008 Jun 15;97(8):697–700. 101. Lee M, Wynne C, Webb S, Nahum AE, Dearnaley D. A comparison of proton and megavoltage X-ray treatment planning for prostate cancer. Radiother Oncol. 1994;33:239–253. 102. Glimelius B, Montelius A. Proton beam therapy do we need the randomised trials and can we do them? Radiother Oncol. 2007 May;83(2):105–109. 103. Goitein M, Cox JD. Should randomized clinical trials be required for proton radiotherapy? J Clin Oncol. 2008 Jan 10;26(2):175–176. 104. Goitein M. Trials and tribulations in charged particle radiotherapy. Radiother Oncol. 2010 Apr;95(1):23–31. 105. Brada M, Pijls-Johannesma M, De Ruysscher D. Current clinical evidence for proton therapy. Cancer J. 2009 Jul-Aug;15(4):319–324. 106. Konski A, Speier W, Hanlon A, Beck JR, Pollack A. Is proton beam therapy cost effective in the treatment of adenocarcinoma of the prostate? J Clin Oncol. 2007 Aug 20;25(24):3603–3608.

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107. Jagsi R, DeLaney TF, Donelan K, Tarbell NJ. Real-time rationing of scarce resources: the Northeast Proton Therapy Center experience. J Clin Oncol. 2004;22:2246–2250. 108. Goitein M, Jermann M. The relative costs of proton and X-ray radiation therapy. Clin Oncol. 2003;15:S37–S50. 109. Lundkvist J, Ekman M, Ericsson SR, Jonsson B, Glimelius B. Proton therapy of cancer: potential clinical advantages and cost-effectiveness. Acta Oncol. 2005;44(8):850–861. 110. Peeters A, Grutters JP, Pijls-Johannesma M, Reimoser S, De Ruysscher D, Severens JL, et al. How costly is particle therapy? Cost analysis of external beam radiotherapy with carbon-ions, protons and photons. Radiother Oncol. 2010 Apr;95(1):45–53. 111. Lodge M, Pijls-Johannesma M, Stirk L, Munro AJ, De Ruysscher D, Jefferson T. A systematic literature review of the clinical and cost-effectiveness of hadron therapy in cancer. Radiother Oncol. 2007 May;83(2):110–122.

2 Physics of Proton Interactions in Matter Bernard Gottschalk CONTENTS 2.1 Introduction................................................................................................... 20 2.1.1 Depth–Dose Distributions of Various Particles........................... 20 2.1.2 Proton Interactions........................................................................... 21 2.1.3 Stopping.............................................................................................22 2.1.4 Scattering........................................................................................... 22 2.1.5 Nuclear Interactions.........................................................................23 2.1.6 The Bragg Peak.................................................................................. 24 2.2 Basics............................................................................................................... 24 2.2.1 Kinematics......................................................................................... 24 2.2.2 Fluence, Stopping Power, and Dose............................................... 25 2.2.3 Energy Lost vs. Energy Deposited................................................. 26 2.2.4 The Fundamental Equation............................................................. 27 2.2.5 Relation between Dose Rate and Beam Current.......................... 28 2.3 Stopping......................................................................................................... 29 2.3.1 Range Experiments...........................................................................30 2.3.2 Sneak Preview: The Range–Energy Relation................................ 32 2.3.3 Stopping Power................................................................................. 32 2.3.4 Mean Projected Range.....................................................................34 2.3.5 Interpolating Range–Energy Tables...............................................35 2.3.6 Range Straggling............................................................................... 36 2.3.7 Water Equivalence............................................................................ 37 2.4 Multiple Coulomb Scattering...................................................................... 37 2.4.1 Experiment......................................................................................... 38 2.4.2 Highland’s Formula.......................................................................... 38 2.4.3 Molière’s Theory............................................................................... 39 2.4.4 The Gaussian Approximation.........................................................42 2.4.5 Scattering Power...............................................................................44 2.4.6 Binary Degraders.............................................................................. 45 2.5 Nuclear Reactions......................................................................................... 46 2.5.1 Terminology......................................................................................46 2.5.2 Overview of Nonelastic Reactions................................................. 47 2.5.3 Nonelastic Cross Section..................................................................48

19

20

Proton Therapy Physics

2.5.4 Nuclear Buildup: Longitudinal Equilibrium................................ 49 2.5.5 Test of Nuclear Models.....................................................................50 2.6 The Bragg Peak.............................................................................................. 52 2.6.1 Beam Energy..................................................................................... 52 2.6.2 Variation of S ≡ −dE/dx with E........................................................ 52 2.6.3 Range Straggling and Beam Energy Spread................................. 53 2.6.4 Nuclear Interactions.........................................................................54 2.6.5 Beam Size: Transverse Equilibrium...............................................54 2.6.6 Source Distance................................................................................. 55 2.6.7 Dosimeter........................................................................................... 56 2.6.8 Electronic and Nuclear Buildup; Slit Scattering........................... 56 2.6.9 Tank Wall and Other Corrections.................................................. 56 2.6.10 Measuring the Bragg Peak............................................................... 56 2.7 Summary........................................................................................................ 57 References................................................................................................................ 57

2.1  Introduction This chapter examines the interactions of protons with matter. A full understanding of these interactions allows us to solve the two main physics problems that arise in proton radiotherapy: designing beam lines, and predicting the dose distribution in the patient. This section is a preliminary non-­mathematical survey. 2.1.1  Depth–Dose Distributions of Various Particles Let’s begin by comparing particles used or formerly used in radiotherapy. Figure 2.1 shows depth–dose distributions for various particles in a water tank, water being a convenient proxy for tissue. The first two particles (upper left) are neutral. They exhibit a dose buildup (too short to see for 120 KeV photons) followed by an exponential decay. As they traverse the water, neutral particles either interact or do not. Thus their number falls exponentially, but the ones that happen to survive are the same as when they entered. Dose is actually delivered by atomic electrons set in motion by the primary particles. It takes a while for the cloud of secondary electrons to build up in the beam, accounting for the buildup region. This feature is clinically useful, as it spares the skin. The remaining particles shown, arranged by increasing mass, are electrically charged. For these, the number of primaries only decreases slightly with depth (explained later), but the energy of each one decreases continuously, so the entire beam stops at more or less the same depth. Moreover, charged particles lose more energy per cm as they slow down, so there’s a

21

Physics of Proton Interactions in Matter

γ

1.

n

1.

e–

1.

22 MeV

Relative dose

.5 0 0

8 MeV 120 KeV 5 10 15 20 25

π–

1.

14 MeV .5 0 0

50 MeV d, Be 5

10 15 20 p+

1.

.05 e– .1 μ – 5 10 15 20 25

6 MeV 0

0

5

10

Ne

1.

400 MeV/A .5

.5

.5

0

160 MeV

78 MeV

0 0

.5

0 5 10 15 20 Depth in water (cm)

0 0

5

10 15 20

FIGURE 2.1 Depth–dose distributions for various particles.

large dose enhancement just before they stop. This “Bragg peak” is sharper, the more massive the particle. The electron peak is very broad because of the small electron mass. The proton peak is much sharper and falls to zero. Actually, there is some distal dose from neutrons set in motion by the protons, but it’s about a thousand times lower than the proton dose, so it doesn’t show up on this plot.* The Ne peak is still sharper than the proton peak, but there is some dose beyond it because some Ne nuclei split into lighter, longer range ions while traversing the water (“fragmentation”). Pions are of historical interest only. Their distal dose comes from the stopping pions interacting with the nucleus, which deposits a local ball of dose. 2.1.2  Proton Interactions Now let’s narrow our focus to protons. They interact with matter in three distinct ways. They slow down by myriad collisions with atomic electrons. They are deflected by myriad collisions with atomic nuclei. Finally, they sometimes have a head-on collision with a nucleus, setting secondary particles in motion. We’ll call these three processes stopping, scattering, and nuclear interactions. Stopping and scattering proceed via the electromagnetic (EM) interaction between the charge of the proton and the charge of atomic electrons or Unwanted neutron dose is a concern in proton therapy because of possible long-term effects (Chapter 18), but it plays no role in prompt (acute) effects.

* 

22

Proton Therapy Physics

nucleus, as the case may be. That interaction is simple and well understood. Therefore, comprehensive and well-tested mathematical theories of stopping and scattering exist. By contrast, our best overall picture of the nuclear interaction is a patchwork of models. Fortunately, nuclear interactions are relatively infrequent, and simple approximations take them into account well enough for purposes of radiotherapy. Because we have these tested theories, most physics problems that occur in proton radiotherapy, whether beam line design or predicting the dose distribution in the patient, can be solved from first principles. Complex beam lines can be designed reliably with computer programs that only take a few seconds to run. Dose prediction in the patient is far more difficult and time consuming, but the difficulties are mathematical. We believe that the underlying physics is well understood. 2.1.3  Stopping The theory of stopping was fully developed by 1933. The important fact is that protons do stop in solid or liquid matter, and beyond the stopping point (“end of range”) the dose is negligible. Proton range is approximately ­proportional to kinetic energy squared. If the incident proton beam is monoenergetic, all protons stop at nearly (though not exactly) the same depth. The slight spread in stopping point, which increases if the incident beam itself has an energy spread, is called “range straggling.” Most important, the rate at which the proton loses energy increases as the proton slows down because, in a given proton–electron collision, more momentum is transferred to the electron, the longer the proton stays in its vicinity. Thus, the rate of energy loss or “stopping power” depends on the energy itself and on the stopping material. When we correct for density, materials high in the periodic table such as lead (Z = 82) have less stopping power than materials like beryllium (Z = 4), water, or plastics. 2.1.4  Scattering The accepted theory of scattering was published in 1947. Except in rare cases, the deflection of a proton by a single atomic nucleus is extremely small. Therefore the observed angular spread of a proton beam leaving a slab of matter is mainly due to the random combination of many such deflections. Because of this and the underlying EM interaction, scattering is more properly known as multiple Coulomb scattering (MCS). If protons scattered in a slab of matter fall on a screen (Figure 2.2), their spatial distribution is very nearly Gaussian (the familiar bell curve of statistics). Multiple-scattering theory predicts, very accurately, the width of that Gaussian given the proton energy and the slab material and thickness. Proton MCS angles (roughly speaking, the half-width of the Gaussian) are small: 16° in the very worst case and usually only a few degrees. Materials high in the periodic table scatter much

23

Physics of Proton Interactions in Matter

L

X0 θ0

MP FIGURE 2.2 Multiple Coulomb scattering in a thin slab. MP, measuring plane. 18

lead

16

MeV, mRad

14

brass

12

θ0

10

aluminum water lexan

8 6

beryllium

∆E

4 2 0

0

10

20

30 40 LR (g/cm2)

50

60

70

FIGURE 2.3 Multiple scattering angle and energy loss for 160-MeV protons traversing 1 g/cm2 of various materials. (Data from M.J. Berger, M. Inokuti, H.H. Andersen, H. Bichsel, D. Powers, S.M. Seltzer, et al. ICRU Report 49 (1993).)

more strongly than materials like water, a trend opposite to that of stopping power (Figure 2.3). 2.1.5  Nuclear Interactions If a primary proton merely scatters elastically off a nucleus, or leaves it mildly excited, we are not that interested, because the outgoing proton retains characteristics (energy and angle) similar to its fellows. More interesting are the occasional “train wrecks” (more properly, nonelastic collisions) where the proton enters the nucleus and knocks out one or more constituent protons, neutrons, or light nucleon clusters. These secondaries (which include the original proton, since we can no longer identify it) tend to have much lower energies and much larger angles than primary protons. A blob of dose is deposited just downstream of the reaction site. Some 20% of 160 MeV protons suffer that kind of reaction before stopping.

24

Proton Therapy Physics

1.1 1.0 0.9 0.8 Dose

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

0

10

20 Depth (cm H2O)

30

FIGURE 2.4 Spread-out Bragg peak (SOBP) obtained by adding shifted, appropriately weighted Bragg peaks. In this example, the range modulator wheel is designed for full modulation, and reduced modulation is obtained by turning the beam off during unwanted steps (beam gating). The slight rounding of the proximal corner is a consequence of beam gating (see Chapter 5).

2.1.6  The Bragg Peak The three interactions come together to determine the shape of the Bragg peak. Much of the technique of proton radiotherapy rests on clever manipulations of the Bragg peak, such as spreading it out (Figure 2.4) to cover the target and spare healthy tissue insofar as possible. Therefore it’s good to know that we really do understand in detail how the observed shape comes about.

2.2  Basics We digress briefly to discuss basic quantities used in describing the proton radiation field, before returning to a quantitative discussion of stopping, scattering, nuclear reactions, and the Bragg peak. 2.2.1  Kinematics At high energies, the proton behaves like a complex system of “quarks” and “gluons.” In the much lower radiotherapy energy range 3–300 MeV the proton is an elementary particle with no internal degrees of freedom, a rest energy mc2 = 938.27 MeV and a charge e = +1.602 × 10–19 C. In the theories of stopping and scattering described later we occasionally need to compute the proton’s

25

Physics of Proton Interactions in Matter

speed v or momentum p, given its kinetic energy E.* Radiotherapy protons are somewhat relativistic (their speed is of order c  300  ×  106 m/s  1 ft/ns), so the relevant equations (see any textbook on special relativity) are as follows:

β≡

pc v = c E + mc 2

(E + mc 2 )2 = ( pc)2 + (mc 2 )2 .

(2.1) (2.2)

From these, if we first define a reduced kinetic energy, τ≡



E mc 2

(2.3)

we can derive several useful equations whose relativistic ( τ  1) and nonrelativistic (τ  1) limits are obvious at a glance:

β2 =

τ +2 τ (τ + 1)2

( pc )2 = (τ + 2)mc 2 E pv =

τ +2 E. τ +1

(2.4) (2.5) (2.6)

The last quantity, pv, occurs frequently in MCS theory. For E = 160 MeV we find β = 0.520 (speed just over half the speed of light), pc = 571 MeV, and pv = 297 MeV. 2.2.2  Fluence, Stopping Power, and Dose Suppose a beam of protons slows down and eventually stops in a water tank. At any given depth we may be concerned with the number of protons, their individual rate of energy loss, or the total rate at which they deposit energy in the water. Let x (cm) be displacement along the beam direction and y (cm) be transverse displacement. The fluence, Φ, is a quantity which depends on position in the water tank. It is defined as the number of protons, during a given exposure or treatment, crossing an infinitesimal element of area dA normal to x.†

Φ≡

dN dA

protons . cm 2

(2.7)

In radiotherapy physics, kinetic energy is often denoted E, unlike particle physics where E usually stands for total (kinetic + rest) energy. † Whether in the beam line or the patient, radiotherapy protons are always directed within a few degrees of the x axis. Other types of radiation require a more general definition of fluence. * 

26

Proton Therapy Physics

The fluence rate is the time derivative of the fluence*:

 ≡ dΦ Φ dt

protons . cm 2 s

(2.8)

The stopping power is the rate at which a single proton loses kinetic energy:

S≡−

dE dx

MeV . cm

(2.9)

The mass stopping power is stopping power “corrected” for density:



S 1 dE ≡− ρ ρ dx

MeV g/cm 2

(2.10)

where ρ (g/cm3) is the local density of the stopping medium. For instance, the mass stopping powers of air and water are similar, whereas the stopping power of air is about a thousand times less than that of water.† The physical absorbed dose, D, at some point in a radiation field is the energy absorbed per unit target mass. In SI units,

D≡

J . kg

(2.11)

The special unit of dose used in radiation therapy is the Gray: 1 Gy ≡ 1 J/kg. To give a rough idea of the numbers, a course of proton radiotherapy might consist of ≈ 70 Gy to ≈ 1000 cm3 of target volume given in ≈ 35 fractions (2 Gy/ session). However, a single whole- body dose of 4 Gy is lethal (with a probability of 50%) even with good medical care. To put this into perspective, assuming the typical thermal power radiated by an adult weighing 80 Kg is 100 W, a lethal dose of ionizing radiation corresponds to the amount of thermal energy given off in 3 s! Ionizing radiation is nasty stuff. An earlier, arguably more convenient unit of physical absorbed dose is the rad: 1 Gy = 100 rad. Older oncologists frequently hedge, saying “centiGray” (cGy) instead of rad. 2.2.3  Energy Lost vs. Energy Deposited It is good to remember that the energy lost by a proton beam exceeds the energy absorbed locally by the patient or water phantom. A fraction of the beam’s energy goes into neutral secondaries (γ-rays and neutrons), which * †

⋅ Sometimes Φ is written φ. In the early literature fluence rate is called “flux.” The often used quantity ρ dx (g/cm2) is the areal density or simply the “grams per square centimeter” of an element of stopping medium of thickness, dx. It is the thickness of a slab of stopping material times its density. To determine it experimentally, one usually measures, instead, mass divided by area.

27

Physics of Proton Interactions in Matter

may deposit their energy some distance away (for instance, in the shielding of the treatment room). Energy is conserved, of course, but only if we take the region of interest large enough and include the very small fraction that may go into changing the energy state of target molecules. 2.2.4  The Fundamental Equation How does physical absorbed dose relate to fluence and stopping power? Suppose dN protons pass through an infinitesimal cylinder of cross sectional area dA and thickness dx. In the cylinder



D≡

energy −(dE/dx) × dx × dN = mass ρ × dA × dx

or

D=Φ

S ρ

(2.12)

Dose equals fluence times mass stopping power. Proton therapy calculations, whether beam line design or dose reconstruction in the patient, usually begin with this formula in one form or another. However, it is not convenient to use SI units throughout. Gray (= J/Kg) is fine, but S/ρ is invariably in MeV/(g/cm2), square meters is far too large an area, and one proton is far too few. Therefore, let Φ = 1 Gp/cm2, where Gp ≡ gigaproton ≡ 109 protons, and let S/ρ = 1 MeV/(g/cm2). After appropriate conversions such as 1 MeV = 0.1602 × 10 –12 J we find

D = 0.1602 Φ

S Gy ρ

(2.13)

with Φ in Gp/cm2 and S/ρ in MeV/(g/cm2) as usually tabulated. Another useful form is found by taking the time derivative of Equation 2.13,  /A = eΦ  ), expressing fluence rate in terms of proton current density (ip /A = Ne 2 assuming a current density of 1 nA/cm , and converting units. We find



= D

ip S Gy Aρ s

(2.14)

with ip/A in nA/cm2 and S/ρ in MeV/(g/cm2). For a current density of 0.0033 nA/cm2 and S = 5 MeV/(g/cm2) (170 MeV protons in water), we find  = 0.017 Gy/s = 1 Gy/min, a typical radiotherapy rate. Typical targets have D areas of several cm2 and there are various inefficiencies involved (discussed next), so we have already shown that the proton current entering the treatment head or “nozzle” must be of the order of nA. In using the last few formulas, we must remember the distinction between absorbed dose (what we are interested in) and the tabulated stopping power

28

Proton Therapy Physics

Range modulator

ip

2 1

Second scatterer

Water tank

A

1 2

FIGURE 2.5 The figure used in deriving Equation 2.15.

which reflects energy lost by the beam, somewhat greater as mentioned earlier. More important, formulas like Eq. 2.14, while extremely useful for (say) estimating the dose rate that might be had from a proposed machine and beam line, must never be used to determine the therapy dose delivered to a patient. That can only be done with the aid of a carefully calibrated dosimeter! 2.2.5  Relation between Dose Rate and Beam Current An important task of the accelerator designer is to estimate the proton current required for a specified dose rate. Though we already have a rough value from the previous section, let’s derive a more precise relation (±10%). We’ll assume passive beam spreading, but, with a little reinterpretation, the result applies to magnetic scanning as well. Suppose a target of known cross sectional area* and known extent in depth is treated with a known proton current at a known incident energy with a passive scattering system which includes a suitable range modulator (see Chapter 5). What is the dose rate averaged over one modulator cycle? Consider Figure 2.5. Eq. 2.14 applies at the entrance to the water tank, where the dose is uniform over a circle of area A. If we wish to reinterpret ip as the current into the scattering system, we must introduce an efficiency factor ε < 1 because not all the protons that enter the scattering system reach A. It can be shown [1] that ε ≈ 0.05 for single scattering and ε ≈ 0.45 for double scattering. Assuming no range modulation for the time being, the dose of interest is that at the maximum of the Bragg peak (BP), which is greater than that at A by f BP, the peak-to-entrance ratio of a pristine BP. Therefore, we must multiply the dose at A by f BP. For a typical Bragg peak f BP ≈ 3.5, surprisingly independent of energy. Now, let’s switch on the range modulator, either a rotating “propeller wheel” or a set of degraders selected by a computer. That reduces the dose at the maximum of the first BP (and therefore the dose everywhere in the SOBP) because now, the deepest peak is only treated a fraction of the time. *

A is the cross sectional area of a cylinder, coaxial with the beam, circumscribing the target.

29

Physics of Proton Interactions in Matter

1.0 0.9 0.8

fMOD

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 m100 / d100 FIGURE 2.6 Dependence on relative modulation of f MOD, the relative dwell time of the deepest step, for a typical set of range modulators. d100 is the depth of the distal corner of the SOBP. m100 is the distance between the corners.

Call that, the fractional dwell time of the first (deepest) step, f MOD. Putting everything together we find, averaged over one modulator cycle,



〉 = εf f 〈D BP MOD

ip  S    Aρ

Gy s

(2.15)

with ip (incident proton current) in nA, A in cm2, and S/ρ in MeV/(g/cm2). Strictly speaking S/ρ is the mass stopping power in water at the water tank entrance, but you can use the incident energy because energy loss in the beam spreading system is small by design. It remains to determine f MOD as a function of modulation. For zero modulation, f MOD = 1. Otherwise, we need to design a set of modulators (1). Figure 2.6 shows f MOD as a function of relative modulation for a typical beam spreading system. The shape of the curve comes mainly from the shape of the Bragg peak. It is little affected by details of the beam spreading system, so Figure 2.6 can safely be used for rough estimates. Dependence on modulation is nonlinear. Therefore Eq. 2.15 implies that, whereas dose rate is strictly proportional to inverse area, it is not proportional to thickness (extent in depth) because the deepest Bragg peak already delivers a considerable dose to the entire volume whatever the irradiation strategy (passive or scanning).

2.3  Stopping Protons slow down in matter, mainly through myriad collisions with atomic electrons. In collisions at a given distance a proton loses more energy, the

30

Proton Therapy Physics

0.6 Faraday cup

0.5 nCoul / 30 MU

monitor CH2 IC absorbers

0.4 0.3

current integrator

0.2 0.1 0.0

0

5

10 g/cm2 CH2

15

20

FIGURE 2.7 Experimental definition of mean projected range. Left: experimental setup. Right: results for two different Faraday cups. (Based on Harvard Cyclotron Laboratory, unpublished data.)

longer it interacts with the electron. Therefore the rate of energy loss increases as the proton slows down, giving rise to the Bragg peak of ionization near end-of-range, the signature feature of proton radiotherapy. We now explore all this in detail beginning with the experimental definition of “range.”* 2.3.1  Range Experiments Early workers, on discovering a new form of radiation, invariably began by seeing how far it would go in various materials. A modern version of that experiment for protons is shown in Figure 2.7. The beam is monitored, to allow successive equivalent runs. It then traverses an adjustable thickness of the material under test. Finally, it stops in a “Faraday cup” (FC), ideally of such size that any large-angle outgoing particles miss it. After each run we measure the charge collected by the FC (effectively a proton counter because the charge of a single proton is well known). The right hand panel shows, for two different FCs, collected proton charge per monitor unit vs. thickness of stopping material. A great deal can be learned from these graphs. Both show a gradual decline followed by a precipitous drop. The decline comes from nonelastic collisions of protons with atomic nuclei. Charged secondary particles from such collisions mostly have short ranges and large angles and therefore do not reach the FC, so we see only a gradual decline in the primary fluence. Protons that escape this fate— those that have only electromagnetic (EM) interactions with electrons or nuclei—all run out of energy at nearly (but not exactly) the same depth and *

Normally (2) one begins with the theory of stopping power and proceeds to the definition of range. We have reversed that order of presentation because range is more immediately accessible to experiment, because the precise experimental definition of range is frequently misunderstood, and because range, determining treatment depth, is very frequently the quantity of greatest interest.

Physics of Proton Interactions in Matter

31

stop. The mean projected range R0 (which we will call “range”) is the depth at which half of them have stopped, as indicated by the arrow. Note that “half” is measured from the corner of the curve. The range, in other words, is the amount of material that would stop half the incident protons if nuclear reactions were turned off. The higher, less linear, curve was taken with an FC much closer to the degrader stack so some charged secondaries were counted along with the primary protons. It had a thicker entrance window, so the residual range was slightly smaller. Alternatively, proton centers often measure range with a “multilayer Faraday cup” (MLFC), a stack of metal plates separated by insulating sheets. Each plate is connected to a current integrator which measures the total charge stopping in that plate, equivalent to measuring −



dN dN dΦ = −∫ dA = − dx dxdA dx

Dose

Diff fluence

Fluence

or differential fluence. One observes a sharp peak (center panel of Figure 2.8) whose maximum (corresponding to the steepest point in the top panel) is the proton range. At clinical beam currents (nA), an MLFC can measure the range to ≈ 0.1 mm water equivalent in a few seconds. All data are acquired simultaneously so no beam monitor is needed.

Depth FIGURE 2.8 Fluence, differential fluence, and dose as a function of depth for proton beams of a given range and different energy spreads, illustrating R0 = d80.

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Proton Therapy Physics

If neither form of FC is available, the range may be measured by scanning a dosimeter down the x axis of a water tank: a measurement of dose, not fluence. We observe a Bragg peak, and the question arises: what feature of the peak corresponds to the mean projected range of the proton beam? The answer is R0 = d80 (2.16) where d80 stands for the depth of water (corrected for tank entrance window, dosimeter wall thickness, and so forth) at the distal 80% point of the peak. This purely numerical result (the “80” is not exact, but is close enough), first found by A. M. Koehler (private communication, ca. 1982), has been confirmed often (3, 4). It follows from the theoretical model of the Bragg peak to be discussed later. As Figure 2.8 shows, if we increase the energy spread of the proton beam, keeping the mean energy the same, the range measured all three ways, in particular the distal 80% point of the Bragg peak, remains the same. In summary, the range R0 of a proton beam is defined as the depth of material at which half the protons that undergo only EM interactions have stopped. It is defined by a fluence measurement. However, a dose measurement may be used instead, provided the result is properly interpreted (R0 = d80). 2.3.2  Sneak Preview: The Range–Energy Relation To give some feeling for the numbers, here is a short range–energy table for water (2): Kinetic energy Range

1 0.002

3 0.014

10 0.123

30 0.885

100 7.718

300 MeV 51.45 cm H2O

This justifies our choice of 3–300 MeV as the clinical regime. Figure 2.9 shows the range–energy relation for some useful materials at clinical energies. At a given energy, the range expressed in g/cm 2 is greater (the stopping power is lower) for heavy materials. The basic form is the same for all materials: nearly linear on a log-log plot. If it were exactly linear, the relation would be an exact power law R = aEb. If the lines were parallel, b would be the same for all materials, and only a would differ. As it is, the power varies slightly with E and also with material. We’ll deal with all that by forgetting about the power law and parameterizing Figure 2.9 separately for each material. Before that, let’s go back to the beginning. The conventional presentation of stopping theory begins with the BetheBloch formula for stopping power. 2.3.3  Stopping Power The theoretical rate of energy loss of a fast charged particle in matter was derived by Bethe and Bloch around 1933. Good modern accounts with references can be found in the range–energy tables of Janni (5) and ICRU Report

33

Physics of Proton Interactions in Matter

3 2

Pb

100

brass

Range (g/cm2)

3 2

Leman

10

H2O

3 2

1 3 2 0.1

3 2

4 5 6 7

10

2

3 4 5 6 100 Energy (MeV)

2

3

4 5

FIGURE 2.9 Proton range–energy relation around the clinical regime for four useful materials. (Data from M.J. Berger, M. Inokuti, H.H. Andersen, H. Bichsel, D. Powers, S.M. Seltzer, et al. ICRU Report 49, 1993.)

49 (2). Specializing to protons, filling in physical constants and ignoring all corrections (as is permissible in the radiotherapy energy regime 3–300 MeV), the mass stopping power in an elementary material of atomic number Z and relative atomic mass A is



Sel 1 dE Z 1  Wm  MeV ≡− = 0.3072 − β2  ln 2  2 ρ ρ dx Aβ  I  g/cm

(2.17)

where β ≡ v/c of the proton (Eq. 2.4) and



Wm =

2 me c 2β 2 1 − β2

(2.18)

is the largest possible proton energy loss in a single collision with a free electron. mec2 ≈ 0.511 MeV is the electron rest energy. I is the mean excitation energy of the target material. It cannot be calculated to sufficient accuracy from first principles so it is effectively an adjustable parameter of the theory. It is found by fitting measured range-energy values (for materials where those exist) and by interpolation for others. It is roughly proportional to Z with I/Z ≈ 10 eV, but irregularities due to atomic shell structure make interpolation difficult (2). Fortunately S/ρ is logarithmic

34

Proton Therapy Physics

in I so that, at 100 MeV for instance, a relative increase of 1% in I only causes a ≈ 0.15% decrease in S/ρ (2). If a material is a mixture of elements, the atoms act separately, and we can visualize the mixture as a succession of very thin sheets of each constituent element. That picture leads easily to the Bragg additivity rule: S S = ∑ wi   ρ i  ρ i

(2.19) where wi is the fraction by weight of the ith element. Compounds are more complicated since their constituent atoms do not act separately. Several strategies are used to deal with that (2). Unfortunately, water is particularly complicated. There is some experimental evidence (6, 7) that Janni (5) is more accurate than ICRU Report 49 (2) for water. In short, choosing I is a complicated business requiring considerable familiarity with the experimental literature. It is mainly for this reason that our own practice is to obtain stopping power and range values by interpolating generally accepted range–energy tables rather than computing them ab initio. Tables can differ from each other by 1%–2%, due solely to different choices of I. A given set of tables may be better for some materials than others. One percent of range at 180 MeV corresponds to ≈2 mm water. Therefore when the treatment depth itself depends on it, we must rely on measured ranges in water and measured water equivalents of other materials, rather than range–energy tables! However, range–energy tables are invaluable in other calculations such as beam line design. Eq. 2.17 refers to the rate of energy loss to atomic electrons only. Protons also lose energy by elastic scattering on atomic nuclei.* This contribution is less than 0.1% above 1 MeV (5). Janni (5) omits it in the clinical regime, but ICRU Report 49 (2) includes it. From now on we will refer to the mass stopping power simply as S/ρ. 2.3.4  Mean Projected Range Once we know S/ρ as a function of β, that is, of E, we can find the theoretical range of a proton by imagining that it enters the material at Einitial and by summing the energy loss in very thin slabs until the energy reaches some very low value Efinal (not 0, because Eq. 2.17 diverges there). The choice of Efinal is not critical. Any very small value will do. Formally, in a homogeneous slab of matter  1 dE    Einitial ρ dx  

R(Einitial ) = ∫

Efinal

−1

dE = ∫

Einitial

dE S/ρ

(2.20) is the theoretical range in g/cm2. Because of multiple scattering, protons actually travel a wiggly path, so strictly speaking, the quantity we have computed is the total pathlength Efinal

That’s different from the nonelastic nuclear reactions which we will discuss later.

* 

35

Physics of Proton Interactions in Matter

rather than the mean projected range, which is smaller by a “detour factor” resulting from scattering. However, that correction is negligible in the clinical regime (0.9988 for 100 MeV protons in water [2]). 2.3.5  Interpolating Range–Energy Tables S/ρ varies roughly as 1/β2 (Eq. 2.17), while β2 varies roughly as E, so Eq. 2.20 implies that R should vary roughly as E2. In fact the exponent is a bit less than 2. For instance, if we fit a power law to the range in water at 100 and 200 MeV (2), we find R ≈ a E b = 0.00244  E 1.75



g/cm 2

(E in MeV)

(2.21)

and this is only 0.5% low at 150 MeV. If we chose a different range for the power-law fit, the constants will come out slightly different. In working with protons we frequently need R(E) or its inverse E(R) at arbitrary values for various materials, so it is well to have an accurate and convenient interpolation routine at hand. The fact that R(E) is nearly a power law implies that a graph of log R vs. log E is nearly a straight line, as we have already seen. Figure 2.10, a log-log graph for three materials over an extended region, shows that the lines eventually curve. From 3-300 MeV they 1000

Range (g/cm2)

100 10 1 0.1 0.01

Pb

0.001

Be

Error (%)

0.0001 0.5

0.0

–0.5 0.1

2 3 4

1

2 3 4 10 2 3 4 Energy (MeV)

100

2 3

1000

FIGURE 2.10 Top: range–energy relation in Be, Cu, and Pb. Bottom: test of cubic spline interpolation. (Data from M.J. Berger, M. Inokuti, H.H. Andersen, H. Bichsel, D. Powers, S.M. Seltzer, et al. ICRU Report 49, 1993.)

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Proton Therapy Physics

2.5 lead 2.0

brass

σS/R0 (%)

water 1.5 lexan

1.0

beryllium 0.5 0.0

0

50

100

150 200 Energy (MeV)

250

300

FIGURE 2.11 Range straggling in several materials. (Data from Janni. Proton Range-Energy Tables, 1KeV–10 GeV. Academic Press, 1982).

are nearly straight, and for Be, Cu, and Pb, nearly parallel: good candidates for cubic spline interpolation (8) for each material separately. This method, in effect a different variable power law for each material, is more than adequate as the lower panel of Figure 2.10 shows.* We require only thirteen input values for each material at 0.1, 0.2, 0.5, 1, …, 500, 1000 MeV. The energy range is generous because computer programs sometimes stray into forbidden territory while carrying out their task. To interpolate a range–energy table by hand, use power law, not linear interpolation, particularly if the table steps are large. Linear interpolation gives a systematically high answer as you can see directly from R ≈ aE2. 2.3.6  Range Straggling Since energy loss occurs as a finite (albeit very large) number of individual interactions, it has a statistical error. Therefore protons, even if their initial energy is exactly the same, will not all stop at exactly the same depth. This is called range straggling, or energy straggling if we focus on fluctuations in energy loss rather than range. The theory is outlined by Janni (5), who also evaluates it. Specifically, he tabulates the standard deviation of straggling expressed as a percentage of the mean projected range. Figure 2.11, a graph of his tables, shows range straggling as a function of incident energy for five useful materials. *

This and many other useful procedures are incorporated in a free “proton desk calculator” LOOKUP by the author (B.G.) (9).

Physics of Proton Interactions in Matter

37

From the graph, straggling ≈ 1.2% of range for light materials and only slightly more for heavy materials. A useful consequence is that the shape of the Bragg peak changes very little when plastic or even some Pb is substituted for water. That will greatly simplify the design of range modulators. 2.3.7  Water Equivalence Water is often used as a proxy for tissue, and it is sometimes necessary to compute the water equivalent of a degrader. For instance, the second scatterer in the standard nozzle used by ion beam applications (IBA) is 0.624 cm Pb. By how much does that decrease the beam penetration in the patient? The water equivalent of a given thickness of any material can be computed exactly if the range–energy relation of the material and that of water are known (10). Of course the answer is only as accurate as the range–energy relation. To avoid that problem, the water equivalent can easily be measured, by placing the degrader upstream of a water tank and measuring the shift in the Bragg peak, as should always be done if the answer is critical (for instance, if it determines treatment depth). If a material is far from water in the periodic table, its water equivalent depends on incident energy and must be used with caution. Water equivalent is independent of energy only if R(E) of the material on a log-log plot (Figure 2.9) is parallel to that of water. The water equivalent of 0.6329 cm Pb is 3.5722 cm at 200 MeV incident but 3.4197 cm at 100 MeV, 1.5 mm less. By contrast, a plastic degrader has the same water equivalent at any radiotherapy energy. That said, if the Pb is located at the start of a beam line and always sees nearly the same proton energy, its water equivalent will be constant.

2.4  Multiple Coulomb Scattering In addition to slowing down in matter, protons scatter, mainly by myriad collisions with atomic nuclei. The angular deflection from a single scatter is almost always negligible. Therefore the main observed effect is the statistical outcome (random walk in angle) of countless tiny deflections. Hence “multiple Coulomb scattering” (MCS), “Coulomb” because the underlying interaction is electrostatic. The MCS angular distribution is very nearly Gaussian, because it’s the sum of many small random deflections (the Central Limit Theorem). However, it’s not exactly Gaussian: the theorem does not really apply because large single scatters in the target, though rare, are not quite rare enough (11). The complete angular distribution has a Gaussian core with a single scattering tail. For most radiotherapy purposes

38

Proton Therapy Physics

we need only consider the Gaussian part, which contains about 98% of the protons. 2.4.1  Experiment Figure 2.2 shows an ideal proton beam entering a target. On emerging the protons have a nearly Gaussian angular distribution, with an rms spread, θ0. If they then drift through a distance, L, to a measuring plane (MP) with little or no additional scattering, a nearly Gaussian fluence distribution of rms spread y0 = L × θ0 results. We can use a dosimeter to measure this fluence distribution because all protons at the MP have very nearly the same energy or stopping power, so dose is proportional to fluence (Eq. 2.12). If we want to deduce θ0 from measurements of y0, we need to worry (for thick targets) about where the protons appear to come from: what is L, exactly? For thin targets, we need to consider the size of the beam and scattering in air along the drift path. Except for these complications the experiment really is simple, and measured values of θ0 for a large assortment of target materials and thicknesses have been reported (12). 2.4.2  Highland’s Formula The theoretical challenge is (a) to predict the exact form of the MCS angular distribution and (b) to predict its characteristic width as a function of proton energy as well as scattering material and thickness. Several more or less successful theories were published in the 1930s and 1940s. By consensus, the most elegant, accurate, and comprehensive theory for incident protons is that of Molière (13, 14), written in German. A paper in English by Bethe (15) improves on Molière’s somewhat and reconciles it with some of the other theories. However it omits two aspects of Molière’s theory critically important to proton radiotherapy: his generalizations to scattering in arbitrarily thick targets (large proton energy loss) and compounds and mixtures. The fact that several American authors were unaware of these generalizations, especially the first, led to some errors and confusion in the literature. We will shortly come to Molière’s theory, at least the bare bones. However, let us first present a formula which is nearly as accurate and far easier to evaluate. In the Gaussian approximation all we need is the dependence of θ0 on proton energy and scattering material. Highland’s formula for θ0 (16) is as follows*:



θ0 =

 L  14.1 MeV L  1 1 + log 10   rad pv LR  9  LR 

(2.22)

* The numerical constant, strictly following Highland’s paper, should be 17.5  ×  1.125/ 2 = 13.92 MeV 17.5  ×  1.125/ 2 = 13.92 MeV . However, the 1986 Particle Properties Data Book gave 14.1, which (for whatever reason) we (12) used in our comparison with experimental data. It has since become the accepted value.

39

Physics of Proton Interactions in Matter

θHighland

θ0 (millirad)

100

10 Pb Cu Al 1 Be 0.001

0.01

x / R1

0.1

1

FIGURE 2.12 Accuracy of Highland’s formula for four elements. x/R1 is target thickness divided by proton range at the incident energy. The points are experimental data at 158.6 MeV. (From B. Gottschalk, A.M. Koehler, R.J. Schneider, J.M. Sisterson M.S. Wagner. Nucl Instr Methods. 1993;B74:467–90. With permission.)

where pv is the kinematic factor we have already met in Eq. 2.6, L is the target thickness, and LR is the radiation length of the target material, which can be found in tables. As its form implies, Eq. 2.22 only applies to targets sufficiently thin so that pv does not decrease much from its initial value. However, it can be generalized (12) to arbitrarily thick targets. Considering its simplicity, the Highland formula so generalized is comprehensive and accurate. Figure 2.12 compares it with experiment for target materials spanning the periodic table over three decades of normalized target thickness and two decades of θ0. It is worth noting that Highland derived his formula by fitting a version of Molière theory (12, 16), not by fitting experimental measurements. 2.4.3  Molière’s Theory Molière’s theory is algebraically complicated.* To give you a flavor, we will only treat the simplest case, a target consisting of a single element (atomic weight A, atomic number Z) which is sufficiently thin so that the incident proton (charge number z, momentum p, speed v) does not lose much energy. We also assume Z is large enough that scattering by atomic electrons is negligible. The task is to compute the distribution of proton space angle  θ given protons of known energy in a target of thickness t g/cm2, where t  proton range. *

The aforementioned free program LOOKUP by the author (B.G.) can be used to compute MCS theory in all its forms (9).

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Proton Therapy Physics

We first calculate a characteristic single scattering angle χc given by

χ2c = c3 t/( pv)2

(2.23)

where 2



 e2  z2 Z2 c3 ≡ 4 πN A   (c)2 A  c 

(2.24)

where NA ≈ 6.022 × 1023 gmolwt−1 is Avogadro’s number, (e2/ħc) ≈ 1/137 is the fine structure constant, and (ħc) ≈ 197 × 10−13 MeV cm is the usual conversion factor. The physical interpretation of χc is that, on average, a proton suffers exactly one single scatter greater than χc in its traversal of the target. Next we compute a screening angle χa using

χ2a = χ20 (1.13 + 3.76 α2 )

(2.25)

χ20 = c2 /( pc)2

(2.26)

where

and the Born parameter, α, is given by

α2 = c1 /β 2

(2.27)

where β ≡ v/c of the proton. The constants are 2



  e 2  c 1 ≡   z Z    c  

(2.28)

and 2



 1  e2  2 1/ 3  c2 ≡    (me c )Z  . 0 885 c .     

(2.29)

The screening angle is that (very small) angle at which the single scattering cross section levels off (departs from Rutherford’s 1/θ4 law) because of the screening of the nuclear charge by the atomic electrons. One of Molière’s key insights was that, though MCS depends directly on that angle, it is insensitive to the exact shape of the single scattering cross section near that angle. Next we compute a quantity,



 χ2c  b = ln  2   1.167 χa 

(2.30)

41

Physics of Proton Interactions in Matter

which is the natural logarithm of the effective number of collisions in the target. Next, the reduced target thickness, B, is defined as the root of the equation (2.31)

B − ln B = b



which can be solved by standard numerical methods. B is almost proportional to b in the region of interest. Finally, Molière’s characteristic multiple scattering angle, θM =



1 (χ c B ) 2

(2.32)

is analogous to θ0 in the Gaussian approximation. Typically it is about 6% larger.* Molière is now positioned to compute the distribution of θ. Defining a reduced angle, θ′ ≡



θ

(2.33)

χc B

he approximates the desired distribution function f(θ) by a power series in 1/B: f (θ) =



f ( 1) (θ′) f ( 2 ) (θ′)  1 1  (0) f (θ′) + +   2 2 πθM 2  B B2 

(2.34)

where n

f

( n)

2  y2 y2  1 ∞ (θ′) = ∫ y dy J 0 (θ′y) e y /4  ln  . n! 0 4   4

(2.35)

f (0) is a Gaussian:

2

f ( 0 ) (θ′) = 2 e − θ′ .

(2.36)

Molière gives further formulas and tables for f (1) and f (2) in reference 15. The foregoing equations, with Bethe’s improved tables for f (1) and f (2) (15), permit one to evaluate the scattering probability density f(θ) if the target consists of a single chemical element with Z  1, and the energy loss is small. Except for rearrangements of physical constants to conform to modern usage, and the normalization of f(θ), the equations are identical to Molière’s. We reiterate that Molière generalized this procedure to arbitrary energy loss, and to compounds and mixtures (12, 14, 17). The generalization to low-Z elements, where scattering by atomic electrons (not just the nucleus) is appreciable, is handled two ways in the literature. Bethe’s approach (15) is simply to substitute Z(Z + 1) for Molière’s Z2 wherever it appears. We call this Molière/Bethe. Fano’s approach (12, *

The 1/ 2 is ours; it makes θM more or less equivalent to θ0 in the Gaussian approximation.

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Proton Therapy Physics

101 100

2 πθ 2M f (θ′ )

10–1 10–2 10–3

0 1 2 3 4 5 6

10–4

B=4

–5

10

10–6

B = 12 0

25

50

(θ′ )2

75

100

125

FIGURE 2.13 Molière angular distribution plotted so that a Gaussian would show up as a straight line. Dashed line: f (0) only. Inset: graph near the origin. (From B. Gottschalk, A.M. Koehler, R.J. Schneider, J.M. Sisterson M.S. Wagner. Nucl Instr Methods. 1993;B74:467–90. With permission.)

17, 18) is more complicated: he gives a correction to b. The Molière/Fano theory fits experimental proton data from 1 MeV to 200 GeV for a wide variety of materials and thicknesses at the few percent level (12). Since this is comparable to experimental error, we do not really know how good Molière’s theory is, but Bethe (15) put it at 1%. There are no adjustable parameters! Though the mathematical definition of B is tortuous, it is easy to show numerically that B has a simple physical interpretation: it is proportional to the logarithm of the normalized target thickness. The constant of proportionality depends on the material. Figure 2.13 shows that the angular distribution depends very weakly on B. 2.4.4  The Gaussian Approximation The first proton measurements were performed by Bichsel, who bombarded targets of Al, Ni, Ag, and Au with 0.77- to 4.8-MeV protons from a Van de Graaff accelerator, using a tilted nuclear track plate detector (19). Figure 2.14 shows the angular distribution plotted in such a way that a Gaussian distribution yields a straight line. The solid line is the full Molière theory. The dashed line is f (0) (the Gaussian term) alone.

43

Physics of Proton Interactions in Matter

104

f (θ)

103

102

10

1

1

2

3

θ2

4

5

6

7

FIGURE 2.14 Figure 5 from Bichsel’s experiment: 2.18-MeV protons scattered from a 3.42-mg/cm 2 Al foil. (From Hans Bichsel. Phys Rev. 1958;112:182–85. With permission.)

Besides showing that Molière theory works well, Figure 2.14 shows that the distribution for small θ is approximately Gaussian but is not best represented by just keeping f (0). The higher f ’s also contribute, even at small θ. This had been noticed earlier by Hanson et al. (20), who suggested using, at small angles, a Gaussian with a reduced width parameter. In our notation Hanson’s recommendation reads

θ0 = θH ≡

1 (χc B − 1.2 ). 2

(2.37)

So far, that’s not a time saver because one still has to do the full Molière computation to evaluate Eq. 2.37. In 1975, however, Highland parameterized the full Molière/Bethe/Hanson theory, obtaining Eq. 2.22. As already noted, this simple formula fits experimental data in the Gaussian region nearly as well as the full theory. Integration of the Molière angular distribution f(θ) shows that approximately 98% of the protons fall into the region well described by a Gaussian. Therefore a single Gaussian distribution suffices for many proton radiotherapy calculations. If a dose outside the MCS Gaussian core needs to be modeled, the halo of nonelastic nuclear reaction secondaries is usually greater than the MCS single scattering tail (21).

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Proton Therapy Physics

2.4.5  Scattering Power Scattering power was introduced by Rossi in 1952 (22), though he did not use that term. It was resurrected and named by Brahme (23) in connection with electron radiotherapy, and now appears regularly in discussions of proton transport. This section is rather technical and may be skipped if you are only interested in computing multiple scattering in a single homogenous slab, for which we have already given several methods. Stepping back a bit, to compute the total energy loss of a proton in a degrader, we can integrate stopping power over the degrader thickness. Stopping power, defined by

(2.38)

S( x) ≡ − dE/dx

depends on the proton speed, and properties of the degrader material, at x (Eq. 2.17). By contrast, in MCS theory, we have outlined the theory without ever mentioning the concept of “scattering power.” Nevertheless—if we so desire— can we (in analogy to stopping theory) define a scattering power as the rate of increase of the variance of the MCS angle,*

T ( x) ≡ d θ2y / dx

(2.39)

such that, integrated over x for a homogeneous slab of arbitrary thickness, it correctly gives the total MCS angle in the Gaussian approximation, namely the Molière/Fano/Hanson result? Also, why would we want to do that, since we already know the answer? Taking the second question first, we assert without proof that any proton transport problem that is, any attempt to handle simultaneously both energy loss and multiple Coulomb scattering, requires a differential description of both processes. We must be able to compute, for any infinitesimal step ∆x of the full degrader, the corresponding infinitesimal changes in energy and MCS angle. That applies equally to deterministic (e.g., Fermi-Eyges [24]) or Monte Carlo methods. Furthermore, it is very desirable that any such computation yield results which, at least over some reasonable range, are independent of the step size ∆x. That covers our motivation for trying to find a workable T(x), essentially a differential description of Molière’s theory. As to the first question, at least six prescriptions for T(x) exist, some considerably more accurate than others (25). We favor (naturally) our own “differential Molière” formula: 2

*

 15.0 MeV  1 TdM ( x) = fdM ( pv , p1 v1 ) ×    pv( x)  LS ( x)

(2.40)

Current practice favors defining T as the rate of increase of projected angle θy rather than the space angle θ of Molière’s theory.

45

Physics of Proton Interactions in Matter

where fdM ≡ 0.5244 + 0.1975 log 10 (1 − (pv/p1 v1 )2 ) + 0.2320 log 10 (pv/MeV) −0.0098 log 10 (pv/MeV) log 10 (1 − (pv/p1 v1 )2 )



(2.41)

and

1 ρZ 2 ≡ αNre2 {2 log(33219 ( AZ)−1/3 ) − 1} LS A

(2.42)

which reproduces Molière/Fano/Hanson theory to ≈ ±2% for normalized target thicknesses from 0.001 to 0.97 (very thin to nearly stopping) over the full periodic table (25). LS is a scattering length, analogous to radiation length LR, and of the same order of magnitude.* pv is the familiar kinematic quantity (Eq. 2.6) at x, the point of interest, while p1v1 is the same quantity entering the degrader. Eqs. 2.40–2.42 apply equally well to mixed slabs. We simply regard LS as a (discontinuous) function of x while pv(x) is computed using the appropriate range-energy relation in each slab. An important characteristic of TdM(x) is that it is nonlocal via the correction factor fdM. Scattering power depends not only on conditions at x (that is, pv and LS) but on how the protons started out (p1v1). To take a simple example, for a 20 MeV proton in Be, d 〈θ2y 〉 / dx is smaller if the overlying thickness of Be is 0.1 cm (protons enter at 23.7 MeV) than if it is 5 cm (protons enter at 102 MeV). How can that be? How can the proton “know” what has gone before? The answer is that, unlike stopping, and for that matter, single scattering, multiple Coulomb scattering is not a primitive process! It makes sense to speak of stopping and single scattering even in an atomic monolayer, whereas it does not make sense to speak of multiple scattering: there are not nearly enough collisions. In a sense the factor fdM is a measure of the proton’s progress toward “Gaussianity.” One finds (25) that any T(x) that has some nonlocality built into it, some sense of the beam’s history, is more accurate than any T(x) that does not. A final comment, on step size. We mentioned that any computation, deterministic or Monte Carlo, should converge as a function of ∆x. Over some range of (suitably small) ∆x’s the answer should not change. Some popular Monte Carlos do not have this property, and using a scattering power approach would remedy that. There is no way that the Molière theory or its proxy, the Highland formula, can be built directly into a Monte Carlo without introducing step size dependence. 2.4.6  Binary Degraders Figure 2.3 shows that high-Z materials (e.g., Pb) are better at scattering, whereas low-Z materials (Be, plastics) are better at stopping. We use Pb if we *

LS/LR = 1.42 for Be decreasing monotonically to 1.04 for Pb. For compounds and mixtures LS obeys the Bragg additivity rule (Eq. 2.19).

46

Proton Therapy Physics

wish to scatter a beam with minimum energy loss and Be if we wish to slow down a beam with minimum scattering. In beam line design we often need to control both scattering and stopping. Instead of scouring the periodic table for the right combination, we use high-Z/ low-Z sandwiches such as Pb/plastic. Figure 2.5 shows two examples. The range modulator’s main job is to decrease beam energy in defined steps, but each step also has to produce the correct MCS angle for the double scattering system. Conversely, the second scatterer’s main job is to produce the correct MCS angle as a function of radius, but we also want the same energy loss at any radius. Mathematical design procedures for such “binary degraders” are described elsewhere (1, 9).

2.5  Nuclear Reactions Although EM interactions of protons dominate, nuclear interactions are by no means rare. They are far harder to model than stopping and scattering. Fortunately, their biological effect turns out to be small, while, in the design of beam spreading systems, they can be taken into account well enough by using experimentally measured—rather than theoretical or Monte Carlo generated— Bragg peaks. 2.5.1  Terminology ICRU63 (27) defines an elastic nuclear reaction as follows: • A reaction in which the incident projectile scatters off the target nucleus, with the total kinetic energy being conserved (the internal state of the target nucleus and of the projectile are unchanged by the reaction) while nonelastic • … is a general term referring to nuclear interactions that are not elastic (i.e., kinetic energy is not conserved). For instance, the target nucleus may undergo breakup, it may be excited into a higher quantum state, or a particle transfer reaction may occur. and inelastic • … refers to a specific type of nonelastic reaction in which the kinetic energy is not conserved, but the final nucleus is the same as the bombarded nucleus.

47

Physics of Proton Interactions in Matter

Thus, p + 16 O → p + 16 O or



16

O ( p , p)

16

O

(2.43)

16

O ( p , p)

16

O *

(2.44)

is elastic (16O is left in its ground state), p + 16 O → p + 16 O *



or

is inelastic (* denotes an excited state), and p + 16 O → p + p + 15 N or



16

O ( p , 2p )

15

N

(2.45)

(quasi-free proton-proton scattering in oxygen) is nonelastic even if the 15N nucleus recoils in its ground state, because it took energy—the “binding energy”—to remove the target proton from the nucleus. When a proton beam slows down and stops in matter, at any given depth we call those particles primaries, which have suffered EM interactions (stopping by collisions with atomic electrons and scattering by atomic nuclei). Particles from inelastic or nonelastic nuclear reactions are called secondaries. Both final state protons in reaction (2.45) are secondaries even though one (we cannot tell which) was the incident proton. All primaries are protons, of course, and all neutrons must be secondaries. Some materials of biological interest, for example, H2O, contain free hydrogen. When an incident proton scatters off free hydrogen, the secondary protons emerge with a relative angle of approximately 90° and share the original kinetic energy. Therefore they look pretty much like secondary protons from reaction (2.45) and should be included in any tally of nonelastic reactions even though the reaction is, technically, elastic. 2.5.2  Overview of Nonelastic Reactions Possible secondaries from nonelastic reactions at therapy energies are protons, neutrons, γ rays, heavy fragments such as alphas, and the recoiling residual nucleus. Heavy fragments other than alphas are in fact quite rare. One measure of the relative importance of each is the fraction of initial energy carried away. For nonelastic interactions of 150-MeV protons with 16O nuclei, Seltzer (27) finds the following: p 0.57

d 0.016

t 0.002

He 0.002 3

α 0.029

Recoils 0.016

n 0.20

The total energy imparted to charged particles is 0.64. Photons, not listed, presumably make off with 0.16. These numbers are from a Monte Carlo model, not direct experiment. Most of the final energy is in protons, neutrons and photons. Alphas stand out among heavy fragments (the alpha is particularly stable) but still have only 2.9% of the total energy.

48

Proton Therapy Physics

Though little of the energy goes into heavy fragments, they could in principle have a significant relative biological effect (RBE) because of their ­high-ionization density (see Chapter 19). This has been investigated by Seltzer (27), Paganetti (28, 29), and others, who find that RBE enhancement due to heavy fragments and recoils is, in fact, small. Their high ionization density is outweighed by the fact that very little energy (that is, dose) goes into those channels. What RBE enhancement there is comes from the much more abundant low-energy protons: secondaries and, at the distal end of the Bragg peak, primaries. Secondaries typically make large angles with the beam (think billiard ball collisions) unlike primaries which, even after multiple scattering, rarely exceed a few degrees. That is important because it means that secondaries produced in the beam line in scatterers or absorbers will clear out of the beam for purely geometric reasons before they enter the patient. 2.5.3  Nonelastic Cross Section We already know from Figure 2.7 that the nonelastic interaction probability per g/cm2 must be fairly independent of energy because the rate of loss of primary fluence is fairly constant. Janni (5) combines theory with experimental data to evaluate the cross section for various elements. Figure 2.15 shows his result for oxygen, plotted as a function of proton range rather than energy. Others (27, 30) use slightly different procedures and experimental data, but also find that the nonelastic cross section is nearly con600

σnonelastic (mB)

500 400 300 200 100 0

0

5

10

15 20 R0 (g/cm2)

FIGURE 2.15 Total nonelastic cross section of oxygen versus proton range.

25

30

35

49

Physics of Proton Interactions in Matter

35 30

Pnonelastic (%)

25 20 15 10 5 0

0

5

10

15 20 R0 (g/cm2)

25

30

35

FIGURE 2.16 Probability of a nonelastic interaction versus proton range in water.

stant at therapy energies, except in the last few cm where it roughly doubles before falling to zero. The total interaction probability for a stopping proton is the integral of the nonelastic cross section over the range. Figure 2.16 shows Janni’s result for water (5). For example, a 209 MeV proton, with a range of 28 g/cm 2, has a 24% probability of a nonelastic reaction before it stops. 2.5.4  Nuclear Buildup: Longitudinal Equilibrium Figure 2.17, a Bragg peak measured with a vertical proton beam, shows a small but definite buildup in the entrance region. That can be explained as follows. A proton beam emerging from air is accompanied by relatively few nuclear secondaries because of the low density of air. Nonelastic reactions increase as soon as the beam hits water, but it takes them a centimeter or two (the characteristic range of secondary protons) to reach equilibrium. After that the primary beam has an admixture of secondaries which is nearly independent of depth. Longitudinal equilibrium has been reached. Nuclear buildup was first observed by Carlsson and Carlsson (31) in 1977. The observed dose defect at the entrance was about 2× smaller than it should be according to the cross section, an observation also true of Figure 2.17 and still not explained. Incidentally, they also measured electron buildup, which is larger but has a much shorter characteristic distance ( 1 mm) . In photon therapy, electron buildup is useful; it leads to skin sparing. Unfortunately, this is not the case in proton therapy because the buildup distance is so short.

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Proton Therapy Physics

1.2

Dose (relative)

1.0 0.8 0.6 0.4 0.2 0.0

0

4

8

12

24 16 20 Range (g/cm2)

28

32

36

40

Meas used 20MAR99

FIGURE 2.17 Nuclear buildup in a Bragg peak. The abscissa should read “depth,” not “range.” (Courtesy of D. Prieels, Ion Beam Applications s.a..)

2.5.5  Test of Nuclear Models Predicting what mix of secondaries, with what energy and angle distributions, one will get when bombarding a given nucleus with protons of a given energy is an extremely complicated business, as might be expected. The nuclear model built into most popular Monte Carlo simulations is a descendant of the Bertini cascade model (32). Basically this model says that at proton energies significantly greater than the proton binding energy, the interaction begins as a quasi-free scatter off a nuclear proton, neutron, or cluster (alpha particle) and continues with possible further scatters until the secondaries emerge, leaving a recoiling residual nucleus behind. The complexity of the model makes a direct test very desirable. The shape of the Bragg peak is not a very good test, because the influence of nuclear secondaries on the shape is small, as we shall see shortly. A far more precise test can be made with the aid of a multi-layer Faraday cup (MLFC) like the one shown in Figure 2.18. It consists of CH2 (polyethylene) plates, in which most of the protons and secondaries stop, separated by thin brass charge collection plates.* The distribution of charge collected in each channel (Figure 2.19) shows a large peak (here reduced 25× for display purposes) preceded by a buildup region that comes entirely from nuclear secondaries and reflects the overall projected range of those secondaries. The three nuclear models tested, including the Bertini model, agree perfectly with each other and rather well with the experimental data (33). *

When the “stopping” plates are insulators, as here, it is the induced charge that is measured, but that equals the stopping charge. Protons stopping in the brass are measured directly.

51

Physics of Proton Interactions in Matter

FIGURE 2.18 A multilayer Faraday cup with CH2 plates (aluminum shield not shown).

2.5

ISABEL

2 pC/GigaProton

+

Bertini +

CEM +

Experimental data 1.5

1

0.5

0

0

+ +++

++ ++++ ++++ + + +++ 10

+

++ + +++ + + + + +++++ + +++

20

+

+ + + + ++

+

+ 30

40

+ 50

+++++++ ++++ 60

Channel number FIGURE 2.19 Buildup of nuclear secondary fluence, observed with a CH2 MLFC and compared with various Monte Carlo nuclear models. (From A. Mascia, J. DeMarco, P. Chow, T. Solberg. Proc. XIVth Intl. Conf. on the Use of Computers in Radiation Therapy, Seoul, May 10–13, 2004, 478–81. With permission.)

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Proton Therapy Physics

2.6  The Bragg Peak By Bragg peak (BP), we mean the entire depth–dose distribution measured in a water tank using a sufficiently broad, quasi-mono-energetic proton beam. We need a carefully measured BP in order to design a range modulator to create a spread-out Bragg peak (SOBP). Many calculations (Monte Carlo [3], analytical [4], numerical [34], and even graphical [A. M. Koehler, private communication]). have established that measured BP’s can be fully explained by combining the physical processes (stopping, scattering, and nuclear reactions) we have studied so far. In this section we’ll show qualitatively how each effect comes in. See Figure 2.20, a sort of summary. 2.6.1  Beam Energy That determines the depth of the peak. We have already learned that the mean projected range equals the depth of the distal 80% point (R0 = d80), not the depth of the maximum. 2.6.2  Variation of S ≡ −dE/dx with E The fact that the stopping power increases as the protons slow down gives rise to the upward sweep of the BP. 1/r2 and transverse size set peak to entrance ratio

overall shape from increase of dE/dx as proton slows

the dosimeter matters

width from range straggling and beam energy spread

10CM.TXT nuclear buildup or low energy contamination

this part is a guess

nuclear reactions take away fron the peak and add to this region

FIGURE 2.20 Ingredients of the Bragg peak.

depth from beam energy

53

Physics of Proton Interactions in Matter

2.6.3  Range Straggling and Beam Energy Spread The peak’s minimum possible width is related to range straggling, σRS ≈ 0.012  × range. There may be an additional contribution σbeam from beam energy spread. The width of the peak region and distal falloff depend on the quadratic sum of the two. More precisely, d20 − d80 = 1.3 × (σ 2RS + σ 2beam )1/2



(2.46)

which is from (A.M. Koehler private communications, 1982). Modern proton therapy facilities combine BP’s to get a flat dose distribution in two very different ways. In passive beam spreading, and in some magnetic scanning systems, degraders just upstream of the patient pull back the BP, and these displaced BP’s are combined (with appropriate weights) to produce an SOBP (see Chapter 4). Even though the degraders are not usually made of water, pulled-back BPs have very nearly the same shape as the pristine BP because, as we saw earlier, range straggling depends very weakly on degrader material. The degraders may be controlled by a computer, or the proper weights and range steps may be built into a classical propeller type range modulator. Otherwise, one may change the proton energy at the accelerator. Then, we must ask how BPs compare at different energies. Because straggling is nearly a constant fraction of range, the absolute width of the BP decreases with range (Figure 2.21). Any technique that changes energy at the accelerator must somehow parameterize this change in shape.

50

Mev / (g/cm2)

40 30 20 10 0

0

10

g/cm2

20

30

FIGURE 2.21 A set of measured Bragg peaks from 69 to 231 MeV. (Courtesy of D. Prieels, Ion Beam Applications s.a.)

54

Proton Therapy Physics

40

dD/dz, MeV cm2/g

35

160 MeV

30 25 20 15 10 5 0 0.0

0.2

0.4

0.6 z/ro

0.8

1.0

FIGURE 2.22 Solid line: Bragg peak including nuclear interactions; dashed line: nuclear interactions turned off. (Data from Martin J. Berger, NIST technical note NISTIR 5226 (1993). Available from the National Technical Information Service (NTIS), U.S. Department of Commerce, Springfield, VA 22161.)

2.6.4  Nuclear Interactions Each nonelastic reaction removes a proton from the EM peak, and the secondaries (having short ranges and large angles) deposit their energy further upstream. Therefore, nuclear interactions lower the peak and raise the entrance region (Figure 2.22). 2.6.5  Beam Size: Transverse Equilibrium MCS affects the Bragg peak somewhat indirectly. The BP, like any depthdose distribution, obeys D = Φ × (S/ρ) (dose = fluence × mass stopping power). Suppose we form a “pencil” beam using a small collimator. As the beam penetrates the water tank, it scatters, so that a given number of protons occupy more transverse area. In other words, the fluence on the central axis decreases with depth. That cancels the tendency of the stopping power to increase with depth. The Bragg peak become less pronounced, the smaller the collimator, as first pointed out by Preston and Koehler (35) (Figure 2.23). To counter that, we need to use a large beam, which we can obtain either by scattering or magnetic scanning (averaging over an integral number of scan cycles). Then at any point, say near end-of-range, the dose field can be thought of as a bunch of pencil beams laid down next to each other. Protons originally directed at some small area, dA, but scattered out, are compensated by protons not directed at dA, but scattered in. That compensation (“transverse equilibrium”) works as long as there are enough nearby pencils

55

Physics of Proton Interactions in Matter

D(o, x) DOSE ON AXIS

100 rc = ∞

80 60 40 2 mm 20

4 mm 3 mm

rc = 1 mm

2

4

6 8 x-cm WATER

10

12

FIGURE 2.23 The relative dose on the axis of a uniform circular proton beam of initial range 12 cm of water and radius rc at the collimator. The curve for rc = ∞ is experimental; the others are calculated. (Data from W.M. Preston, A.M. Koehler. The effects of scattering on small proton beams. Unpublished manuscript (1968), Harvard Cyclotron Laboratory. A facsimile is available in BGdocs.zip at http://physics.harvard.edu/~gottschalk.)

to do the scattering in, that is, as long as the beam surrounding dA is big enough. How big is big enough? You need to compute beam spreading in a water tank, a basic proton transport problem is beyond the scope of this chapter; see Preston and Koehler (35). There’s a simple experimental test, though. If you move the scan axis 1 cm to the side and measure the same BP, the beam is big enough. A way of getting the right answer with a single pencil beam is to use a detector which is much larger than the beam even at end of range. Such a detector sees all the protons at any depth. It integrates radially over the fluence factor, which therefore drops out. To summarize: when measuring the Bragg peak with a view to large-field modulator design, either use a small detector in a broad beam or a large detector in a pencil beam. 2.6.6  Source Distance To ensure transverse equilibrium, we usually spread the beam transversely, either by single or double scattering. Either way, the scattering system will have an effective origin from which the protons appear to spread out as from the apex of a cone. That cone is smaller at the entrance to the water tank than deeper into the tank. Put another way, the fluence falls as 1/r2, where r is the distance from the effective origin to the dosimeter. This effect

56

Proton Therapy Physics

lowers the peak-to-entrance dose ratio. It must be corrected, unless the system being designed has the same effective r as was used during the BP measurement. 2.6.7  Dosimeter Different dosimeters may give different peak/entrance ratios in the same beam. Sometimes the problem is intrinsic. For instance, some diodes overrespond in the peak region (36) relative to a plane-parallel ionization chamber (IC). Sometimes, the difference is geometric in origin. For instance, a “thimble” IC yields a lower peak/entrance ratio than does a plane-parallel IC (37). 2.6.8  Electronic and Nuclear Buildup; Slit Scattering Several effects may contaminate the entrance region. You will not normally see electronic buildup since the buildup distance is very short. Nuclear buildup may be seen with a vertical beam (beam entering water from air) but should be ignored, at least with passive beam spreading, because the range compensator will usually have enough buildup material to mask it. If there is a collimator near the water tank, slit scattered protons may be observed as a dose enhancement in the entrance region, so this should be avoided. 2.6.9  Tank Wall and Other Corrections For design purposes we usually want a BP which approximates, as well as possible, what would be seen with the raw beam (no scatterers or degraders) entering an ideal water tank (no wall) and an ideal dosimeter (no wall). Because of scatterers, tank wall (usually rather thick in commercial water phantoms), and dosimeter wall, the first bit of this ideal BP is not actually measured. As Figure 2.20 ”this part is a guess” shows, this region can be approximated well enough by linear extrapolation of the first bit of the measured part. 2.6.10  Measuring the Bragg Peak All the items enumerated should be kept in mind when measuring a BP to be used in designing a large-field range modulator. If the dosimeter is small, make sure the beam is broad. Use the dosimeter you plan to use later for QA. Set accelerator energy selector slits (if any) at their working setting to get the same beam energy spread. Record the thickness of all materials upstream of the dosimeter active volume (scatterers, tank wall, dosimeter wall) so you can correct the depth in water for them. Be sure you know and record the effective origin so you can correct the BP for 1/r2.

Physics of Proton Interactions in Matter

57

2.7  Summary We began with a qualitative survey, some basic proton kinematics, and definitions of the dosimetric quantities: fluence, stopping power, and dose. Using these, it was already possible to estimate how much proton current we need for a given dose rate and treatment volume. We then presented the basic interactions of protons in some (though by no means complete) mathematical detail. These processes (stopping, scattering and nonelastic nuclear) interact to determine the shape of the pristine Bragg peak, the basic proton depth–dose curve from which therapy dose distributions are constructed. Stopping and scattering are relatively simple, while nuclear reactions are relatively rare. The upshot is that many problems arising in proton radiotherapy physics can be solved from first principles. That is certainly true of beam line design. It is also true of dose reconstruction in the patient, though the mathematical difficulties are formidable. They mainly relate to the fact that, due to the interplay of inhomogeneities in the patient (e.g., bones, air, implants) with multiple Coulomb scattering, protons can arrive at a single point with many different energies (and therefore, stopping powers). Until now, time-consuming Monte Carlo calculations (see Chapters 9 and 12) are the only fully satisfactory way of handling this problem.

References





1. B. Gottschalk. Lectures (BGtalks.zip) and a draft textbook (PBS.pdf in BGdocs. zip) available for free download at http://physics.harvard.edu/~gottschalk or the Particle Therapy Co-Operative Group (PTCOG) website: http://ptcog.web. psi.ch/. 2. M.J. Berger, M. Inokuti, H.H. Andersen, H. Bichsel, D. Powers, S.M. Seltzer, et  al. Stopping Powers and Ranges for Protons and Alpha Particles. ICRU Report 49 (1993). 3. Martin J. Berger, Penetration of proton beams through water I. Depth-dose distribution, spectra and LET distribution. NIST technical note NISTIR 5226 (1993). Available from the National Technical Information Service (NTIS), U.S. Department of Commerce, Springfield, VA 22161. 4. Thomas Bortfeld. An analytical approximation of the Bragg curve for therapeutic proton beams. Med Phys. 1997;24(12):2024–33. 5. J.F. Janni. Proton Range-Energy Tables, 1KeV–10 GeV. Atomic Data and Nuclear Data Tables, 27 parts 1 (compounds) and 2 (elements) (Academic Press, 1982). 6. M.F. Moyers, G.B. Coutrakon, A. Ghebremedhin, K. Shahnazi, P. Koss, et al. Calibration of a proton beam energy monitor. Med Phys. 2007;34(6):1952–66.

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7. Ethan W. Cascio and Surajit Sarkar. A continuously variable water beam degrader for the radiation test beamline at the Francis H. Burr Proton Therapy Center. Proc. IEEE Radiation Effects Data Workshop (2007). 8. W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling. Numerical Recipes: the Art of Scientific Computing, Cambridge University Press (1986). 9. B. Gottschalk Software (BGware.zip), including Windows executables, special files and Fortran source code. Available for free download at http://physics. harvard.edu/~gottschalk. 10. B. Gottschalk. Comments on “Calculation of water equivalent thickness of materials of arbitrary density, elemental composition and thickness in proton beam irradiation.” Phys Med Biol. 2010;55:L29–L30. 11. C. Kittel. Elementary Statistical Physics. Wiley (1967). 12. B. Gottschalk, A.M. Koehler, R.J. Schneider, J.M. Sisterson M.S. Wagner. Multiple Coulomb scattering of 160 MeV protons. Nucl Instr Methods. 1993;B74:467–90. We have discovered the following errors: Eq. 2 should read Ξ(χ) =

1 χ2c 2 π (χ + χ2a )2

and in Table 1 the heading α should read α2, and ×109 under χc should read ×106. 13. G. Molière. Theorie der Streuung schneller geladener Teilchen I Einzelstreuung am abgeschirmten Coulomb-Feld. Z Naturforschg. 1947;2a;133–45. 14. G. Molière. Theorie der Streuung schneller geladenen Teilchen II Mehrfach- und Vielfachstreuung. Z Naturforschg. 1948;3a;78–97. 15. H.A. Bethe. Molière’s theory of multiple scattering. Phys Rev. 1953;89;1256–66. Four entries in the second column (the Gaussian) of Table II are slightly incorrect (A. Cormack, private communication), but the error (corrected in our programs) is at worst 1%. 16. V.L. Highland. Some practical remarks on multiple scattering. Nucl Instr Methods. 1975;129:497–99; Erratum, Nucl Instr Methods. 1971;161:171. 17. W.T. Scott. The theory of small-angle multiple scattering of fast charged particles. Rev Mod Phys. 1963;35;231–313. 18. U. Fano. Inelastic collisions and the Molière theory of multiple scattering. Phys Rev. 1954;93:117–20. 19. Hans Bichsel. Multiple scattering of protons. Phys Rev. 1958;112:182–85. 20. A.O. Hanson, L.H. Lanzl, E.M. Lyman, M.B. Scott. Measurement of multiple scattering of 15.7-MeV electrons. Phys Rev. 1951;84:634–37. 21. E. Pedroni, S. Scheib, T. Böhringer, A. Coray, M. Grossmann, S. Lin, et al. Experimental characterization and physical modeling of the dose distribution of scanned proton pencil beams. Phys Med Biol. 2005;50:541–61. 22. Bruno Rossi. High-Energy Particles. Prentice-Hall, New York (1952). 23. A. Brahme. On the optimal choice of scattering foils for electron therapy. Technical report TRITA-EPP-17, Royal Institute of Technology, Stockholm, Sweden (1972). 24. H. Svensson, P. Almond, A. Brahme, A. Dutreix, H.K. Leetz. Radiation Dosimetry: Electron Beams with Energies between 1 and 50 MeV. ICRU Report 35 (1984). 25. B. Gottschalk. On the scattering power of radiotherapy protons. Med Phys. 2010;37(1);352–67. 2

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26. Chadwick et al. Nuclear Data for Neutron and Proton Radiotherapy and for Radiation Protection. ICRU Report 63 (2000). 27. Stephen M. Seltzer. An assessment of the role of charged secondaries from nonelastic nuclear interactions by therapy proton beams in water. NIST technical note NISTIR 5221 (1993). Available from the National Technical Information Service, NTIS, U.S. Department of Commerce, Springfield, VA 22161. 28. H. Paganetti, M. Goitein. Radiobiological significance of beam line dependent proton energy distributions in a spread-out Bragg peak. Med Phys. 2000;27:1119–26. 29. H. Paganetti, M. Goitein. Biophysical modeling of proton radiation effects based amorphous track models. Int J Radiat Biol. 2001;77:911–28. 30. Martin J. Berger. Status of proton transport calculations. Unpublished NIST technical note (June 1992). 31. C.A. Carlsson, G.A. Carlsson. Proton dosimetry with 185 MeV protons: dose buildup from secondary protons and recoil electrons. Health Phys. 1977;33:481–84. 32. Hugo W. Bertini, Low-energy intranuclear cascade calculation. Phys Rev. 1963;131:1801–21. 33. A. Mascia, J. DeMarco, P. Chow, T. Solberg. Benchmarking the MCNPX nuclear interaction models for use in the proton therapy energy range. Proc. XIVth Intl. Conf. on the Use of Computers in Radiation Therapy, Seoul, May 10–13, 2004, 478–81. 34. H. Bichsel, T. Hiraoka. Energy spectra and depth-dose curves for 70 MeV protons. Int J Quant Chem. 1989;23:565–74. 35. W.M. Preston, A.M. Koehler. The effects of scattering on small proton beams. Unpublished manuscript (1968), Harvard Cyclotron Laboratory. A facsimile is available in \BGdocs.zip at http://physics.harvard.edu/~gottschalk. 36. A.M. Koehler. Dosimetry of proton beams using small silicon diodes. Rad Res Suppl. 1967;7: 53–63. In unpublished errata the author presents a corrected Figure 4b consistent with an output change of +0.32%/°C. 37. H. Bichsel. Calculated Bragg curves for ionization chambers of different shapes. Med Phys. 1995;22(11):1721–26.

3 Proton Accelerators Marco Schippers CONTENTS 3.1 Introduction................................................................................................... 62 3.2 Consequences Imposed by the Dose Application Technique................ 62 3.2.1 Dose Spreading in Depth................................................................ 63 3.2.2 Lateral Dose Spreading....................................................................63 3.3 Cyclotrons......................................................................................................65 3.3.1 RF System of a Cyclotron................................................................. 67 3.3.2 Cyclotron Magnet............................................................................. 70 3.3.3 Technical Issues................................................................................. 70 3.3.4 The Average Field............................................................................. 71 3.3.5 Focusing Properties.......................................................................... 73 3.3.6 Proton Source.................................................................................... 77 3.3.7 Practical Issues.................................................................................. 78 3.3.8 Beam Intensity Control.................................................................... 79 3.3.9 Beam Extraction................................................................................ 79 3.4 Synchrotrons................................................................................................. 82 3.4.1 Operation........................................................................................... 83 3.4.2 Ion Source and Injector....................................................................84 3.4.3 Acceleration and RF.......................................................................... 86 3.4.4 Extraction........................................................................................... 87 3.4.5 Recent Developments in Therapy Synchrotrons..........................88 3.5 Novel Accelerator Technologies..................................................................90 3.5.1 FFAG Accelerators.............................................................................90 3.5.2 Linear Accelerators........................................................................... 91 3.5.3 Linac-Based Systems for Proton Therapy...................................... 92 3.5.4 Dielectric Wall Accelerator.............................................................. 92 3.5.5 Laser-Driven Accelerators............................................................... 94 3.6 Concluding Remarks.................................................................................... 97 Acknowledgments................................................................................................. 98 References................................................................................................................ 98

61

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3.1  Introduction Until the 1990s proton therapy was performed in nuclear physics laboratories that were equipped with a particle accelerator. Typically an (isochronous) cyclotron or a synchrocyclotron was available, and in most cases the medical program had to compete with the (nuclear) physics program. In this period most of the pioneering proton therapy research was performed and most of the dose delivery concepts were developed, for example, in Berkeley, California (1, 2), Cambridge, Massachusetts (3), PSI (Switzerland) (4–6), and Uppsala, Sweden (7). When the efficacy and success of proton therapy became more established, dedicated facilities started to emerge, with the first hospital-based facility built in Loma Linda, California (8). Around that time also commercial companies started to develop accelerators and offered complete treatment facilities, including gantries. Nowadays the cyclotron and the synchrotron are the two types of accelerators that are offered by companies and that have proven to be reliable machines in clinical facilities. Many good textbooks and proceedings of accelerator schools exist on accelerator design (9, 10), but in this chapter the emphasis will be on relevant issues for proton therapy to understand the reason for the typical design choices and to become aware of the important technical and accelerator physics issues that could be discussed in a selection and acquisition procedure. Also these details will help to understand striking features one simply encounters when looking at an accelerator in more detail or that one might read in machine descriptions. Although proton therapy equipment consists of clearly identifiable groups of components, each having a specific task, this modularity may misleadingly suggest that these different modules are independent. There is, however, a very strong interdependence between the design of these components and the type and quality of the beam delivery system at the patient. In this chapter the relation between certain accelerator specifications and the quality and type of the dose delivery method will be discussed first, followed by a detailed description of the currently used accelerators: the cyclotron and the synchrotron. After a short overview of new developments in accelerator physics that may be applied in proton therapy in the coming one or two decades, some words of caution will be given in the conclusions.

3.2 Consequences Imposed by the Dose Application Technique Several important specifications of the accelerator and beam delivery system depend on the chosen technique to apply the proton dose to the tumor. As these techniques (11) will be described in detail in Chapters 4–6, only aspects relevant for the accelerator and beam delivery will be discussed here.

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63

3.2.1  Dose Spreading in Depth To distribute the dose in depth, the energy of the protons has to be adjusted before they enter the patient. In some accelerator types one can accelerate the protons up to the needed energy and transport these protons to the patient; examples of such accelerators are synchrotrons, linear accelerators, and fixed-field alternating gradient (FFAG) accelerators. It is important that the change to another beam energy is sufficiently fast (to limit the treatment time and to allow fast switching between treatment rooms) and accurate (to set the range with sufficient accuracy). In accelerators such as cyclotrons and synchrocyclotrons this is not possible, because they work at one specific proton energy only. To obtain a lower energy, the protons are slowed down in an adjustable amount of material. This can be done just after the beam has been extracted from the accelerator, in a degrader, or just before the patient in one of the beam-modifying devices in the treatment nozzle. In case of the upstream use of a degrader and in cases where the accelerator can set the energy, all following beam line magnets must be adjusted according to the chosen energy. This needs some dedicated requirements for the magnets, the power supplies, and the control system. If the energy adjustment is performed in the nozzle, a stack with a variable number of plates (range shifter), a plate with ripples (ridge filter), or a rotating wheel with an azimuthally changing thickness (range modulation wheel) is used. Both the upstream location and the nozzle location have their specific advantages and disadvantages with respect to transmission, energy spectrum, and beam emittance (11). It is important to consider the different uses of an energy varying system. If it is for adjusting the maximum used range in a certain treatment, or at a certain gantry angle, it is quite acceptable if the change can be performed within a few seconds. However, range modulation must be done fast (in the order of 0.1 s) to limit the treatment time. Therefore, the following are relevant parameters for the accelerator choice and the beam transport system design: the needed speed of the energy change, the accuracy of the obtained energy (range), and the effect on beam parameters such as intensity, energy spread, and beam broadening. Currently upstream energy modulation is only performed at PSI (Paul Scherrer Institut, CH) and at RPTC (Rineker Proton Therapy Center) in München (D). All other proton therapy facilities use the degrader or accelerator energy to set the maximum needed energy in a field and perform the modulation in the nozzle. 3.2.2  Lateral Dose Spreading Beam spreading in the lateral direction is necessary because the typical 1-cm size of a proton beam is much smaller than typical tumor dimensions. To irradiate target volumes of sizes between a few centimeters (e.g., eye treatments) and up to 30–40 cm (e.g., sarcoma), one needs dedicated beam-spreading

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systems, because spreading the beam by static beam optics alone cannot be done to this size. The most commonly used method is passive scattering (Chapter 5), at which the beam is broadened by multiple scattering of the protons in a (set of) foil(s) or thin plate(s). Just before the patient the broad beam is collimated to the shape that matches the tumor shape, as seen from the direction of the incident beam. Because the beam is going through several millimeters of material of high atomic number Z, up to 10 MeV will be lost. The larger the required beam size, the more material will be needed and the more energy will be lost. When specifying the accelerator energy one should be aware of this loss. Also one should keep in mind that, if no dedicated beamfocusing measures are taken, up to 90% of the intensity can be lost at the collimator(s) in the nozzle, which will generate neutrons (see Chapter 18). Finally, the beam transport system should provide accurate beam alignment with respect to the scattering system. In double-scattering systems a poor alignment will cause an asymmetry (tilt) in the lateral dose profile at the tumor. If the necessary beam size is larger than what can reasonably be accomplished with (double) scattering, beam wobbling can be added to the system. In a wobbling system, a fast-steering magnet deflects the beam and sweeps it along a certain trajectory, so that an additional area is covered by the beam. The trajectory can be a circular path, a sawtooth-shaped path, or a set of parallel lines (raster scanning). This periodic movement of the beam is repeated many times a second. For the accelerator this implies that an eventual periodic time structure in the beam (e.g., beam intensity pulses) should not interfere with this periodic motion; otherwise severe under- and overdosage will occur locally in the dose pattern. In general risks of interference should be evaluated for any periodic change in the beam characteristics, for example, due to a range modulator wheel. The best coverage of the target volume in combination with the lowest dose in the surrounding normal tissue is obtained with the pencil beam–­ scanning technique (see Chapter 6). Here fast-steering magnets (scanning magnets) are used to aim the beam sequentially at volume elements (voxels) in the target volume and at each location a specific dose is deposited. This can be done on a discrete grid (spot scanning), using a “step-and-shoot” method (6), or by moving the pencil beam in a continuous way along a certain trajectory within the target volume (raster scanning) (12). For spot scanning the specifications on the accelerator are rather relaxed. If the beam is switched off when one moves to the next spot, the only specification of the accelerator is that the beam intensity should be sufficient. The beam positioning must be fast and typically must be correct within a millimeter. Continuous scanning techniques can be grouped into two categories: time driven and event driven. In the time-driven category, the scanning magnets have a prescribed speed, and the beam intensity is set as a function of the position of the pencil beam. In this case the intensity of the beam must be adjustable within, for example, a fraction of a millisecond (depending on

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scanning speed) and set to the desired value with an accuracy of a few percent. Unexpected fluctuations or interruptions in the beam intensity or a pulsed beam are not desired. In event-driven systems the beam intensity is more or less fixed or just taken as it comes from the accelerator. The speed of the pencil beam motion (i.e., the speed by which the scanning magnet changes) is adjusted according to the necessary voxel dose and eventually corrected for the actual beam intensity. With such systems the stability of the beam intensity is less critical, although too large or too fast fluctuations are difficult to compensate by the speed of the scanning magnets. More details of tolerance conditions in scanning systems are discussed in Chapter 6. An important problem to be dealt with in radiation therapy is the motion of the tumor and/or critical healthy tissue during the dose administration (see Chapter 14). This motion can, for example, be caused by breathing. Especially for time-dependent dose administration techniques, such as pencil beam scanning, this is a problem. Different strategies are being pursued to deal with this problem. The first one is beam gating (13–15), at which one suppresses the beam when the target is not at its correct place. The second one is to perform continuous scanning in a very fast way (16, 17): a target volume of 1 liter is re-scanned 15–20 times during the 2-min dose delivery. One might also apply an on-line correction of the beam position, the intensity, and the energy to “follow” the motion (tumor tracking or adaptive scanning) (18). All three methods have direct implications for accelerator specifications related to (control of) beam intensity as a function of time. Typically, pulsed machines are less suitable for scanning applications, unless the repetition rate is sufficiently high (kHz) and the dose per pulse can be adjusted with sufficient accuracy (a few percent).

3.3  Cyclotrons Modern isochronous cyclotrons dedicated for proton therapy accelerate protons to a fixed energy of 230 or 250 MeV (19–22). Compared to the classical cyclotrons in accelerator laboratories, the new cyclotrons (see Figure 3.1 for two examples) are rather compact, with a magnet height of approximately 1.5 m and typical diameter between 3.5 m (100 tons) and 5 m (200 tons), when equipped with superconducting coils or with room temperature coils, respectively. Usually some extra space is needed above and/or below the cyclotron for the support devices of the ion source and equipment to open the machine. The most important advantages of a cyclotron are the continuous character of the beam (continuous wave [CW]) and that its intensity can be adjusted very quickly to virtually any desired value. Although the cyclotron has a fixed energy, the beam energy at the patient can be adjusted very fast and

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Liquid He closed circuit

Jacking system and pumps

Jacking system

pumps FIGURE 3.1 Top: the 250-MeV superconducting cyclotron of Varian, the first of which was installed by ACCEL at the Paul Scherrer Institute, Switzerland. (Adapted from PSI; M. Schillo, M., et al., Proc. 16th Int. Conf. Cycl. Appl., 37–39, 2001; Schippers, J.M., et al., Proc. 18th Int. Conf. Cycl. Appl., 15–17, 2008.) Bottom: the 230-MeV proton cyclotron of IBA (Louvain la Neuve, Belgium), the first of which was installed in Boston, MA. (Courtesy of IBA; IBA website: http://­w ww .iba-protontherapy.com/.)

accurately by means of a fast degrader and an appropriate beam line design. In addition the simplicity of the design concept and the relatively few components are often considered as advantages for the reliability and availability of the accelerator. The major components of a typical compact cyclotron are as follows (Figure 3.2): • A radio frequency (RF) system, which provides strong electric fields by which the protons are accelerated • A strong magnet that confines the particle trajectories into a spiralshaped orbit, so that they can be accelerated repeatedly by the RF voltage • A proton source in the center of the cyclotron, in which hydrogen gas is ionized and from which the protons are extracted • An extraction system that guides the particles that have reached their maximum energy out of the cyclotron into a beam transport system

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Proton Accelerators

Magnet

Area at ground potential septum RF “Dee”

Extractor -HV

pole

coil Vacuum chamber

Ion source

FIGURE 3.2 Schematic view of the major components of a cyclotron: left: the magnet, the RF system (Dees), and (right) the ion source, and extraction elements. The protons being accelerated are schematically indicated on their “spikes.”

The RF system consists of usually two or four electrodes (because of their shape in the first cyclotrons built, often called “Dee”) that are connected to a RF generator, driving an oscillating voltage between 30 and 100 kV with a fixed frequency somewhere in the range of 50–100 MHz. Each Dee consists of a pair of copper plates on top of each other with a few centimeters in between. The top and bottom plate are connected to each other near the center of the cyclotron and close to the outer radius of the cyclotron. The Dees are placed between the magnet poles. The magnet iron outside the Dees is at ground potential. When a proton crosses the gap between the Dee and the grounded region, it experiences acceleration toward the grounded region when the Dee voltage is positive. When it approaches the Dee at the negative voltage phase, the proton is accelerated into the gap between the two plates. During its trajectory within the electrode or in the ground potential, the proton is in a region free of electric fields, and at those moments the voltages on the electrodes change sign. The magnetic field forces the particle trajectory along a circular orbit, so that it crosses a gap between Dee and ground several times during one circumference. In the example shown in Figure 3.2 a proton is accelerated eight times during one turn. For example, when the electrode voltage is 60 kV at the moments of gap crossing, the proton gains ΔE = 0.48 MeV per turn. Due to the energy gain the radius of the proton orbit increases, so that it spirals outward. The maximum energy Emax (typically 230 or 250 MeV) is reached at the outer radius of the cyclotron’s magnetic field, after approximately Emax/ΔE turns (530 in the example). 3.3.1  RF System of a Cyclotron The RF system is the most challenging subsystem in a cyclotron because many contradicting requirements need to be dealt with. Important operational parameters are the RF voltage and the frequency.

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A minimum value of the RF voltage is needed to make the first turn, which starts at the ion source in the center and must pass apertures and connections between the top and bottom halves of the Dees; see Figure 3.12 in Section 3.3.6, proton source. A high RF voltage is advantageous because it yields a large ΔE, which enhances the turn separation. This makes the beam less sensitive to small local errors in the magnetic field, and it is a prerequisite to obtain high extraction efficiency. Further, the period (1/frequency) of the RF voltage at each Dee must be synchronous to the azimuthal location of the protons at all radii. The time T, a proton (with electric charge q and mass m) needs to make one turn with radius r, depends on its velocity v and the strength of the magnetic field B. For a circular orbit the Lorentz force Bqv acts as the centripetal force:



mv 2 = Bqv. r

(3.1)

The proton velocity can be written as v = 2πr/T. With Equation 3.1 this yields the time required for one turn:



T=

2πm . qB

(3.2)

Note that this time T does not depend on the radius or the velocity of the particle. This means that all particles are at the same azimuthal angle in the cyclotron. As indicated in Figure 3.2, they are all within a cloud resembling a rotating spike of a wheel. Although pulsed at the RF frequency of the accelerating voltage, the beam intensity extracted from the cyclotron can be considered a CW for all applications in particle therapy. The ratio between the RF frequency and the orbit frequency of the protons must be an integer number, the harmonic number h. In case of one electrode covering 180° of the pole, one typically uses h = 1, and in case of two or four electrodes of 45° (as used in Figure 3.2) h = 2 can be used. In Figure 3.3 two typical RF electrode configurations are shown. The magnet pole consists of hills and valleys, and the Dees can be mounted in the valleys, so that the gap between the upper and lower hill can be minimized. In the IBA and Sumitomo cyclotrons the space in the valley is also used to mount extraction components. The Dee is mounted on a copper pillar (stem), and the valley wall is covered with a copper sheet (liner). At the bottom of the valley the stem is connected with the liner. The combination of Dee, stem, and liner acts as a resonant cavity. This means that a current can flow back and forth along the stem, with a frequency determined by the resonance frequency of the cavity. The Dee will get a negative potential when the electrons flow to the edge of the Dee, and when the electrons flow to the grounded liner, the Dee will get a positive potential. A quality factor Q

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Proton Accelerators

cr yosta

acceleration gaps

t

Dee

dee liner IBA

coil

hill

Hill

Dee

Magnet pole

liner

ACCEL / Varian

RF current

hill

liner Hill coupler Sharp plate

coil ~RF signal

FIGURE 3.3 The IBA/SHI cyclotron (http://www.striba.com) with 2 Dees (left), the Varian cyclotron with 4 Dees (middle), and a sketch of the RF currents in the cavity, creating a voltage across the acceleration gap (right). (After Schippers, J.M., Rev. Acc. Sci. Technol. II, 179–200, 2009.)

of the cavity is defined in terms of the ratio of the energy stored in the cavity to the energy being dissipated in one RF cycle and can have a value between 3000 and 7000. The current is driven by a coupler, an antenna that emits the RF power from the external generator into the cavity. By slightly modifying the volume of the cavity (e.g., by shifting the connection between stem and liner), the resonance frequency of the cavity slightly changes. Because the oscillation frequency is enforced by the RF generator, this detuning of the cavity yields a change in the power absorbed in the cavity and hence a change in Dee voltage. This can be used for fine regulation of the Dee voltages. The RF currents float along the inner surface of the cavity and can be of the order of kiloampere. Also high voltages are obtained across small gaps. These conditions imply rigorous cooling, good vacuum, and clean surfaces. A lot of power (60–120 kW) is concentrated in small components, making the RF system usually one of the most vulnerable subsystems of a cyclotron. The RF generator operates in the FM frequency range and uses typical techniques for radio transmitters. Between 100 and 200 kW RF power is needed in total. The amplifier consists of several stages in series of which the final stage is a high-power vacuum tube (typically a tetrode or triode) (see Figure 3.4). Recent developments (23) aim for a replacement by many parallel coupled solid state amplifiers. This might potentially offer higher reliability due to the possibilities of redundant amplifier units. A cyclotron with a separate amplifier for each Dee can work with smaller amplifiers. In this case the phases of the Dee voltages must be carefully synchronized at the amplifiers. It is also possible to connect only one Dee to an amplifier (which must then provide all power) and to use a coupling to the other Dees in the central region of the cyclotron. When the Q-value of the cavities is high enough, it requires only a weak coupling to get all cavities co-oscillating. In this case the tuning of the cavities must be set such that the Dees oscillate in the correct phase with respect to each other.

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(b)

End stages

Control Pre amplifiers Transformers

(a)

rectifiers transformers rectifiers 1100A 1m

preamps & control RF power

FIGURE 3.4 (a) Picture of a 150-kW, 72-MHz, RF amplifier. (Adapted from the Paul Scherrer Institute.) (b) Top view of a design developed by Cryolectra, consisting of six racks filled with 24 solidstate amplifiers of 1.45 kW. (After Getta, M., et al., Proc. PAC09, TU5PFP081, 2009.)

3.3.2  Cyclotron Magnet Specifications of the magnetic field are determined by the beam dynamics. First, the field must be isochronous: at each radius r it must have the appropriate strength to match the time T a proton needs to make one turn, as given in Equation 3.2. Second, the shape of the field lines must provide a focusing force, to confine the space in which the protons are moving. A small gap between the upper and lower pole (hills) helps to limit the current in the main magnet coil but is also advantageous for field shaping and the reduction of RF fields outside the Dee. The real magnetic field must be correct within a few times 10−5. Although small local deviations can be accepted at some locations, a repetitive encountering of the beam with such a distortion often leads to systematic trajectory distortions, yielding instabilities and beam losses. Therefore, careful selection and shaping of the iron and field mapping are essential steps in the production phase of a cyclotron (24, 25). Once the cyclotron has been commissioned and the field optimized, one usually need not care much anymore about the magnetic field. Sometimes small adjustments of the current through the magnet coil are necessary to compensate for temperature changes of the iron or changes in component positions after a service. However, when judging cyclotron designs, the magnet design may have strong implications for the operational quality and eventual future upgrades of the cyclotron. 3.3.3  Technical Issues The magnetic field strength in the commercially available cyclotrons is between 2 and 3.5 T. Conventional copper magnet coils are used (19,

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20), and for the past few years superconducting coils have been used as well. Advantages of superconducting coils are the low power consumption (20 kW including cryo-coolers vs. 300–350 kW) and especially the stronger magnetic field. This allows the cyclotron to be smaller and less heavy, but more importantly, because the iron is magnetically saturated, it makes the magnetic field much less sensitive to small imperfections in the iron. Also, when switching on, cycling (a ramping procedure to erase the “magnetic history,” in which the magnet is first set at a higher field than needed) is not needed. In the superconducting (SC) cyclotron at PSI (Varian) (21) the coil is cooled by means of liquid helium. As is also visible in Figure 3.3, the SC coil is suspended in a vacuum cryostat. In addition to that, the coil is surrounded with a heat shield (at 40 K) and many layers of super insulation. The outside of the cryostat is at room temperature. Therefore, opening of the cyclotron does not require warming up of the coil and temperature effects due to gradual heating of the coil are not present. Disadvantages of the SC coil are the risk of a quench due to operational errors (which are normally prevented by the control system) or when a high-intensity beam is lost or stopped close to the coil and, although very unlikely, the long downtime in case of a severe technical problem with the coil or its cryostat. 3.3.4  The Average Field According to Equation 3.2, the magnetic field in the cyclotron should be homogeneous. However, when the energy of the protons becomes larger than 20–30 MeV, their velocity becomes a considerable fraction of the speed of light c (v/c = 0.2 at 20 MeV). Because of relativistic effects, this yields an increase of the proton mass m with respect to its rest mass m0: m(r ) =

1 1 − v(r )2 / c 2

m0 = γ(r )m0.

(3.3)

At 20 MeV this is a 2% effect, but at 250 MeV, with v/c = 0.61, this yields a mass increase of γ = 1.27. In a homogeneous field this would imply (see Equation 3.2) that the orbit frequency would drop with energy. With increasing energy (i.e., radius) the protons would lose pace with the acceleration voltage and would no longer be accelerated. Until the late 1950s, the method to accelerate protons in a cyclotron to energies above about 30 MeV was by adapting the RF to the radius of the proton orbit, a technique that has experienced a revival in recent designs of very compact high-energy synchrocyclotrons (26). As a consequence of the RF modulation, the beam intensity extracted from these synchrocyclotrons (the RF has to modulate its frequency synchronous to the mass increase) is pulsed at a repetition rate of typically 1 kHz.

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Initially synchrocyclotrons of 160–200 MeV were used for proton therapy at Harvard, Berkeley, and Uppsala (27). However, the more modern cyclotrons use an increase of the magnetic field with radius to cope with relativistic effects and keep the cyclotron isochronous: B(r ) = γ(r )B0 .



(3.4)

Here B0 is the field strength that would be needed if relativity were ignored. As an example, the field strengths of the 250-MeV cyclotron at PSI (Varian [24]) and the 230-MeV cyclotron of IBA (28) are plotted as a function of radius in Figure 3.5. With this method, the protons do not loose pace with respect to the RF signal and the beam remains CW. Two methods are commonly used to increase the field with radius. In the IBA and SHI cyclotrons (11) the gap between the magnet poles is decreasing with radius, as can be seen in Figure 3.3. The method employed in the SC cyclotron of Varian, takes advantage of the very strong magnetic field close to the SC coils. At fields above 2.5 T the iron is saturated and gives an almost constant (i.e., independent of the current through the coil) contribution of 40-60% to the total magnetic field. The rest of the field is coming directly from the coil (29–31), and this part increases with radius, as shown in Figure 3.6. IBA

2.0 1.8 1.6

B (T)

1.4 1.2 0

3.2

20

40

60

80

100 r, cm

Varian

3 2.8 2.6 2.4 2.2 2

0

10

20

30

40 50 60 Radius (cm)

70

80

90

FIGURE 3.5 The average magnetic field strength as a function of radius. Top: For the IBA cyclotron. (Data from Karamysheva, G.A., Phys. Part. Nucl. Lett., 6, 84–90, 2009.) Bottom: For the de Varian SC-cyclotron. (Data from Geisler, A., et al., Proc. 17th Int. Conf. Cyclotr. Appl., 18A3, 2004.)

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Proton Accelerators

3

total

B (T)

2

iron

1 0 40

coil 50

60 70 Radius (cm)

80

FIGURE 3.6 Contributions of the (saturated) iron and the coil to the average magnetic field.

3.3.5  Focusing Properties A magnetic field that increases with radius, however, would cause a lack of vertical beam stability. Contrary to a field that decreases its strength with radius, in which particles are pushed back to the median plane by the Lorentz force after a vertical excursion, particles are pushed toward the poles in a field that increases with radius. This is illustrated in Figure 3.7. The radial variation of a magnetic field can be expressed by means of a field index, n:



n(r ) = −

r dB(r ) . ⋅ B(r ) dr

(3.5)

If B decreases with radius (i.e., dB/dr is negative), n has a positive value, and the field has vertically focusing properties. The relativistic correction of Equation 3.4, yields a positive dB/dr, so that the field index is negative, associated with defocusing in the vertical plane. In typical proton therapy cyclotrons, the field index (Equation 3.5) varies from 0 in the center to ­approximately −0.5 at extraction. To compensate for this defocusing, additional vertical focusing

FIGURE 3.7 Vertically focusing and defocusing in a cyclotron with a magnetic field that is decreasing with radius (top) and in a cyclotron with a field that is increasing with radius (bottom).

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Proton Therapy Physics

Valley Hill

Pole extension f

d

f

d

d f

Hill

Bz(θ) 0

r

f d

B(R)

θ

Magnet pole

2fB0

Valley π θ(radian)

2π

FIGURE 3.8 Pie-shaped hills and valleys on a pole give an azimuthally (θ) varying magnetic field strength. At the hills, the orbit has a smaller radius of curvature due to the stronger field. Because the boundary between hill and valley is not crossed perpendicularly, alternating vertical focusing and defocusing occurs at these boundaries.

power must be added. This is achieved by a variation of the field in the azimuthal direction, by adding pie-shaped pieces (hills) to the pole, as shown in Figure 3.8. Along a turn a proton thus experiences stronger magnetic fields when crossing the pole hills and weaker fields when crossing the valleys (the average value of the field along a turn is, of course, equal to the isochronous one). In the strong field the orbit is slightly more curved than in the weaker field. Therefore, the protons do not cross the boundary between the two regions perpendicularly. When a proton is not traveling in the median plane, it will experience an azimuthal component of the magnetic field, which is no longer parallel to the beam. This component creates a vertical component of the Lorentz force, proportional to the difference in field strength, the distance of the proton to the midplane and tan(φ)/r, with φ being the angle between the trajectory and the normal to the field step. Depending on the traveling direction, this force is directed either toward the median plane or toward the pole. This repetitive focusing and defocusing always results in a net focusing force. The focusing strength of these field steps is often expressed by means of the flutter, F(r): 2



B(r )2 − B(r ) F (r ) = 2 B(r )

(3.6)

where the brackets <> denote the average over one turn. Typical values of flutter can be in the order of 0.05. With increasing saturation of the iron, the

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Proton Accelerators

Valley

ψ

R Hill

FIGURE 3.9 By twisting the hill into a spiral shape, the angle y increases with radius, so that the vertical focusing is maintained at a large radius.

nominator in Equation 3.6 becomes constant and above a certain radius the flutter decreases with radius. In addition the vertical Lorentz force decreases with increasing r. Therefore, the focusing effect of the flutter must be enhanced with increasing radius in the cyclotron. This is done by increasing the angle between the proton trajectory and the field step with radius; the hill must be twisted to a spiral with spiral angle ψ(r), as shown in Figure 3.9 and as was also visible in Figure 3.3. The restoring forces ensure vertical stability. The proton tracks perform a vertical oscillation around the equilibrium orbit in the median plane with frequency or tune Qz (instead of Q the symbol ν is also frequently used for these betatron oscillations). The strength of the focusing is given by Qz2: a strong focusing yields a high betatron frequency. The total focusing power in the vertical plane can then be written as the sum of the above contributions. For such an azimuthally varying field (AVF) cyclotron consisting of N sectors (hills), one gets the following:



Qz2 (r ) ≈ n(r ) +

N2 F(r )(1 + 2 tan 2 ψ (r )). N2 − 1

(3.7)

Typical values of Qz are about 0.2, which suffices for the (weak) vertical focusing. At the extraction of the cyclotron Qz can increase to very large values (>1) due to the grazing crossing of the fringe field at the outer edge of the cyclotron pole. Therefore, it is important to guide the protons as fast as possible through this region to prevent a too dramatic increase of the vertical beam size. In a cyclotron, focusing in the horizontal plane is rather straightforward and is automatically achieved because the isochronicity requirement of Equation 3.4 determines a fixed relation between the horizontal (= radial) betatron frequency Qr and the relativistic mass increase γ(r) defined in Equation 3.3:

Qr (r )2 ≈ 1 − n(r ) = γ (r )2 .

(3.8)

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Proton Therapy Physics

Sh

ift

of or bi t

ce nt er

–

+

FIGURE 3.10 At the Qr = 1 betatron resonance the center of the orbit is shifted by a small magnetic bump.

In addition there is a contribution of a few percent from the spiral shaped hills and valleys. The quantity Qr is always greater than unity; radial focusing is strong. Note that the second equality in Equation 3.8 is valid until the field starts to flatten off just before extraction because there the isochronicity criterion is not maintained anymore (this depends on the extraction method, as will be discussed later in this section). The horizontal betatron frequency plays an important role in the central region and at the extraction. In these regions dB/dr = 0, so n = 0 and Qr ≈ 1. As illustrated in Figure 3.10 such an oscillation yields in fact a radial shift of the orbit. In the central region the initial centering is quite sensitive to small-field distortions. These can cause an accumulation of orbit shifts and lead to large precessions (changes in the position of the orbit center) of the beam orbits. In a working machine beamcentering corrections may be necessary after a service involving exchange of components. Slight shifts of electrode positions or of the ion source may result in such centering errors. However, corrections can be made easily with small trim coils attached on the pole or by changing the insertion depth of iron trim rods in pockets in the central pole region. Just before the extraction radius, the Qr = 1 resonance is crossed again, and this is used to extract the beam, as will be discussed later. Although in some designs a betatron resonance is used to advantage, in general one must be very careful. Excitation of a resonance will cause an increase of the oscillation amplitude and may have beam loss as a consequence. Also coupling resonances, in which there is an exchange of amplitude between radial and vertical oscillations, are possible. In general resonances occur at radii in the cyclotron, where

mQr(r) + nQz(r) = p,  in which m, n, and p are integer numbers.

(3.9)

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In the design phase of the machine one tries to adjust the spiral and flutter to avoid such resonances. If a resonance cannot be avoided, one tries to tune the field (and RF voltage) such that it is crossed in a minimum number of turns, so that small errors in the magnetic field do not have the chance to excite such resonances. After commissioning of the cyclotron, the tunes are fixed and one only needs to be aware of resonances in case of small changes in orbit positions due to machine changes, or upgrades. 3.3.6  Proton Source Currently all commercially available cyclotrons are equipped with a proton source in the center of the cyclotron. External sources are only of interest if other particles also need to be accelerated. The internal sources operate by exploiting the Penning effect (32, 33): the ionization of gas by energetic electrons in an electrical discharge. The ion source consists of two cathodes at a negative voltage of a few kilovolts located at each end of a vertical hollow cylinder at ground potential (chimney), into which also the H2 gas is flushed (about 1 cm3/min) (see Figure 3.11). Free electrons are created by heating a filament or, in the case of a “cold-cathode source,” by spontaneous emission from the cathode in the strong electric field between cathode and ground. In this field the electrons Internal “cold cathode” proton source

cathode, -HV pole

arc

Vertical

-80 KV Dee 1 Chimney filled with plasma

Dee 3

deflection plates

Cathode, -HV

pole

Cooling water

FIGURE 3.11 Schematic view of the ion source of the “cold-cathode” type (= no filament used) and the first few turns.

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Dee 4 Prot o In fi ns rst tur n

Dee 1

Hpu lle

chimney

r t ha st on ot ed Pr tart late s oo t

H2+

Dee 3

slit

Dee 2

FIGURE 3.12 Orbits in the central region of different ion species coming out of the source. To prevent acceleration of unwanted particles, a slit is selecting the protons that travel at the correct RF phase. The radii of the orbits are determined by the amplitude of the RF voltage, which should be high enough to get around the obstacles in the central region.

are accelerated, and they will ionize the gas. They are confined along the magnetic field lines and bounce up and down between the cathodes, thus increasing the ionization of the gas. The ions (H+, H2+, H–, etc.) and electrons form a plasma that fills the chimney volume. Because a plasma is an electric conductor, external electric fields hardly penetrate the plasma. However, protons and other ions that diffuse to a little hole in the chimney wall will experience the electric field from the nearest Dee (the puller). When the Dee is at negative potential, protons that escape from the plasma will accelerate toward the Dee. If they arrive at the right phase, they will cross the gap to the puller and will be further accelerated, as shown in Figure 3.12. Because of the narrow acceptance windows in time and in the further acceleration path, only a fraction of the protons leaving the source is actually being accelerated. 3.3.7  Practical Issues Important specifications of the ion source are: the total proton current extracted from the source within a not too large emittance, the stability of the intensity, and the time between services (goes on cost of operational

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time of the cyclotron). At an ion source service, one typically exchanges filaments (if used), cathodes (worn out by sputtering), and the chimney (extraction hole increases by sputtering). Modest operational conditions and a careful material choice (heat properties, electron emission, sputtering resistance) are of importance to obtain a source lifetime of 1–2 weeks or even up to a month. 3.3.8  Beam Intensity Control The beam intensity is regulated by adjusting the arc current between the cathodes and ground, the gas flow and the current through the filament (if present). Usually the proton current reacts rather slowly (milliseconds to seconds) to changes in these parameters. In these kinds of sources it has been observed that an intensity increase also leads to an increase of the emittance (beam divergence) of the beam coming out of the source (34). By selecting the fraction of the beam around the maximum of the emittance, a very stable beam intensity (a few percent at kilohertz band width) can be obtained routinely (35). This is essential for fast line scanning. In the IBA cyclotron the beam intensity is regulated at the source by a feedback loop from the measured beam intensity. At PSI the ion source is operated at a fixed setting. A pair of adjustable radial apertures (phase slits) close to the cyclotron’s center sets the maximum intensity. Between 0 and this maximum, the intensity is regulated with an accuracy of 5% within 50 μs by a vertically deflecting electric field and a vertical collimator, cutting the beam in the first few turns, as shown in Figure 3.13. This fast intensity regulation at the vertical collimator by the vertical deflector (see Figure 3.14) is used for intensity control during line scanning. 3.3.9  Beam Extraction The extraction efficiency is an important specification of a cyclotron. A low efficiency means severe beam losses, which will cause radioactive components in the cyclotron (36) and enhanced wear and dirt deposition on insulators. This reduces the availability of the cyclotron and increases the radiation dose to the maintenance staff. Considering that an extraction efficiency of 25% implies nine times (!) more lost protons per extracted proton, compared with a cyclotron with 75% extraction efficiency, one should strive for extraction efficiencies of at least 60–70%. The major problems to overcome with the extraction of the beam from a compact cyclotron are to separate the protons to be extracted from those that still have to make one or more turns and to prevent destruction of the extracted beam in the grazing passage of the rapidly decreasing fringe field. The design of the extraction is therefore aimed at an increase of the orbit separation at the appropriate location and to cross the fringe field as quickly as possible, followed by a reduction of the vertical focusing to compensate

80

Vertical position (mm)

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4

effects of vertical deflector

2

Apertures of vertical collimator

0

Defl. = 1 kV

–2 –4

puller 0

2000 1000 Azimuthal angle in cyclotron (degr)

Beam passes at vertical collimator (Defl. = 1 kV)

Foil burns on the lower collimator jaw 100

120

140

Radius in cyclotron (a.u.)

FIGURE 3.13 In the PSI cyclotron a fast regulation of the beam current is performed by means of vertical deflection of the beam (top). The aperture (middle) is crossed six times. Bottom: Beam passages at the lower aperture limiter by means of foil burns. Due to the vertical betatron oscillations, the beam is mostly cut at the first three crossings.

for a vertical over-focusing and by a horizontal focusing to keep a moderate beam width. The extraction is performed by several extraction elements, of which the first one is a septum (see Figure 3.2). This thin vertical blade is aligned parallel to the beam and separates the extracted beam from the ones that still have to make one or more turns. The septum should be able to withstand power dissipation due to beam particles that hit the septum. A bar-shaped cathode is positioned parallel to the septum at a larger radial position. The electric field between this cathode (at several tens of kilovolts) and the septum deflects the beam more outward into a channel between the coils and through the yoke. In this extraction channel additional steering and the (de) focusing is performed by permanent magnets and/or field-shaping iron blocks. Close to extraction radius the orbit separation is decreasing because of two effects. First, the radius of each orbit increases linearly with the momentum p and thus approximately with √E. A constant ΔE thus leads to smaller

81

Extracted beam intensity

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0

1 Voltage on vert.defl. (kV)

2

FIGURE 3.14 The extracted beam intensity as a function of the voltage on the vertically deflecting plates, mounted in Dee 3 of the PSI cyclotron.

distances between sequential orbits. In addition ΔE decreases because of loss of isochronism in the decreasing magnetic field (see Figure 3.5 and the inset in Figure 3.15). The orbit separation can be increased by exciting the Qr = 1 resonance to shift the center of the orbits. This already creates a larger separation between two turns, as shown in Figure 3.10. However, a stronger effect can

γ 1.0 Qr 0 0.7

255

0=u

3.0 B (T) 2.0

0.85

Radius septum location

Energy (MeV)

0.75 0.8 Radius (m)

kick at Qr=1

250

fi

No

245

242.5

These orbits do not exist (extracted)

ith W

247.5

240 79.5 extracted beam

p um

252.5

b eld

mp bu d l fie

Septum

Consecutive turns 80

80.5

81

81.5

82

82.5

Radius (cm)

FIGURE 3.15 To obtain a large-turn separation, one uses the precession of the orbits, after exciting the Qr = 1 resonance at the radius where the field index n = 0. The precession is caused by a phase advance of the betatron oscillation due to Qr < 1 beyond the resonance. To illustrate the precession, orbits also are drawn, which do not exist when the beam is extracted. Along the radial direction the precession shifts consecutive turns to smaller radii, followed by a jump to a large radius. This is the optimal location for a septum to split off the extracted beam.

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be achieved when a precession of the orbits is used, which becomes effective a few turns later. Because of the decreasing magnetic field beyond the maximum, Qr starts to decrease. For Qr < 1 the phase of the betatron resonance starts to shift to a larger azimuth, and an orbit precession is starting, as illustrated in Figure 3.15. When looking along one radial line, one then observes that the orbit with next higher energy is at smaller radius than the previous one. However, when continuing the precession with a few turns, this will be followed by a sudden increase of the distance between two sequential orbits, as demonstrated in Figure 3.15. This is an optimal location for a septum that splits the extracted beam off. The resonance is excited by kicking the beam with a magnetic bump, created with little coils or with iron trim rods. The orbit separation is further increased by a high-energy gain per turn and by a using a small horizontal beam emittance already at the beginning of the acceleration. A high-energy gain per turn is accomplished by high Dee voltages and many Dees and by limiting the phase slip due to loss of isochronicity after crossing the field maximum. A small horizontal emittance can be achieved by cutting the beam sufficiently with slits and collimators in the central region (low energy: low power loss and low or no activation). Application of this resonant extraction method in the PSI cyclotron (Varian) has resulted in a routinely obtained extraction efficiency of 80%. In the IBA and SHI cyclotrons another approach, self-extraction, is pursued (10). In these cyclotrons the acceleration continues to a maximum possible radius, and the field is kept isochronous by using a elliptical pole gap (visible in Figure 3.3). This gap is very narrow at the pole edge, so that the field drops to zero in a very short radial distance (see Figure 3.5). With this technique one strives to guide the beam out of the main field and through the fringe field very quickly. A groove in one hill is made near the extraction radius, to get the extraction at a well-specified azimuthal angle. The beam is deflected further by means of a septum and extraction cathode. To limit the beam size, also in these cyclotrons several (de)focusing elements are following a septum.

3.4  Synchrotrons The first hospital-based proton therapy facility at Loma Linda Medical Center (California) was equipped with a synchrotron built by Fermilab (37) (Figure 3.16) and started operation in 1992 (8). Equipment based on the design used at Loma Linda has become commercially available from Optivus Proton Therapy (San Bernadino, CA) (38). The proton synchrotron designed by Hitachi (13) (see Figure 3.16) is in use at centers in Tsukuba and Fukui in Japan and also at MD-Anderson Cancer Center

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Proton Accelerators

BM1

RF cavity

ST

BMPi

SX

QD

BM

ST

QF

SM

Beam from injector BM

j in

ec

ti

on

ST

QF 7m

Deflector for extraction

BMPi RF acceleration stage

QD

QD RFC QF

Ex tra

ct

BM

ed

be

am

QD Septum Magnet for extraction

ST QF

R1.4 m

BM RF Kicker

SX

Extraction

QD

BM

FIGURE 3.16 Left: the synchrotron used at Loma Linda with the 2-MeV injector mounted on top of the synchrotron ring. (Adapted from Coutrakon, G., PTCOG 47, 2008, and PTCOG 49, 2010.) Right: The synchrotron of Hitachi (injector not shown). (Adapted from Hiramoto, K., et al., Nucl. Instr. Methods B, 261, 786–790, 2007, and http://www.tassauusa.org.)

in Houston, Texas, and one by Mitsubishi in Shizuoka, Fukushima, and Kagoshima, Japan (39). All machines provide protons between 70 and 250 MeV. For proton therapy synchrotrons and cyclotrons are quite competitive, but for heavy-ion therapy synchrotrons are currently the only machines in operation. Recognized advantages of a synchrotron are that the protons are accelerated until the desired energy, that almost no radioactivity is created due to beam losses (40), and that low-energy protons have the same intensity as high-energy protons (no transmission loss in a degrader [41]). The space required for a proton synchrotron is larger than for a cyclotron: the synchrotron itself has a diameter of 6–8 m, and the injection system consisting of an ion source, one or two linear accelerators in series (radio frequency quadrupole [RFQ] and drift tube linac [DTL]), and a beam transport system has a length of 6–10 m. At the Loma Linda facility, a relatively small footprint has been achieved by mounting the injector on top of the synchrotron. A synchrotron (+ injection) consists of many small components that can be built in series and that gives relatively easy access to the machine parts. 3.4.1  Operation The acceleration process in a synchrotron is in cycles (spills), each consisting of the following: • Filling of the ring with a bunch of 2 × 1010 protons of 2 MeV (Loma Linda) or 1011 protons of 7 MeV (Hitachi, Mitsubishi) • Acceleration until the desired energy between 70 and 250 MeV

84

Beam energy

Proton Therapy Physics

Slow extraction < 0.5 sec 0.5 – 5 sec. Deceleration Acceleration Injection Time

FIGURE 3.17 A typical spill from a synchrotron. The machine is filled with protons of 2 or 7 MeV; the protons are accelerated to the desired energy and slowly extracted. The unused remaining protons are decelerated and dumped.

• Slow extraction of the protons into the beam line • Ramping down to the initial situation, eventually with deceleration and dumping unused protons at low energy This sequence (shown in Figure 3.17) takes too long to be useful for energy modulation. The energy selected to be extracted is chosen for each gantry angle used in a treatment and is equal to the maximum energy used at that angle. Modulation is then done in the nozzle by means of a modulator wheel or ridge filters. A synchrotron itself consists mainly of a lattice with bending magnets and focusing elements. Quadrupole magnets are used to focus the beam, and sextupole magnets are used to increase the acceptance of beam energy spread. In some synchrotrons, the bending magnets are shaped such that the focusing properties are added to the bending field. By applying strong focusing schemes (field index n >> 1) small beam diameters can be achieved. The periodicity of the lattice imposes also a periodic shape of the beam envelope. However, in the design care must be taken that the period of the betatron oscillation of individual protons does not coincide with a characteristic dimension of the machine, such as the circumference. The huge number (~109) of revolutions a proton makes in the ring yields an extreme sensitivity to small errors in magnet alignment, magnetic fields, or power supply ripples, which easily induces a periodic distortion. In the design phase the focusing lattice (quadrupole strengths) is designed such that the working points (the tunes) are far away from a betatron resonance condition (Equation 3.9); otherwise this will unavoidably lead to beam loss. 3.4.2  Ion Source and Injector For the proton ion sources there is a wide choice of commercially available types, typically based on ionization by microwaves and a special configuration of coils or a permanent magnet to confine the electrons

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Proton Accelerators

Electrodes

~VRF

Acceleration gaps

FIGURE 3.18 Typical RFQ and DTL linac configurations, for a preaccelerator to inject the beam into the synchrotron.

(33, 42). The source is usually set at a positive potential, to preaccelerate the protons toward an RFQ, acting as first linear accelerator. An RFQ consists of four rods, parallel to the beam direction. Each rod is shaped with a wave-like structure along its length, as shown in Figure 3.18. The rods are mounted in a resonant cavity such that the pairs of opposing rods have a 180° phase shift of the RF voltage with respect to the orthogonal pair. The component of the electric field along the beam direction provides the acceleration, and the radial components provide focusing. Acceleration up to 2–3 MeV is achieved, and subsequently the protons can be accelerated to 7 MeV in a DTL (see Figure 3.18). Also the operation of a DTL is based on electromagnetic oscillations in tuned structures. The structures support a traveling wave of alternating voltages on cylindrical electrodes between which the protons are accelerated. The electrode lengths increase along the tube, in accordance with the velocity of the accelerated particles. Injection in the ring must be done at the correct phase with respect to the RF of the ring. One can inject all particles at once (single turn injection) or gradually add particles to the circulating beam. Because the injection system should not touch the already circulating beam, the new protons are added next to the protons that are already in the ring. The emittance of the circulating beam therefore increases, until the acceptance of the ring is filled. To reduce treatment time it is important to fill the ring with as many protons as possible. This gives possibilities to lengthen the extraction phase and to reduce dead time between spills (43). The maximum intensity in the machine is limited by space charge or coulomb repulsion forces. The higher the injection energy, the lower these defocusing space charge forces and thus the higher the amount of protons that can be stored in the ring. For single-turn injection, intensity may also be limited by the maximum beam current from the injector to fill the ring in one turn. The maximum intensity can be increased by allowing more circulating bunches at the same moment in the ring and by modifying the time structure of the RF

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Proton Therapy Physics

voltage across the acceleration gap, to spread the bunch in the longitudinal direction (12). 3.4.3  Acceleration and RF The acceleration phase usually lasts approximately 0.5 s and thus takes place over many turns (~106). The energy of the circulating particle bunch is increased in an RF cavity located in the ring. The increasing proton momentum p needs a synchronous increase of the magnet strengths in the ring, because the protons must remain in an orbit with a constant average radius. Following Equation 3.1 this yields p = r = const. Bq



(3.10)

The increase of the magnetic field drives the frequency of the RF voltage: the frequency must remain synchronous to the increasing revolution frequency (~1–8 MHz) and increases (nonlinearly) in time: f ( p) =



p 1 . 2 πr m0 γ( p)

(3.11)

Therefore the RF cavities are nonresonant (quality factor Q < 1) wide-band structures and of moderate power (12). A widely used type of cavity is the induction cell, such as the one developed by Hitachi (44), as shown in Figure 3.19. An induction cavity consists of ferrite rings (magnetic cores) that surround the beam pipe. Around each core a coil has been wound, to induce a accelerating gap magnetic core (FINEMET) RF current inner conductor outer conductor multifeed coupling

RF power source ( solid-state amp.)

FIGURE 3.19 The RF acceleration device used in a synchrotron consists of an induction cavity, filled with magnetic cores. The cores drive an RF current (dashed line) which causes an RF voltage across the acceleration gap in the center of the cavity. (Adapted from Saito, K., et al., Nucl. Instr. Methods A., 402, 1–13, 1998.)

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magnetic field in the ring. The electric current through the coil is driven with the RF frequency and induces an RF magnetic field in the ferrite ring. On its turn, this varying field induces an electric current in the beam pipe, which acts as the inner conductor. An outer conductor surrounding the cores is closing the loop for this driven current. However, in the center of the device the inner conductor is interrupted. Across the gap an RF voltage of a few hundred volts is built up by the RF current, so that protons that cross the gap at the correct RF phase will be accelerated. This moderate RF voltage is sufficient, because the protons pass the gap many times during the acceleration phase. The applied frequency and voltage need to be controlled as a function of the magnetic field in the ring magnets, as given in Equation 3.11. The system is much simpler than the high-power, narrow bandwidth systems used for cyclotrons. The RF power can be generated with reliable solid-state amplifiers. 3.4.4  Extraction Instead of fast extraction in a single turn, a slow extraction scheme is necessary for accurate dose application at which the beam is spread over the tumor with scanning techniques or with additional range modulation. The time during which protons are extracted varies between 0.5 and 5 s, depending on the amount needed at the extracted energy. The extracted beam intensity can be regulated and is constant on average, but at several kilohertz, a ripple or noise of up to 50% is present. This ripple depends on the extraction method and is caused by the extreme sensitivity of the beam orbit to small misalignments and to ripples in power supplies. Several methods to extract the beam are currently applied (see Figure 3.20). Resonant extraction–based schemes, in which the machine tune is slowly shifted toward a resonance (e.g., Qr = 1/2 or 1/3), in effect narrow the stable phase space of the beam, because resonance bands are approached by the set tune. Particles with a large oscillation amplitude will then slide into the unstable region of the phase space, so that their oscillation amplitude will grow until they pass the extraction septum at the external side. The shift of the beam tune is performed by changing the fields of specific quadrupoles and/or sextupoles in the ring (37). However, while getting the phase space of the circulating beam more and more empty, the quadrupoles need to shift the tune closer and closer to the resonance to catch the protons with the smallest amplitudes as well. A disadvantageous consequence of this method is that the position and/or size and/or energy of the extracted beam are varying at the entrance of the beam line during the extraction period. Alternatively one can give quasi-random sideward kicks to the beam with a dedicated RF kicker. The RF knock-out method increases the circulating beam emittance, and particles that are kicked out of the stability region are guided to the extraction septum. With this method the extracted beam position, size, and momentum remain constant during the spill (12). This method

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Proton Therapy Physics

Beam pipe

Stability limit beam

Normal tune; no extraction Near resonance: decreased stability region

Unstable orbits extracted

Resonant extraction RF kicker increases emittance

Unstable orbits extracted

RF Knock-out FIGURE 3.20 The betatron oscillation amplitude of the unperturbed beam tune (top) remains below the stability limit. In a resonant extraction method (middle) the tune is continuously shifted toward a resonance, which brings the stability limits tighter. The particles exceeding their amplitude outside the stability region will be extracted. In the resonant extraction scheme (bottom) the beam is kicked randomly, and the amplitude is increasing. Particles leaving the original stability region will be extracted.

also easily allows a fast on-off switching of the extracted beam intensity, which is conveniently used for gating on the respiration motion of the patient (45, 46). In both methods the extracted intensity is controlled by a feedback of a beam intensity monitor on the acting extraction elements. The horizontal emittance and momentum spread of a beam from a synchrotron is typically up to a factor 10 smaller than the emittance of a cyclotron beam. However, the emittance shows large asymmetries, which must be taken into account for preserving an angular independence of the beam characteristics when using rotating gantry systems. 3.4.5  Recent Developments in Therapy Synchrotrons Scale reduction is of interest for synchrotron systems. Balakin et al. (47) are building a small ring of 5 m in diameter for proton acceleration up to 330 MeV. The protons are injected by a 1-MeV linear accelerator. Similar studies of a

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Proton Accelerators

a)

Extraction beam energy Injection beam intensity

Beam energy

b)

0

4

8

12 Time[sec]

16

20

Energy changes of extracted beam during a spill

Time FIGURE 3.21 (a) Spill structure of a rapid cycling synchrotron. (Adapted from K. Hiramoto, Synchrotrons, educational session PTCOG 49, 2010.) After single turn beam injection and acceleration to the desired energy, the beam is used after a slow extraction; (b) energy variation during a spill. The  beam energy is decreased in small steps during the slow extraction process. (Adapted from Iwata, Y., et al., Proc. IPAC10, MOPEA008, 79–81, 2010.)

“table top” proton/carbon ion synchrotron are reported by Endo et al. (KEK, Tsukuba, Japan) (48). The relatively low cost of such accelerators is expected to be the major advantage of these small machines. Efforts toward a more rapid cycle of the synchrotron have been reported in the last few years. In a proposal for a rapid-cycling synchrotron (49), the beam is kicked out in a single turn extraction after single-turn beam injection and acceleration to the desired energy. This sequence is repeated at ~30 Hz. Single-turn extraction implies, however, that the amount of protons per pulse can be adjusted very accurately. A slow extraction combined with fast cycling has been demonstrated in the Hitachi synchrotron (43); see Figure 3.21a. A considerable decrease in the unused time between the spills can also be obtained when the ring is not completely ramped down, filled, and ramped up to the next energy. When there are sufficient protons in the ring, one could ramp down to the next energy, extract the necessary amount of protons, and repeat this until all protons have been used (50). First attempts (Figure 3.21b) to explore this method at the HIMAC synchrotron have been reported recently (50). Of course, use of this method implies sufficiently high initial beam intensities in the ring as well as very good control of the extracted beam intensity.

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3.5  Novel Accelerator Technologies All other acceleration principles that are being investigated by different groups are aiming at scale reduction, with an affordable single treatment room facility as goal. This would decrease the financial gap due to the scale difference between current photon therapy and the typical state of the art multiroom proton therapy centers. Although the costs per treatment room are not expected to be lower than for a facility with multiple rooms, the initial investment costs will of course be lower. Such facilities may be of advantage for certain regions, for example, a city with a population of a few million people, located relatively far away from other population centers. For extended regions with more homogeneously spread populations as in Europe, the large centers with multiple treatment rooms are expected to operate more economically. 3.5.1  FFAG Accelerators For several years, it has been investigated whether a fixed-field alternating gradient (FFAG) accelerator would be a suitable accelerator for proton therapy (51–57). In this concept, the AVF cyclotron described above is split up in separate sector magnets, with alternating signs of the magnetic fields, as schematically shown in Figure 3.22. The RF frequency is varying, similar to that in a synchrocyclotron. The beam optics in scaling FFAGs is designed such that the betatron frequencies of the orbits at all energies are equal, so that all orbits are scaled replicas of each other. In nonscaling FFAGs the tunes are allowed to vary, and even the periodicity of the magnet structure is decoupled from the beam motion. In fact this scheme resembles a (curved) linear accelerator with very strong alternating focusing and defocusing elements. Because of the very strong focusing properties, the nonscaling FFAGs are smaller than the scaling FFAGs. However, the magnet design and large gradients of opposing signs make the design process very complicated. Also, the cavity and RF generator are complicated: high electric fields are needed, but also a varying frequency.

a) focusing defoc defoc hig he ne low rg y en erg y

b)

defocusing foc foc hig h low

en

ene

erg

rgy

y

FIGURE 3.22 Schematic configuration and orbit structure of (a) a scaling FFAG and (b) a nonscaling FFAG.

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The major advantage of FFAGs is the very large acceptance in beam energy and emittance, which is useful in particle physics applications that need reacceleration of reaction products. A possible advantage of an FFAG in proton therapy may be its capacity to have much faster repetition rates than synchrotrons and synchrocyclotrons and thus achieve high-beam intensities. Also the optics and magnetic field setting may change from pulse to pulse, allowing fast energy changes between each pulse (53). On the other hand the scaling FFAGs are not small (radius 7–8 m) or light (150–200 tons). The nonscaling FFAGs are very complex to design, to build, and to operate and need very complex RF amplifiers. Both types of FFAGs need a ~10-MeV injection system, which can be a cyclotron or another FFAG (52). For proton therapy the most promising spin-off from FFAG technology is the use of the very strong gradients, alternating along a beam line. This FFAG-type of beam optics is proposed for a new type of gantry design (58). The large-momentum acceptance may prevent the need of changing magnetic field when changing beam energy. This could speed up the energy modulation considerably. 3.5.2  Linear Accelerators Linear accelerators are the most widely used accelerators in radiation therapy. Electrons are accelerated to typically 6-25 MeV and create Bremsstrahlung photons in a target or are used directly. However, compared to electrons, it is much more difficult to accelerate protons or heavy ions with linear accelerators. This is because electrons quickly reach relativistic velocities and can be assumed to have a constant speed, close to the speed of light. This allows long repetitive structures of equal dimensions, all working at the same phase shift with respect to each other. Protons of 250 MeV have only reached 61% of the speed of light, so here one must take the increase of speed into account within the whole accelerator structure. For this reason the low-energy part of a linear accelerator consists of stages with different types of accelerators, for example, such as those used in a synchrotron injector described above. For proton therapy an important issue of linear accelerators is the time structure of the beam. Many developments have occured to improve the time structure toward high frequency (3 GHz) and a repetition rate as high as possible (100–200 Hz) to allow for spot scanning. The RF power is generated by a series of klystrons, each driving a section of the linac. A linear accelerator made of sequentially operating acceleration stages offers the natural advantage to allow rapid (determined by repetition rate) and continuous energy variation of the accelerated beam. This can be accomplished by switching off the output RF power of a number of klystrons and by adjusting the power of the last active klystron. If a high enough repetition rate and sufficient accuracy of the dose per pulse can be achieved, a linac may then be suitable for rapid spot scanning.

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3.5.3  Linac-Based Systems for Proton Therapy To overcome the problems at low energies, the cyclinac concept has been developed (59). Here a cyclotron of 60 MeV (more recently 30 MeV) is used as an injector for a linear accelerator with side-coupled cavities (SCLs). The small 3-GHz structures allow the use of very strong electric fields. This reduces the number of acceleration cavities and thus the length of the accelerator. A prototype of the linac LIBO (Linac Booster) with a design value of the accelerating field of 15.7 MV/m has been made and tested successfully (60): a gradient of up to 27 MV/m was reached. In the final design this linac will consist of several tanks, each with a number of copper cavities made of basic units. These “half-cell plates” are built with very-high-accuracy machining. The RF in each tank is driven by a klystron. A possible layout of a clinical facility is shown in Figure 3.23. Recently a new cavity design to cover the energy range 15-66 MeV has been presented (61), which would allow a relatively cheap commercial cyclotron as injector. Higher gradients of the accelerating electric field and thus shorter structures are a natural line of development; however, there are limits to what can be achieved. The first limitation is given by the peak power that can be injected into a linac tank, and the second limitation is the maximum electric field on the surface of the cavity wall. In case of low velocities CCLs, this is four to five times larger than the average accelerating field. From many data on breakdown phenomena collected during the last 20 years, the limit of the acceleration field in 3-GHz CCLs seems to be just above 30 MV/m (62). Higher frequencies (e.g., 5.7 GHz) will also allow stronger acceleration fields, but at the cost of a reduced transversal acceptance. 3.5.4  Dielectric Wall Accelerator In induction cavities the achievable electric RF field across a vacuum gap seems to be limited to 10-20 MV/m. However, the longitudinal space taken Isotope production targets

m

oo tr en tm ea Tr

r rato cele c a ar Line Cyclotron (30 MeV)

s FIGURE 3.23 Layout of the cyclotron driven linac concept. A 30-MeV cyclotron is used for isotope production or injects protons into a linear accelerator of the LIBO type. (Adapted from Amaldi, U., et al., Nucl. Instr. Methods Phys. Res. A, 579, 924–936, 2007.)

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by the ferrite cores adds to the length of the accelerator and reduces the effectively obtainable average acceleration field to only a few megavolts per meter. In systems that have been developed to replace the ferrite core, an insulating ring is mounted around an acceleration gap. The ring is surrounded by a dielectric, which is sandwiched between two conducting sheets. One sheet has been put on a high voltage, and the other sheet is grounded. A sudden shorting of the high voltage to ground creates a traveling voltage wave in the dielectric, which leads to a strong longitudinal electric field at the inside of the insulating ring (63). This coreless induction accelerator is limited by the breakdown field strengths in the dielectric and along the insulator surface. Along the surface of the insulator a spark typically develops by electrons that repeatedly bombard the surface, thus creating an electron avalanche. To obtain a very strong accelerating field, one can prevent the development of a spark by shortening the time that the field is present. For conventional insulators shortening the high-voltage pulse from 1000 to 1 ns yields an increase of the surface breakdown field from 5 to 20 MV/m. During the last decade new castable dielectrics have been developed as well as a new insulator configuration. This is made of a stack of floating conductors sandwiched between sheets of insulators. With this high-gradient insulator (HGI) an increase of a factor 5 in the surface breakdown field strength has been demonstrated (64). A dielectric wall accelerator (DWA) can be constructed by stacking rings of HGI material, and at frequent intervals along the stack a conducting sheet is inserted and connected to a high-voltage switching circuit (Blumleins). These switches are normally open. When these laser-driven switches are closed, an electric field is produced at the inside of the HGI ring. By successive closing of the switches along the stack, the region of strong electric field is shifted along the stack, and protons traveling in phase with this wave will be accelerated. An average accelerating field of more than 100 MV/m can be possible for 3-ns pulses, as has been demonstrated on small HGI samples (65). This would allow an accelerator design of about 2-m length for 200-MeV protons, as shown in Figure 3.24. This concept has been further developed in the design of a single-room treatment facility, to be put on the market HGI rings

scanning system

2 ns pulses with 100 mA protons at 10 Hz

~5000 electrodes, each with 2 HV switches (25 kV) FIGURE 3.24 The DWA consists of a stack of special insulators, between which a traveling electric field of 100 MV/m is traveling. Protons are accelerated and aimed at a voxel in the target. (Adapted from Caporaso et al., Nucl. Instr. Methods B, 261, 777, 2007; Caporaso et al., Proc. PAC 2009 TH3GAI02; TomoTherapy. Website: http://www.tomotherapy.com/news/view/20070614_tomo_proton/.)

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by the company TomoTherapy (66). The system is pulsed with a repetition frequency of several tens of hertz. Energy variation per pulse can be achieved by setting only the appropriate amount of switches. An interesting feature may be the possibility to impose a variation of the accelerating field of a few percent. This may offer a potential for energy spread and transverse spreading of the beam, which can be of interest for eye treatments (≤70 MeV). The key components for a DWA are operating at the limit of current technology: high-gradient vacuum insulators, high bulk breakdown strength dielectrics for pulse-forming circuits, and switches that operate at high voltage. To cope with distortions inherent to the use of Blumleins, other accelerating architectures that surround the HGI (induction concentrator) are also being studied (65). In this challenging project there are still some obstacles to overcome, and the system is not expected to be simple or very small in size due to insulation, cooling requirements (67), and the distance needed behind a scanning system. At this moment the achieved repetition rate of several tens of Hertz is too slow for scanning. A very important aspect for proton therapy with respect to the ion source is the safe and accurate control of the very high amount of protons per pulse, which is still part of the developments of the proton source (68). 3.5.5  Laser-Driven Accelerators The approach of using a laser to generate energetic proton beams for proton therapy can be of interest, because the laser and light transmission components can be installed in normal rooms, without the need of heavy concrete shielding. Further, one might save a lot of weight when the easily transportable light beam is coupled on a rotatable gantry, because magnets are not needed anymore. Also scanning the light beam would in principle provide opportunities for pencil beam scanning. A concept of these ideas is illustrated in Figure 3.25 (69). The acceleration of particles by means of strong laser pulses is developing in a young and vastly changing field (70). At the moment most experience has been obtained with the target normal sheet acceleration (TNSA) method (71). As shown in Figure 3.26, a high-intensity laser irradiates the front side of a solid target, which may be saturated with hydrogen when protons are to be accelerated. At the front surface, a plasma is created due to the energy absorption in the foil. The electrons in this plasma are heated to high energies and penetrate through the target and emerge from the rear surface. This induces strong electrostatic fields, which pull ions and the protons out of the target at its rear surface. The highest proton energies observed in this method are about 20 MeV (72). This has been achieved with a laser power intensity of 6 × 1019 W/cm2 and a pulse length of 320 fs. Currently, much work is being done to model

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Mirror b

e

d

ng L i g h fro t g u m id las e er

c

f

protons

a

mi

Laser target emitting protons and energy filter

co

y x Couch

FIGURE 3.25 The concept of a treatment facility using protons that are generated by a laser. (Adapted from Ma, C.M., et al., Laser Phys. 16, 639–646, 2006.)

the interaction of the laser with the target and to make predictions for other target geometries and materials (see the curve in Figure 3.27) (72). The observed agreement between experimental data and scaling laws derived from fluid models and numerical simulations have yielded an accurate description of the acceleration of proton beams for a large range of laser and target parameters (73). Extrapolation of this model to calculate the optimum target and laser beam parameters for delivering a 200-MeV beam from different ­thicknesses of targets indicate that the needed laser power is as high as 1022 W/cm2. Apart from the quest to obtain higher proton energies, the obtained energy spectrum is also of concern. The observed energy spectra (Figure 3.28) show a broad continuum (74) that is not suitable for proton therapy. Although some filter and energy compression techniques are proposed (69), one must be aware of neutron production when simple filtering techniques are used just before the patient. Thin foil, doped with hydrogen –+ Laser light –+ –– +

+ – Laser light ++ – pushes –– +++ – electrons out + ––– ++ – – + + + –– ++ – Electric field from electrons accelerates protons out of foil

FIGURE 3.26 An intensive laser accelerates electrons from a proton-enriched area (polymer) at the far side of a titanium foil. This creates a strong electric field that accelerates protons out of the surface. (Adapted from Schwoerer, H., et al., Nat. [Lond.] 439, 445–448, 2006.)

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Maximum proton energy (MeV)

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25

0

Laser energy (J) 4 8

12

20 15 10

Model derived from scaling laws, fitted to the data

5 0

0

2×1019 4×1019 6×1019 Laser intensity (W cm–2)

FIGURE 3.27 The measured and modeled proton intensities as a function of laser power. (Adapted from Fuchs, J., et al., Nat. Phys. 2, 48–54, 2006.)

Nr of protons per pulse

Even though the field is developing very fast (75), it is expected that it will  still take many years to develop a laser-driven medical facility for ­proton/ion therapy (76). First of all one currently relies on a huge extrapolation from the values on which the current models are based to power densities above 1022 W/cm2. No experimental results have yet been obtained for this regime. The physical systems are highly complex and suffer from instabilities and uncertainties. To date it is by no means certain that placing such a higher-power pulse on the target will lead to the desired energy of protons at the required intensity (77). Second, the obtained proton beam intensities are still far too low, for example, 109 protons per pulse in a broad energy spectrum (72) or 108 protons per pulse with a peak energy still well below 10 MeV (78). Even neglecting losses due to energy selection and collimation of the proton beam, this would require an increase of the repetition rate to 10–100 Hz, which is currently at the limit of the advertised new generation lasers. 109 108 107 106 105 104

0

2 4 6 8 Proton energy (MeV)

10

FIGURE 3.28 Measured proton energy spectrum, obtained with a peak laser power of 6 × 1019 W/cm 2, focused at a thin aluminum foil. (Adapted from Malka, V., et al., Med. Phys. 31, 1587–1592, 2004.)

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An alternative method uses radiation pressure acceleration (RPA), sometimes referred to as the laser piston regime (79). Here the light pressure of a laser pulse incident on a foil, with thickness less than 100 nm, accelerates the whole foil as a plasma slab. Simulations predict that the RPA method can provide higher proton energies and less energy spread than TNSA. However, the RPA method faces even more technological challenges.

3.6  Concluding Remarks The AVF isochronous cyclotron and the synchrotron will remain the workhorses in proton therapy for the coming decade. These machines are still being improved, and a huge amount of experience and expertise has been built up to operate these machines safely and reliably. The systems have been discussed at conferences and in expert review panels and have undergone certification processes at various authorities. This process has taken about two decades, hereby even not taking into account the valuable work done by the pioneers in the laboratories in the decades before. New developments such as those discussed in this chapter are to be encouraged and are essential to make proton therapy as accessible for patients as photon therapy. However, a few words of caution should be addressed here. Providing a source of protons of therapeutically interesting energy is not sufficient for operating a patient treatment facility. The beam characteristics at the patient (energy, energy spread, beam size and emittance, intensity, time structure, reproducibility, low-neutron background) are of major importance and the safety requirements to prevent a wrong dose or dose at a wrong location in the patient should not be underestimated. Safety actions typically lead to switching the beam off. However, the availability of the beam is as important in a running treatment program. This is not only for the convenience of the patient and to obtain good accuracy, but also to prevent errors due to neglecting or bypassing frequently occurring system warnings. Therefore, before a claim is made that a new technology will soon outdate the currently used systems, it first needs to be proven that the new technology can at least provide the same quality of the treatment as used today. Next one should realize that the claimed advantage very often goes at the cost of compromising other parameters. Here the consequences of “cheap” protons providing inadequate treatments should not be underestimated: apart from the consequences for the patients themselves, suboptimal treatment results will have a catastrophic impact on proton therapy in general when the treatment outcomes are not significantly better than those of photon treatments. This will endanger the operation of centers in which good, high-quality treatments are being given.

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Also the reliability of the new technology should be evaluated critically. Does this new technique allow patient treatments at least 14 hours a day, 5–6 days a week, without major interruptions? Furthermore, in relation to implementation into clinical practice, an honest and fair estimate should be given of the time it will take to have the new technology available, mature, and safely and routinely useable in a clinical environment. To make a claim, as some vendors do, that a first system release to customers is planned for 2–3 years after announcing the successful first proof of principle, is simply misleading and usually much more optimistic than realistic estimates of the developers themselves.

Acknowledgments I thank my colleagues from the Division of Large Scale Research Facilities and the Center of Proton Therapy at the Paul Scherrer Institut for sharing their valuable and long years’ experience with me. Knowing how an accelerator works in principle is one thing, but the organization and detailed knowledge needed to develop, use, and maintain a reliable and safe treatment facility is another thing. Especially I thank Christian Baumgarten, Markus Schneider, and Rudolf Dölling for reading and commenting on the manuscript. Also I acknowledge the numerous discussions and interesting details I have learned from my colleagues at proton therapy centers and the international community of accelerator physicists during conferences, site visits, and personal discussions.

References

1. Pirruccello MC, Tobias CA, eds. Biological and Medical Research with Accelerated Heavy Ions at the Bevalac, 1977–1980, Lawrence Berkeley Laboratory, LBL-11220, 1980; 423. 2. Chu WT, Ludewigt BA, Renner TR. Instrumentation for treatment of cancer using proton and light-ion beams, Rev. Sci. Instr. 1993; 64:2055–2122. 3. Wilson R. A Brief History of the Harvard University Cyclotrons, Cambridge, MA: Harvard University Press, 2004. 4. Von Essen C, Blattman H, Dodendoerfer GG, et al. The piotron: Methods and initial results of dynamic pion therapy in phase II studies, Int. J. Rad. Onc. Biol. Phys.1985; 11:217–226. 5. Egger E, Schalenbourg A, Zografos L, et al. Maximizing local tumor control and survival after proton beam radiotherapy of uveal melanoma, Int. J. Radiat. Oncol. Biol. Phys. 2001; 51:138–147.

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6. Pedroni E, et al. The 200 MeV proton therapy project at the Paul Scherrer Institute: Conceptual design and practical realisation, Med. Phys. 1995; 22(1):37–53. 7. Larsson B. Application of a 185 MeV proton beam to experimental cancer therapy and neurosurgery: A biophysical study, Ph.D. Thesis, University of Uppsala, 1962. 8. Slater JM, Archambeau JO, Miller DW, et al. The proton treatment center at Loma Linda University Medical Center: Rationale for and description of its development. Int. J. Radiat. Oncol. Biol. Phys. 1992; 22:383–389S. 9. Humphries S. Principles of Charged Particle Acceleration, John Wiley and Sons (ISBN 0-471-87878-2, QC787.P3H86), 1986 http://www.fieldp.com/cpa.html. 10. Proceedings of the Cern Accelerator Schools CAS, Zeegse (2005). http://cas .web.cern.ch/cas/Holland/Zeegse-lectures.htm. 11. Schippers JM. Beam delivery systems for particle radiation therapy: Current status and recent developments, Rev. Acc. Sci. Technol. 2009; II:179–200. 12. Haberer T, et al., Magnetic scanning system for heavy ion therapy, Nucl. Instr. Methods A. 1993; 330:296–305. 13. Hiramoto K, et al. The synchrotron and its related technology for ion beam therapy, Nucl. Instr. Methods 2007; B261:786–790. 14. Yamada S, et al. HIMAC and medical accelerator projects in Japan, Asian Particle Accelerator Conference 1998, KEK Proceedings 98–10. 15. Tsunashima Y, et al. Efficiency of respiratory-gated delivery of synchrotronbased pulsed proton irradiation, Phys. Med. Biol. 2008; 53:1947–1959. 16. Phillips MH, et al. Effects of respiratory motion on dose uniformity with a charged particle scanning method, Phys. Med. Biol. 1992; 37:223–233. 17. Pedroni E, et al. The PSI Gantry 2: A second generation proton scanning gantry, Z. Med. Phys. 2004; 14:25–34. 18. Saito N, et al. Speed and accuracy of a beam tracking system for treatment of moving targets with scanned ion beams, Phys. Med. Biol. 2009; 54:4849–4862. 19. IBA website: http://www.iba-protontherapy.com/. 20. Sumitomo Heavy Industries Ltd. Website: http://www.shi.co.jp/quantum/ eng/product/proton/proton.html. 21. Schillo M, et al. Compact superconducting 250 MeV proton cyclotron for the PSI proton therapy project, Proc. 16th Int. Conf. Cycl. Appl., 2001; 37–39. 22. Schippers JM, et al. First year of operation of PSI’s new SC cyclotron and beam lines for proton therapy, Proc. 18th Int. Conf. Cyclotrons and Appl., Catania, Italy, 1–5 October 2007, Rifuggiato D, Piazza LA. INFN-LNS Catania, Italy 2008; 15–17. 23. Getta M, et al. Modular High Power Solid State RF Amplifiers for Particle Accelerators, Proceedings of PAC09, Vancouver (2009), TU5PFP081. 24. Geisler A, et al. Status Report of the ACCEL 250 MeV Medical Cyclotron, Proceedings of 17th Int. Conf. on Cyclotrons and their Applications, Tokyo (2004) 18A3. 25. Jongen Y, et al. Progress report on the IBA-SHI small cyclotron for cancer therapy, Nucl. Instr. Methods 1993; B79:885–889. 26. Still River Systems. Website: http://www.stillriversystems.com/. 27. Graffman S, et al. Proton radiotherapy with the Uppsala cyclotron. Experience and plans, Strahlentherapie 1985; 161:764–770. 28. Karamysheva GA, Kostromin SA. Simulation of beam extraction from C235 cyclotron for proton therapy, Phys. Part. Nucl. Lett. 2009; 6:84–90.

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29. Baumgarten C, et al. Isochronism of the ACCEL 250 MeV medical proton cyclotron, Nucl. Instr. Methods Phys. Res. A. 2007; 570:10–14. 30. Schippers JM, et al. Beam-dynamics studies in a 250 MeV superconducting cyclotron with a particle tracking program, Nukleonika. 2003; 48:S145–47. 31. Schippers JM, et al. Results of 3D dynamic studies in distorted fields of a 250 MeV superconducting cyclotron, Proc. of 17th Int. Conf. Cyclotrons and Appl., Tokyo, 2004 Oct, 435. 32. Wolf B, ed. Handbook of Ion Sources, Boca Raton, FL: CRC Press, 1995, ISBN 0-8493-2502-1. 33. Brown IG, ed. The Physics and Technology of Ion Sources, Wiley-VHC, Freiburg, 2004, ISBN 3-527-40410-4. 34. Forringer E, et al. A cold cathode ion source, Proc. 16th Int. Conf. Cycl. Appl., 2001, 277–279. 35. Schippers JM, et al. Beam intensity stability of a 250 MeV SC Cyclotron equipped with an internal cold-cathode ion source, Proc. 18th Int. Conf. Cyclotrons and Appl., Catania, Italy, 2007, ed. D. Rifuggiato , L.A.c. Piazza, INFN-LNS Catania, Italy, 2008; 300–302. 36. Schippers JM, et al. Activation of a 250 MeV SC-Cyclotron for Proton Therapy, Proc. Cyclotrons 2010, 19th Int. Conf. Cyclotrons and Appl., 2010 6–10 Sept, Lanzhou, China. 37. Coutrakon G. Synchrotrons for proton therapy, PTCOG 47, 2008, and educational session PTCOG 49, 2010. 38. Website of Optivus: http://www.optivus.com/index.html. 39. Mitsubishi. Website: http://global.mitsubishielectric.com/bu/particlebeam/ index.html. 40. Moyers MF, Lesyna DA. Exposure from residual radiation after synchrotron shutdown, Radiat. Measure. 2009; 44:176–181. 41. van Goethem MJ. et al. Geant4 simulations of proton beam transport through a carbon or beryllium degrader and following beam line, Phys. Med. Biol. 2009; 54:5831–5846. 42. Hara S, et al. Development of a permanent magnet microwave ion source for medical accelerators, Proc. EPAC 2006; 1723. 43. Hiramoto K. Synchrotrons, educational session PTCOG 49, 2010. 44. Saito K, et al. FINEMET-core loaded untuned RF cavity, Nucl. Instr. Methods A. 1998; 402:1–13. 45. Yamada S, et al. HIMAC and medical accelerator projects in Japan, Asian Particle Accelerator Conference 1998, KEK Proceedings 98–10. 46. Tsunashima Y, et al. Efficiency of respiratory-gated delivery of synchrotronbased pulsed proton irradiation, Phys. Med. Biol. 2008; 53:1947–1959. 47. Balakin VE, et al. TRAPP-Facility for Proton Therapy of Cancer, abstract in Proc. EPAC 1988, 1505. 48. Endo K, et al. Compact Proton and Carbon Ion Synchrotrons for Radiation Therapy, Proc. EPAC 2002; 2733–2735. 49. Peggs S, et al. The Rapid Cycling Medical Synchrotron, RCMS, Proc. EPAC 2002; 2754–2756. 50. Iwata Y, et al. Multiple-energy Operation with Quasi-DC Extension of Flattops at HIMAC, Proc. IPAC10, MOPEA008, 2010; 79–81. 51. Symon KR, et al. Fixed field alternating gradient particle accelerators, Phys. Rev. 1956; 103:1837–1859.

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52. Keil E, et al. Field Alternating Gradient Accelerators (FFAG) for Fast Hadron Cancer E, Therapy, PAC 2005, Proceedings Knoxville, Tennessee, 1667–1669. 53. Antoine S, et al. Principle design of a protontherapy, rapid-cycling, variable energy spiral FFAG , Nucl. Instr. Methods A. 2009; 602:293–305. 54. Blumenfeld I, et al. Energy doubling of 42 GeV electrons in a metre-scale plasma wakefield accelerator, Nature 2007; 445:741–744. 55. Prior CR, ed. Theme Section: FFAG Accelerators, Beam Dynam. Newslett. 2007; 43:19. 56. Craddock MK, Symon KR. Cyclotrons and fixed-field alternating-­gradient accelerators, Rev. Acc. Sci. Technol., 2008; I:65–97. 57. Trbojevic D. FFAGs as accelerators and beam delivery devices for ion cancer therapy, Rev. Acc. Sci. Technol. 2009; II:229–251. 58. Trbojevic D, et al. Superconducting Non-Scaling FFAG Gantry for Carbon/ Proton Cancer Therapy, Proc. PAC07, 3199–3201. 59. Crandall K, Weiss M. Preliminary Design of a Compact Linac for TERA, TERA 94/34, ACC 20; 1994. 60. De Martinis C, et al. Beam Tests on a Proton Linac Booster for Hadrontherapy, Proc. EPAC 2002; 2727–2729. 61. Amaldi U, et al. CLUSTER: A high-frequency H-mode coupled cavity linac for low and medium energies, Nucl. Instr. Methods Phys. Res. A. 2007; 579:924–936. 62. Wuensch W. High Gradient Breakdown in Normal-Conducting RF Cavities, Proc. EPAC02, 2002; 134–138. 63. Pavlovski A, et al. A coreless induction accelerator, Sov. J. At. En. 1970; 28:549. 64. Caporaso GJ, et al. Compact accelerator concept for proton therapy, Nucl. Instr. Methods B. 777. 65. Caporaso GJ, et al. Status of the Dielectric Wall Accelerator, Proc. PAC 2009 TH3GAI02. 66. TomoTherapy. Website: http://www.tomotherapy.com/news/view/20070614_ tomo_proton/. 67. Caporaso GJ, et al. The dielectric wall accelerator, Rev. Acc. Sci. Technol, 2009; II:253–263. 68. Chen YJ, et al, Compact Proton Injector and First Accelerator System Test for Compact Proton Dielectric Wall Cancer Therapy Accelerator, Proc. PAC 2009, TU6PFP094. 69. Ma CM, et al. Development of a laser-driven proton accelerator for cancer therapy, Laser Phys. 2006; 16:639–646. 70. Tajima T, et al. Laser acceleration of ions for radiation therapy, Rev. Acc. Sci. Technol. 2009; II:201–228. 71. Wilks SC, et al. Energetic proton generation in ultra-intense laser—solid interactions, Phys. Plasmas. 2001; 8:542–549. 72. Fuchs J, et al. Laser-driven proton scaling laws and new paths towards energy increase, Nat. Phys. 2006; 2:48–54. 73. Zeil K, et al. The scaling of proton energies in ultrashort pulse laser plasma acceleration, New J. Phys. 2010; 12:045015. 74. MalkaV, et al. Practicability of protontherapy using compact laser systems, Med. Phys. 2004; 31:1587–1592. 75. Ledingham K. Desktop accelerators going up? Nat. Phys. 2006; 2:11–12.

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4 Characteristics of Clinical Proton Beams Hsiao-Ming Lu and Jacob Flanz CONTENTS 4.1 Proton Dose Delivery................................................................................. 103 4.2 Beam Specifications.................................................................................... 105 4.2.1 Scattering Systems.......................................................................... 106 4.2.2 Pencil Beam Scanning.................................................................... 108 4.3 Beam Energy and Treatment Depths....................................................... 109 4.4 Field Size...................................................................................................... 110 4.5 Dose Rate..................................................................................................... 111 4.6 Lateral Penumbra........................................................................................ 113 4.7 Distal Penumbra......................................................................................... 117 4.8 Dose Uniformity......................................................................................... 118 4.9 Characteristics of Proton Therapy Treatment......................................... 119 Summary............................................................................................................... 122 References.............................................................................................................. 122

The characteristics of a proton beam are largely determined by the intrinsic physical properties of the protons, the accelerators generating the beam, and the devices used to control the beam. Different beam nozzle designs can affect the beam properties substantially. Before one can design nozzle-beam-shaping systems, such as those discussed in the next couple of chapters, we will explore here the basic beam properties from a clinical point of view and how the clinical requirement could be related to the design features and the operational settings of the delivery system. Although the majority of proton therapy treatments today are given by scattered beams, the use of scanning beams has now evolved outside of research facilities, so our discussions will consider both such systems.

4.1  Proton Dose Delivery Despite the distinguished properties as a physical particle, protons are used in therapy in more or less the same manner as photons used in conventional radiotherapy. Indeed, its relative biological effectiveness (RBE) does depend 103

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on the linear energy transfer (LET) and can become substantially large at the falling edge of the Bragg peak. However, as discussed in Chapter 19, the overall effect can be accounted for by a constant RBE value of 1.1 in most situations. As a result, one can essentially prescribe proton treatment with the same amount of cobalt equivalent dose for the same level of expected local control as in a conventional therapy treatment. Proton doses are prescribed in Gy(RBE) (1). The application of a constant RBE is often viewed as an advantage of protons over heavier particles with much more complicated radiological effects, given the rich and invaluable clinical experiences about local control and normal tissue toxicity obtained from conventional radiotherapy over many years and from many patients. For this reason, we will consider only the physical dose in the following discussions. In current practice of radiotherapy, treatment is usually prescribed to a volume of tissue in the patient, that is, the target volume. A number of volumes with different definitions are often used to guide the treatment planning and delivery processes. These include gross target volume (GTV), clinical target volume (CTV), and planning target volume (PTV). For a more detailed explanation of these volumes and their implications in the treatment process, see Chapter 10. The objective of the treatment is that every tissue element in the target volume should receive the same amount of dose, in order to achieve the same level of cell response based on relatively simple biological models. The patient may receive multiple courses of treatments and each course may have a different target volume prescribed to a different dose, but for each fraction the goal is to deliver a homogeneous dose distribution to the target volume of the treatment course. During proton treatment, at any one point in time the accelerator and the beam transport system can only transport to the patient a mono-energetic beam with a small cross section. The depth–dose distribution of such a ­pencil-like beam is the Bragg peak with a sharp peak in depth (introduced in Chapter 2). It has a Gaussian-shaped cross section and is highly variable. To obtain a homogenous depth–dose distribution over the target volume for the rationale discussed above, one must build a superposition of many Bragg peaks with the proper intensities and locations. As an example, Figure 4.1 shows the depth–dose distribution (solid line) in a homogeneous medium of such a superposition for the case in which a homogeneous distribution is achieved in a single field. It contains a number of Bragg peaks (dotted lines) in the same beam direction, but with different incident proton energies and thus different Bragg peak locations spread out in depth, therefore, the term spread-out Bragg peaks (SOBPs). The dose distribution in Figure 4.1 shows several features. First, it delivers a uniform dose distribution in depth across the target volume (darker grey area). Second, it preserves the sharp distal fall of the Bragg peak: therefore the ability of the proton beam to spare normal tissue behind the target volume (light grey area). On the proximal side of the target volume, the dose changes

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130 120 110 100 90 80 70 60 50 40 30 20 10 0

Target volume

0

2

4 6 8 10 12 Water equivalent path length (cm)

Normal tissue

14

FIGURE 4.1 A schematic view of SOBP construction, showing the SOBP depth–dose distribution (solid line) and the component Bragg peaks (dashed lines).

gradually (i.e., a soft knee). Third, the total entrance dose has increased from about 30% due to the deepest Bragg peak to nearly 80% due to the additional shallower peaks. These features are the main clinically relevant properties of the proton beam in the longitudinal direction. Two main categories of methods are used to produce superpositions of Bragg peaks for clinical use. They either use materials in the beam path to modify the beam energy, or to modify the energy coming from the accelerator, as described in detail in Chapters 5 and 6. In the following sections, we briefly describe the principles of these methods and the specification of the beams they produce.

4.2  Beam Specifications A number of parameters are needed to describe the physical properties of the proton beam. Historically, they are often defined in relation to the manner in which the beam is produced and characterized by measurements. The beam model for treatment planning also needs to be specified by a set of parameters. It is critical from the clinical point of view that these two sets of parameters be unified to avoid any potential confusion or misrepresentation. That is, the same set of parameters is used to describe the beam model in the treatment-planning system, to specify the desired beam production in the beam control system, and to specify the quality assurance measurements. For this reason, we will discuss here only those specifications currently adopted clinically. Readers interested in the historical evolution of the beam specifications for various purposes should see references provided herein.

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4.2.1  Scattering Systems In systems that use beam scattering to spread the beam, the small beam coming to the nozzle is scattered to a large area and the scatterers are specially designed so that the beam has a uniform penetration and uniform intensity across the scattered area specified for clinical use. At the same time, the energy of the beam is modulated to spread out the location of the Bragg peaks over the target volume in depth. The system is usually configured to produce a homogeneous dose distribution with the same penetration across the beam, as shown in Figure 4.1. For patient treatment, the beam is collimated by an aperture to match the target volume and a range compensator (usually a Lucite block with varying thicknesses) to “pull back” the most distant Bragg peaks to conform to the distal surface of the target volume (see Chapter 5). Figure 4.2 shows the parameters used to describe the SOBP dose distribution. The distribution is normalized to 100% at the dose plateau. The parameters are defined in terms of positions in depth at the given dose levels: d20, d80, and d90 at the distal end, with p90 and p98 on the proximal side. The distal margin of the SOBP is given by the distance between d20 and d80, corresponding to the 20% and 80% dose levels. This quantity has been termed distal dose falloff (DDF) (1). The dose at the surface entrance is also a useful parameter for characterizing the dosimetric property. The most clinically relevant parameters are the beam range and modulation width of the SOBP. The beam range is defined as the depth of penetration at 90%, that is, d90. Historically, the modulation width was defined as the width of the dose plateau at the 90% level, that is, the distance in depth from p90 to d90. In our institution, however, we recently changed our definition of modulation width to Mod98, as indicated in Figure 4.2, for the following advantages (2):



1. For SOBP distributions with large modulation width, the proximal “knee” becomes much softer. As a result, the p90 value becomes overly sensitive. A small difference in dose normalization, or measurement, for the same SOBP, could result in a large difference in p90. The p98 point, on the other hand, is at the steepest part of the knee and is therefore well-defined. 2. For cases where the target volume extends close to the patient body surface, the dose plateau of the SOBP must extend close to surface as well to provide full dose coverage. In that case, the p90 point would go outside of the body surface and becomes totally undefined, whereas the p98 is still valid. Mod98 clearly reflects better the extent of the high dose region required to cover the target volume.

Figure 4.3 shows the lateral dose distribution at the middle of the SOBP dose plateau produced by a scattering system with the beam range of 13 cm

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Characteristics of Clinical Proton Beams

p98

Dose (%)

100 90 80

Range Mod98 d90

p90

d80

Dose at entrance

50

Distal margin d20

20 0

0

2

4 6 8 10 12 Water equivalent path length (cm)

14

FIGURE 4.2 Specification of SOBP depth–dose distribution produced by scattering.

and a modulation width of 5 cm (m98). The field size is defined at the 50% level, as for a photon field. For the lateral penumbra, both 20%–80% and 50%–95% values are used for the specification. Although the former is used traditionally to reflect the general quality of the penumbra, the latter is particularly needed for determining the margins of aperture for a given treatment beam (see Chapter 10). The absolute dose delivered by the SOBP field is controlled by the monitor unit ion chamber located downstream from the scatterers and range modulators. The SOBP beam has a well-defined output factor, expressed as the dose measured at the dose plateau of the SOBP in centi-Gray per monitor unit reading (cGy/MU), as for the photon beam. The difference here is that the output factor depends on both the beam range and modulator width. For a given SOBP treatment field with a specific combination of range and

Field size

Dose (%)

100 95 80

50-95%

50 20 0 –3

20-80% –2

1 –1 0 Lateral position (cm)

FIGURE 4.3 Specification of lateral dose distribution produced by scattering.

2

3

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modulation width, the output factor must be first determined either by measurement or by modeling (3, 4). The required monitor unit for the treatment delivery can then be computed for the prescribed dose. The calibration of the monitor unit chamber follows the procedure described in IAEA Report 398 (5). Note that the dose calibration is usually based on the physics dose, whereas the prescription is given in Cobalt Gray equivalent (CGE). The proper conversion of 1.1 must be included in the monitor unit computation (Chapter 19). 4.2.2  Pencil Beam Scanning In pencil beam scanning, the pencil beam transported to the beam nozzle by the beam transport system is directly sent into the patient without interacting with any scattering or energy-modulation devices (Chapter 5). An orthogonal pair of magnetic dipoles is used to steer the thin beam to reach the full lateral extent of the target volume. The dose distribution is delivered by placing the Bragg peak in the patient one location at a time and then one layer at a time by varying the beam energy. Three main categories of dose delivery have been used: uniform scanning, single-field uniform dose (SFUD), and multifield uniform dose (MFUD). Uniform scanning uses a fixed scanning pattern with constant beam intensity for each layer. The relative intensities of the layers are fixed to produce a flat dose plateau longitudinally for a homogeneous medium. It also uses an aperture for beam collimation and a range compensator for distal conformity, just as for beams produced by scattering. However, the size of the spread-out beam is only slightly larger than the aperture size and can result in lower secondary radiation when compared to a non-optimized scattered beam field. The dose distributions produced by uniform scanning are largely the same as those by scattering, except that the maximum field size is no longer limited by the scattering system. Because of this, the beam is treated in the same manner as scattering in treatment planning, as well as in delivery. That is, the beam is specified by the range and modulation width for the overall dose distribution as those given in Figure 4.2, rather than the energy and intensity of each individual Bragg peak (6). For SFUD, both the scanning pattern and the beam intensity are customized for a treatment field, but the resultant dose distribution by each field is still uniform over the target volume. This is not required in MFUD, often termed as intensity-modulated proton therapy (IMPT), where the homogeneous dose distribution over the target volume is constructed only by the combination of two or more treatment fields (Chapter 10). For both SFUD and MFUD, the treatment planning system considers each pencil beam Bragg peak explicitly, rather than their combinations of any type as for uniform scanning or scattering. The concept of modulation width becomes irrelevant. The specification of a treatment beam is basically a list of Bragg peaks, each with the energy of the proton, the lateral location

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of the peak projected unto the isocenter plane, and the number of protons, often given in the unit of Giga-protons (109). In this case, the quality of the beam is determined largely by the quality of the individual pencil beam. The dose distribution of the pencil beam is essentially a Bragg peak longitudinally and a Gaussian transversely. The width of the peak reflects the energy spread of the protons, and the sigma of the Gaussian gives the spot size of the beam. Note the spot size is defined as the width of the Gaussian in air at the isocenter (Chapter 6).

4.3  Beam Energy and Treatment Depths In treatment by scattering, each beam is usually made to deliver a homogeneous dose distribution covering the entire target volume, except for the case of patching or matching (Chapter 10). That is, for a given beam direction, the deepest Bragg peak must reach the deepest point of the target volume with sufficient margins considering the various effects due to the distal penumbra and uncertainties in treatment planning and patient setup. In treatment by pencil beam scanning where the intensity and the energy of each pencil beam can be controlled individually, the homogenous dose coverage can be achieved by multiple beams from multiple directions. In that case, not all the beams have to reach the distal edges of the target volume. Ideally, the treatment beam should take the shortest paths to reach the tumor to minimize the volume of normal tissue on the beam path. However, the entrance dose of the proton beam is often substantial and it is necessary to spread it out over the normal tissue around the target volume by using multiple beam directions including those with long beam paths. Beam direction may also be restricted by the geometric position of the target volume in relation to the nearby critical organs. Prostate treatment is such an example where the rectum is situated right next to the prostate on the posterior side. Naturally, the best approach is from the anterior so that the sharp distal falloff of the proton beam can be used to cover the target volume while sparing the rectum behind. This would require, however, a precise control of the beam range in patient with millimeter accuracy, which is not currently possible. As a result, one can only use lateral fields with a substantially long beam path going through more than half of the patient’s body (7). At our facility, the beam is supplied by cyclotron at 230 MeV, with the beam range in water at about 34 cm. In scattering mode, the maximum treatment depth achievable is 29.3 cm (2). Although it is large enough for most patients, occasionally some deep-seated tumors (e.g., prostate or pancreas) in an exceptionally large patient could benefit from a longer range. The minimum range achievable in our scattering system is 4.6 cm. The need for a lower value could occur, for example, for pediatric patients, or for superficial

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target volumes such as postmastectomy chest wall. In these cases, one could shorten the range by increasing the minimum thickness of the compensator, although it could increase the distance between the patient and the aperture thereby degrading the lateral penumbra of the beam. In the pencil beam scanning mode at our facility, the maximum beam range is 32 cm whereas the minimum is 7 cm. Again the range shifter must be used for superficial target volumes. As mentioned earlier, range uncertainty in patient has been a challenging issue for proton therapy. Some techniques have shown promising results (Chapter 15) but have not been used widely in the clinic. As a result, most of treatments do not use the distal fall off for narrow margin sparing. The exception is the patching technique, where the distal end of the patch field meets the lateral penumbra of the through beam (Chapter 10). In that situation, a large range uncertainty can substantially distort the designed treatment dose distribution. Even in a homogenous medium, a millimeter change of the beam range could create hot or cold spots of 5%–10%. For this reason, the patching technique is used for shallower target volumes, mostly in head and neck area, requiring only short beam paths and thus relatively small range uncertainty in patient. Moreover, alternate patch points are used and rotated daily to even out the potential hot and cold spots. In any case, it is critical that the delivery system can maintain an accurate beam range.

4.4  Field Size The majority of cases treated by protons have relatively small target volumes, with a few exceptions including medulloblastoma and large sarcomas. As proton treatment facilities become more accessible, proton treatment will expand to more indications including late-stage diseases often with nodal involvement and thus much larger target volumes, or multiple targets. Although one can, in principle, design the system to provide always the largest field size possible, practical considerations must be included, such as nozzle size, gantry size, and dose rate. In scattering systems, large field size requires large and heavy apertures and compensators that are difficult to handle (Chapter 5). For pencil beam scanning, larger field size requires stronger or longer scanning magnets. The IBA (Ion Beam Application) scattering system used at our institution has a field size up to 25 cm in diameter, although the effective field width up to 2% dose heterogeneity is about 22 cm. The system has three sizes of snouts: 12, 18, and 25 cm in diameter. The smaller snout allows for lighter apertures and compensators, and most importantly closer patient contact leaving smaller air gaps and thus better lateral beam penumbra preservation. At our facility, the 12-cm snout is used for close to 70% of treatment fields, with

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18- and 25-cm snouts at about 15% each. Note that we currently limit prostate treatment to less than 10 per day. The usage of the small field size could be substantially larger at centers with significantly more prostate patients. At our facility, the field size for pencil beam scanning is a rectangle of 30 × 40 cm at the isocenter. The substantially larger field size is particularly useful for the treatment of medulloblastoma, one of the treatments that benefits the most from proton therapy. The target volume in this case is the entire CNS including the whole brain and the spinal cavity extending inferiorly nearly to the coccyx and could be as long as 80+ cm, particularly with young adult patients. With scattering, the treatment is often broken into four parts using five fields, two laterals for brain, and three abutting spinal fields each covering a portion of the spinal cavity. Feathering must be used to even out the hot and cold spots at the junction. With repeated setup verifications between different fields due to the isocenter move, the entire treatment could take 30–40 minutes. Any increase of field size allowing for a smaller number of fields will be substantially appreciated by both patient and staff.

4.5  Dose Rate An external beam radiotherapy system must be able to produce a high enough dose rate so that the treatment can be delivered in a reasonably short amount of time. This is not only in consideration of the efficiency in facility utilization. It is directly related to treatment quality. In most of the treatment procedures today, the patient is first set up by image guidance (e.g., two-dimensional radiography, cone-beam computed tomography, and portal imaging), and the treatment is then delivered using one or a few treatment fields, under the assumption that the patient does not change his/her body configuration from the time of the last imaging to the completion of the dose delivery. Although this assumption is more valid for certain types of treatment with appropriate patient immobilization devices than for others, it is clear that the longer the treatment takes, the more likely the patient will change the body configuration and affect the quality of the treatment. Typically, proton treatment setup used to take more time than photon treatment given the required accuracy for the treatment, as mentioned above; however with the advancement of image guidance in photon treatments, similar setup times can occur. It was found in a recent study that during prostate treatment, the target volume can stay within a 5-mm margin only for 5 min. If an endorectal balloon is used, the margin is reduced to 3 mm but still only for 5 min (S. Both, private communication). In this case, the lack of sufficiently high dose rate would require increasing the planning margins of the target volume and delivering more doses to normal tissues nearby. Patient fatigue is another

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consideration for reducing the treatment time, particularly for elderly or pediatric patients. However, this does not mean that one should use the highest dose rate possible. Instead, it should be low enough to give the operator a reasonable amount of time to stop the treatment in response to sudden patient movement or any unanticipated equipment problems. The majority of the therapy patients today are treated with a regular fractionation schedule with a daily dose of 1.8–2.0 Gy. The most commonly used dose rate for conformal photon treatment is 2–4 Gy/min. For intensity-­ modulated radiation therapy (IMRT) treatment, an even higher dose rate (e.g., 6 Gy/min) is often used because each segment of the multileaf collimator (MLC) pattern can irradiate only a small portion of the target volume. Note that even with such a high dose rate, the treatment may still take a long time because of the large number of segments in each field and the large number of field directions used. This is the main reason for the recent trend toward arc delivery together with intensity modulation, for example, RapidArc, volumetric-modulated arc therapy (VMAT), and tomotherapy. Proton treatment, on the other hand, does not usually require a large number of treatment fields for each treatment fraction because of its superiority in minimizing dose to normal tissues around the target volume. A large number of fields may be needed to satisfy the total dose constraints on the critical organs over the whole treatment course, but only a subset of these fields are sufficient to deliver the daily prescription with acceptable dose tolerance for the surrounding normal tissues. Most of treatment uses two fields a day, alternating between different field combinations. For regular fractionated treatment (i.e., 1.8–2.0 Gy per fraction), this means 0.9–1.0 Gy per field. Dose rates consistent with delivering a field in up to a few minutes are consistent with the targeting issues identified above and still much less than the overall setup time. A dose rate of 1.0–4.0 Gy/min will be reasonable, but the intensity required of the accelerator to achieve this dose rate is highly dependent on the target field size. Naturally, for hypofractionated treatment a much higher dose rate will be desirable. The extreme case is stereotactic radiosurgery treatment where each field could deliver up to 8 Gy. Another type of treatment where a higher dose rate may be appreciated is respiratory gating where the beam is turned on only for a portion of the respiration cycle, usually 30% centered on the end of respiration phase (8). Ideally, the dose rate should be three times more than normal if the usual amount time is to be used for the treatment. However, the dose rate should not be too high, given that the treatment is to be delivered over a sufficient number of respiratory cycles to average out the uncertainties due to breathing irregularities. The dose rate ultimately depends on the beam current transported to the nozzle entrance where it is to be scattered in scattering mode or to be guided into the patient directly in scanning mode. This largely depends on the capability of the accelerator and the energy selection system. For some cyclotrons, the beam current can be continuous and generally has a high operating

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current (e.g., 300 nA at the cyclotron exit). However, the fixed energy of the beam must be reduced by the energy selection system to the appropriate value before being sent to the patient and this could reduce the beam current significantly. As a result, the smaller is the beam range required, the lower the dose rate. For synchrotron-based accelerators, dose rate does not depend on the beam energy as much, given the absence of the energy selection system. However, the beam is not delivered continuously but in “spills,” and the overall peak beam current reaching the nozzle must be adjusted accordingly to allow adequate average beam intensity. In scattering mode, the dose rate also depends on the scattering design, particularly the intended field size. Obviously, the larger the field size, the lower the dose rate for a given beam current intensity at the nozzle entrance. In fact, in some situations the scattering system was designed to give a small field size for particular types of treatment, for example, for prostate treatment only where the maximum field size is 12 cm in diameter. For our system in scattering mode, the dose rate for 4.6-cm beam range is 1.5 Gy/min at the maximum beam current (i.e., 300 nA at the cyclotron exit). At a beam range of 16 cm, the dose rate can be as high as 10 Gy/min. For pencil beam scanning, the dose can be delivered spot-by-spot (in step-n-shoot mode) or line-by-line (in continuous scanning) and then layerby-layer. The overall dose rate is usually specified by the time to deliver a uniform dose to a 10-cm cube, or 1 liter of tissue equivalent material. Note that this depends not only on the beam current intensity for each scan layer, but also the time between the layers for beam energy change and the corresponding adjustments of the beam transport system. For the same incident beam current, the effective dose rate will also depend significantly on the target size to be treated.

4.6  Lateral Penumbra A sharp lateral penumbra is essential for sparing critical organs adjacent to the target volume. This happens to be one of the most attractive features of the proton beam. The lateral penumbra achievable in the patient depends on the design of the beam delivery system and also the nature of interaction between protons and tissues in the patient. The beam nozzle is generally designed to keep the penumbra as sharp as possible, although in some situations a less sharp penumbra may be beneficial, for example, for beam patching (Chapter 10). Another example is for treatments where large patient setup uncertainties must be tolerated. For scattering, the lateral beam penumbra is affected by the source size and source position, the position of the aperture, the range compensator, the air gap between the compensator and patient’s body surface, and naturally,

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the depth of tissue that the beam must penetrate before reaching the target volume (Chapter 5). The scatterers and the modulator determine the source size and are positioned far upstream, as far as possible from the aperture, resulting a much longer source-to-axis distance (SAD), >200 cm, than that for photon beams (100 cm). The aperture should be as close to the patient as possible to reduce the effect of source size. This also reduces the air gap that degrades the penumbra substantially (Chapter 5). In the patient, a proton beam interacts with tissues very differently from megavoltage photon beams (Chapter 2). For the latter, the main mechanism is attenuation due to Compton scattering where the scattered photons essentially escape from the beam. As a result, the lateral penumbra is mainly determined by the beam source size and source position, and increases only moderately as the beam goes through the patient. For protons, on the other hand, the main interacting mechanism is multiple Coulomb scattering (MCS). A proton changes its direction very little after each interaction, but stays in the beam. The change accumulates rapidly and increases the beam penumbra much faster than in the case of a photon beam. Figure 4.4 plots the lateral penumbra for a 6-MV photon beam and that for a scattered proton beam (range, 14 cm; modulation width, 10 cm), at both 4- and 10-cm depths. Clearly, the proton penumbras are much sharper than the photon counterparts. However, it increases drastically as depth increases from 4 to 10 cm, whereas the photon penumbra increase is moderate. Figure 4.5 shows the increase of beam penumbra of protons over deeper depths, again together with those for higher energy photon beams. Overall, at shallower depths, the proton penumbra (both 20%–80% and 50%–95%) is smaller than that of photon beams, but it increases rapidly with depth and becomes larger than the 15-MV photon beam for depths greater

Dose (%)

110 100 Photon (4 cm) Photon (10 cm) 90 Proton (4 cm) 80 Proton (10 cm) 70 60 50 40 30 20 10 0 –1 –0.8 –0.6 –0.4 –0.2 0 0.2 0.4 0.6 0.8 1 Lateral position (cm)

FIGURE 4.4 Lateral beam profiles in the penumbra region for scattered beam with range of 14 cm and modulation width of 10 cm (m98) at both 4- and 10-cm depths in water. The profiles of a 6-MV photon beam at the two depths are also shown for comparison.

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Characteristics of Clinical Proton Beams

80–20 % Distance (cm)

1.2 1.1

18 MV

15 MV

1.0 0.9 0.8 0.7 0.6 0.5 1.2

50–95 % Distance (cm)

Proton (R28/M10)

1.1

15 cm

20 cm

Proton (R28/M10)

18 MV

25 cm 15 MV

1.0 0.9 0.8 0.7 0.6 0.5

15 cm

20 cm Depth (cm)

25 cm

FIGURE 4.5 Measured lateral beam penumbra (20%–80% upper and 50%–95% lower) as functions of depth in water for 15- and 18-MV photon beam and for a scattering beam with range of 28 cm and modulation width of 10 cm.

than 17 cm for 20%–80% and 22 cm for 50%–95%. It is interesting to note that this is the typical treatment depth in current prostate treatment where only bilateral fields are used. It is exactly the reason why proton plans do not demonstrate any substantial dosimetric benefit over IMRT in terms of dose to anterior part of the rectal wall situated right next to the prostate target volume (7). Safai, Bortfeld, and Engelsman (9) investigated the properties of the lateral beam penumbra for a scattering system. Figure 4.6 shows the measured and modeled penumbra (20%–80%) as a function of depth in water for two broad pristine Bragg peaks with ranges 22.1 cm (T0 = 183 MeV) and 7.85 cm (T0 = 102 MeV), where T0 denotes the initial beam energy. Two sets of data were obtained for each beam range, with and without a 4-cm-thick plate of poly(methyl methacrylate) (PMMA) to simulate the contribution of the range compensator. The air gap was 10 cm without the PMMA and 6 cm with it. For all configurations, the penumbra increases with depth, as was the case shown in Figure 4.5. The lower energy beam starts with a slightly larger value at the surface, but increases much more rapidly than the higher energy beam. The PMMA plate broadens the penumbra for both beam energies, more at a depth than near the surface because of reduced beam energy. At the end of the beam range, the penumbras are comparable with or without the PMMA plate. Note that although the data given here are from pristine

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26 1.6

24

20

18

16

14

12

10

8

6

4

2

measurement w/o PMMA measurement w/4.0 cm PMMA prediction

1.4 Penumbra (80%–20%) [cm]

22

1.2

1.6 1.4 1.2

T0 = 183 MeV

1

0

1 0.8

0.8 T0 = 102 MeV

0.6

0.6

0.4

0.4

0.2

0.2

0

0

2

4

6

8

10 12 14 16 18 Depth in water (dw) [cm]

20

22

24

0 26

FIGURE 4.6 Measured (symbols) and modeled (lines) lateral beam penumbra (20%-80%) as functions of depth in water for two scattered beams with beam ranges of 21.1 cm (left) and 7.85 cm (right), with and without 4.0-cm plate of PMMA. (From Safai S, et al., Phys Med Biol., 53, 1729, 2008. With permission).

Bragg peaks without range modulation, it was shown that the lateral penumbra of SOBP fields is almost independent of the beam modulation width and, therefore, follows the same trend described here (10, 11). In pencil beam scanning, the main source of the penumbra broadening before the patient is the scattering by the air column extending from the end of the nozzle to the patient’s body surface. Safai, Bortfeld, and Engelsman modeled this effect for a single Gaussian beam (σ = 3 mm) and compared the results with a broad Gaussian beam but with an aperture and compensator (9). It was found that if the vacuum window is at the same upstream location as in a scattering system, the penumbra for the uncollimated pencil beam is significantly larger than that for the collimated beam at the surface. Of course no scanning system would have an air column that long. In depth of water, however, the uncollimated penumbra increased much slower than the collimated and became less than the latter at larger depths that were greater than 18 cm. This is partly due to the very different effective source positions (i.e., divergence) of the beam. Overall, the collimated penumbra is superior at shallow depths, but is inferior at greater depths. The authors concluded that for most of the clinical sites (e.g., head and neck) the penumbra of a pencil beam is inferior to that of a collimated divergent beam, unless the vacuum window is moved downstream substantially or the beam spot size is reduced to 5 mm or less (9). The investigation reported in Safai’s work focused on the penumbra of a single pencil beam. Clinically, what is more relevant in terms of organ sparing is the

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lateral penumbra of the composite dose distribution as the superposition by all individual pencil beams used for a treatment field. As discussed in Chapter 6, such a superposition with a uniform dose plateau can be built by using evenly spaced pencil beams with a constant intensity, but the resultant composite lateral penumbra will be broader than that for the individual pencil beam. However, composite doses with an equally acceptable dose plateau can also be obtained by using nonuniform spacing together with modulated intensities optimized to produce a much sharper penumbra, nearly the same as for a single pencil beam. For either case, though, the smaller the spot size for the individual pencil beam, the narrower the lateral penumbra of the total dose distribution. Is it always better to have a smaller spot size for proton beam scanning? Trofimov and Bortfeld studied the issue in their efforts to develop a set of clinically relevant specifications for pencil beam scanning (12). They pointed out that, for deep tumors, a finer pencil beam would not necessarily lead to any significant improvement in dose conformity, simply because the main contribution to the spot size at the tumor comes from MCS along the beam path in patient. For shallower target volumes, they performed treatment planning using a range of spot sizes for a head and neck case where this perhaps matters the most. It was found that reducing the spot size from 8 to 5 mm led to a marked improvement in dose conformality for the target volume, whereas the difference was not as dramatic from 5 to 3 mm. They concluded that for most clinical cases, pencil beams of widths σ = 5 mm will be sufficient for delivery of the target-conformal planned dose with a high precision. Reducing the beam spot size below 5 mm does not lead to substantial improvement in the target coverage or sparing of healthy tissue.

4.7  Distal Penumbra The distal penumbra of the SOBP dose distribution is determined primarily by the deepest few Bragg peaks. The penumbra (50%–95%) is the smallest with only the deepest peak, but increases up to a millimeter as more peaks are added to build up the dose plateau as shown in Figure 4.1. In relatively homogeneous medium without a high gradient in tissue density, the distal beam penumbra is always much sharper than the lateral one. It increases moderately with energy due to range straggling in the patient and also by scattering and range modulation components in the nozzle if scattering is used. The former is unavoidable, but the latter can be eliminated by using pencil beam scanning, or minimized by reducing the water equivalent thickness of those components. For the scattering system at Massachusetts General Hospital (MGH), the distal penumbra increases monotonically from 3.5 to 5.0 mm (20%–80%) over the beam range of 4.8 to 25 cm. However, for a beam range of 25 to 28 cm, the penumbra is only 4.7 mm, actually smaller due to the use of a very thin second scatter.

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When high-gradient tissue inhomogeneity is present, range mixing can occur. The distal penumbra can be degraded substantially and could be much larger than the lateral penumbra. The extreme case is when the beam passes along the interface between a high-density and a lower density medium, where the distal dose falloff can be seriously distorted. The situation is investigated in Schaffner, Pedroni, and Lomax (13). Needless to say, the compensator causes additional range straggling that will also increase the distal penumbra. A thick compensator and in particular those with sharp variations in thickness should be avoided if possible. It should be pointed out that although the distal beam penumbra is much sharper than the lateral, it is not always used clinically for tight margin sparing because of uncertainties in predicting the beam range in the patient (Chapter 13). The recent development using posttreatment PET (positron emission tomography) imaging based on treatment-induced isotope activities has shown very promising results for in vivo range verification, as described in Chapter 16. Although it works well mainly for coregistered bony structures in the head and neck, for soft tissue target volumes in other parts of the body the accuracy drops substantially for various reasons. In any case, the method is still at the research stage and is not widely available. In current practice, the range uncertainty issue is managed by adding an additional amount to the beam range in treatment planning, usually 3.5%, to head off the potential “undershooting” (Chapter 10). Although this guarantees the coverage of the distal aspect of the target volume, it also risks overdosing the normal tissue behind the target volume. A good example is the treatment of prostate cancer mentioned above. Anterior or anterior oblique fields have never been used, despite the fact that such fields can utilize the sharp distal penumbra (~4 mm for 50%–95%) to separate the prostate and the rectum behind. Instead, only lateral fields are used, relying solely on the much broader lateral beam penumbra (>10 mm for 50%–95%) to spare the rectum. The reason is because when a water-filled endorectal balloon is used to immobilize the prostate, as widely practiced, the anterior rectal wall is only about 5 mm thick and is situated right next to the posterior side of the prostate in many areas. If an anterior field is used for treatment, the typical beam range is about 15 cm and its 3.5% will be 5 mm, just the thickness of the anterior rectal wall. Therefore, the usual method of adding extra range will risk delivering the full dose to the anterior rectal wall, which is clearly unacceptable given rectal bleeding as the leading treatment toxicity for prostate treatment.

4.8  Dose Uniformity A proton beam has the unique ability that a single beam can be used to deliver a homogeneous dose across the entire target volume, as opposed to a photon beam where multiple fields must be used to achieve a similar

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coverage through superposition. In scattering, this is achieved by carefully designing the scattering components including scatterers and range modulators (or ridge filters in some systems) so that the dose in the SOBP is uniform in the dose plateau both in depth and laterally across the field size required. Naturally, this specification is for a homogeneous phantom, whereas in patient it could be larger due to the effect of tissue inhomogeneity. The details of the scattering systems will be discussed in Chapter 5. We only comment here that given the sensitive dependence of the scattering property on the beam energy, it is a formidable task to design a scattering system that accommodates all clinically relevant beam ranges with sufficient quality and at the same time provides convenience and efficiency that are critical in day-to-day clinical practice. With a method developed only recently, it was possible to optimize a critical component of the system so that for all the beam ranges, the dose uniformity in depth is within 2% (2). Note that the double-scattering system is very sensitive to beam steering and a slight change in the beam spot position on the scatters can seriously affect the field flatness and symmetry. This requires an effective monitoring system and also frequent quality assurance verifications by independent means. For pencil beam scanning, the total dose distribution is constructed by individually delivered Bragg peaks and its uniformity will directly depend on the accuracy of the delivery (i.e., the beam energy and the spot location). Inaccuracies in the beam energy will create uneven distances between adjacent layers in depth and thus cause ripples in depth that could exceed the 2% requirement, particularly at the shallower part where the Bragg peak is distinctively narrow. Across the field, when the spot is not accurately positioned as planned, the superposed Gaussian distribution will contain spikes and valleys, both of which could exceed the uniformity requirement. The accuracy requirement in delivery for keeping an acceptable level of dose uniformity and how it is achieved with the current technological capability will be discussed in Chapter 6.

4.9  Characteristics of Proton Therapy Treatment The distinguished physical characteristics of the proton beam discussed above also result in some special characteristics of the proton therapy treatment itself in comparison to treatment by photon and/or electron beams. Proton beams have been used to treat nearly all major types of cancer at all treatment sites (e.g., central nervous system, head and neck, lung, esophagus, liver/pancreas, prostate, rectum, and sarcomas), and the list is ever increasing. Recently, a proton beam was used for postmastectomy irradiation for the first time. Although these conditions are also treated by photon/electron

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beams, which is the only choice for the majority of patients today, treatment using protons can be quite different, given the unique physical properties of the beam. Undoubtedly, the sharp distal dose falloff gives the proton the most important advantage in sparing normal tissues near the target volume. The clinical implication of this is best illustrated by the spine fields used in the treatment of medulloblastoma, a condition occurring most often in pediatric and/or young adult patients. The protons from a posterior beam stop right behind the spinal target volume, leaving no dose to the rest of the body, whereas a photon treatment would give up to 50% of the prescription dose to the anterior portion of the body (14). Another unique feature made possible by the sharp distal falloff is the patching technique widely used in scattering and uniform scanning (Chapter 10). We must note that although the sharp distal dose falloff can offer great potentials for normal tissue sparing, it also makes the dose distribution extremely sensitive to uncertainties in treatment planning and patient setup (Chapter 13). The range of the proton beam in the patient depends largely on the water equivalent path length (WEPL) along the beam. If the WEPL value changes by 1 cm, the location of the distal falloff will change by 1 cm, causing either an undershoot, missing the distal portion of the target volume by one full centimeter, or an overshoot, delivering full dose to a centimeter of normal tissue behind the target volume. In contrast, the same magnitude of change in WEPL in a photon treatment will only change the dose at most by 3%–4%, for example, for a 10-MV beam. A patient setup error in an IMRT treatment may cause a shift of the so-called “dose cloud,” missing some peripheral regions of the target volume. In a proton treatment, the same error may also distort the dose cloud substantially, due to the mismatch between the beam energy distribution and the tissue heterogeneities along the beam path. The presence of a dose plateau in Figure 4.1 means that a single proton field can deliver the uniform dose to the target volume, which is not possible with photon or electron beams. This allows for the use of only one or two fields for each treatment fraction to deliver the prescription dose, although the whole treatment course may use a large number of treatment fields to spread the dose to normal tissues. Many patients are treated in this manner, that is, with only one or two fields per fraction, but with different fields or field combinations on different days. This is very different compared to a photon treatment where each fraction uses the same number of fields throughout the treatment course. When the total prescription dose for a fraction is delivered by only one or two fields, the uncertainties involved in each field become much more important. This plus the sensitive nature of the proton dose distribution mentioned above determines that proton treatment requires highly accurate patient setup. Note that because the treatment beam stops in the patient completely, a photon-like portal imaging is not possible and one must rely entirely on x-ray imaging. Usually, the patient is first setup with an orthogonal pair of

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images to produce the correct anatomical configuration, and then for each treatment field, the patient is imaged again along the beam direction, often with the aperture when available, to ensure target volume coverage and normal structure avoidance. As a result, the time for patient setup is generally longer than with a photon treatment. Can treatment be delivered with only fixed beam line, rather than a gantry system? This seems to be a question relevant only in particle therapy. A gantry system is large and expensive. Moreover, the beam transport system on the gantry adds another layer of complexity to the whole system. The answer to this question really depends on the specific treatment site and treatment techniques involved. Treatments of ocular melanoma have always used fixed beam lines. At Francis H. Burr Proton Therapy Center (FHBPTC) at MGH, a fixed horizontal beam is also used to perform stereotaxic radiosurgery and stereotaxic radiotherapy treatment by placing the patient in an immobilization system called STAR (Stereotactic Alignment Radiosurgery) system with six degrees of freedom. Current prostate treatment uses only lateral beams as mentioned earlier and therefore can be treated by only fixed horizontal beam lines as indeed practiced at some centers. For other treatment approaches using anterior and anterior oblique beams currently under development, the gantry will be required. For some treatment sites such as nasopharynx and skull base chordoma, however, it is clearly difficult without a gantry. Figure 4.7 shows the number of fields at each gantry angle for all the patients treated in a 12-month period for one gantry treatment room at FHBPTC. Of all the fields, 23% used only lateral beams, 41% used just the four normal angles (0°, 90°, 180°, and 270°), and 59% used other gantry angles. Interestingly, the treatment planners only varied the gantry angle at 5° increments. One can interpret this graph to indicate that it may be possible to treat patients with a combination of fixed-field beams and a gantry, instead of building multiple-gantry systems. There may be some logistical issues, but the data are interesting.

Number of fields

1600 1400 1200 1000 800 600 400 200 0

0

90

180 270 Gantry angle (degree)

FIGURE 4.7 Distribution of the number of treatment fields over gantry angles for all patients treated in a gantry room over a 12-month period.

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Summary A survey of the properties of proton beams and how they are used in clinical treatment has been presented. Although proton therapy has existed for decades, the more widespread use is only from a few to several years old, and current clinical practice is now being augmented by investigations of the effects of modifying the beam properties. It is interesting to point out that one of the characteristics of proton beams is that their properties can, in fact, be modified. Thus it becomes even more important to understand what works best clinically and to evaluate the design of any proposed beamspreading system, considering how it will be used clinically. One issue may be the construction of multipurpose systems as opposed to single-use systems. In much the same way that a gantry is more expensive than a fixed beam line, the use of a beam for multiple treatment sites may also be more expensive. However with the increase in the use of scanning beams, this may not be an issue any longer. The properties of the beam must be matched to the characteristics of the clinical target and the beam delivery modality, and understanding how the beam characteristics can be used and modified is an essential part of optimal treatment delivery.

References

1. ICRU Report 78. Prescribing, recording, and reporting proton-beam therapy. International Commission on Radiation Units and Measurements, (2007). 2. Engelsman M, Lu HM, Herrup D, Bussiere M, Kooy HM. Commissioning a passive-scattering proton therapy nozzle for accurate SOBP delivery. Med Phys. 2009 Jun; 36(6), 2172–80. 3. Kooy HM, Schaefer M, Rosenthal S, Bortfeld T. Monitor unit calculations for range-modulated spread-out Bragg peak fields. Phys Med Biol. 2003; 4, 2797–808. 4. Kooy HM, Rosenthal SJ, Engelsman M, Mazal A, Slopsema R, Paganetti H, et al. The prediction of output factors for spread-out proton Bragg peak fields in clinical practice. Phys Med Biol. 2005; 50, 5847–56. 5. IAEA Report 398. Absorbed dose determination in external beam radiotherapy: an international code of practice for dosimetry based on standards of absorbed dose to water. International Atomic Energy Agency, (2000). 6. Farr J, Mascia AE, His WC, Allgower CE, Jesseph F, Schreuder AN, et al. Clinical characterization of a proton beam continuous uniform scanning system with dose layer tacking. Med Phys. 2008; 35, 4945–54. 7. Trofimov A, Nguyen PL, Coen JJ, Doppke KP, Schneider RJ, Adams JA, et al. Radiotherapy treatment of early-stage prostate cancer with IMRT and protons: A treatment planning comparison. Int J Radiat Oncol Biol Phys. 2007 Oct 1; 69(2), 444–53.

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8. Lu HM, Brett R, Sharp G, Safai S, Jiang S, Flanz J, et al. A respiratory-gated treatment system for proton therapy. Med Phys. 2007; 34, 3273–78. 9. Safai S, Bortfeld T, Engelsman M. Comparison between the lateral penumbra of a collimated double-scattered beam and uncollimated scanning beam in proton radiotherapy. Phys Med Biol. 2008; 53, 1729–50. 10. Oozeer R, Mazal A, Rosenwald JC, Belshi R, Nauraye C, Ferrand R, et al. A model for the lateral penumbra in water of a 200 MeV proton beam devoted to clinical applications. Med Phys. 1997; 24, 1599–604. 11. Urie MM, Sisterson JM, Koehler AM, Goitein M, Zoesman J. Proton beam penumbra: Effects of separation between patient and beam modifying devices. Med Phys. 1986; 13, 734–41. 12. Trofimov A, Bortfeld T. Optimization of beam parameters and treatment planning for intensity modulated proton therapy. Technol Cancer Res Treat. 2003; 2, 437–44. 13. Schaffner B, Pedroni E, Lomax AJ. Dose calculation models for proton treatment planning using a dynamic beam delivery system: An attempt to include density heterogeneity effects in the analytical dose calculation. Phys Med Biol. 1999; 44, 27–42. 14. Clair WH, Adams JA, Bues M, Fullerton BC, Shell SL, Kooy HM, et al. Advantages of protons compared to conventional X-ray or IMRT in the treatment of a pediatric patient with medulloblastoma. Int J Radiat Oncol Biol Phys. 2004; 58, 727–34.

5 Beam Delivery Using Passive Scattering Roelf Slopsema CONTENTS 5.1 Scattering Techniques................................................................................ 126 5.1.1 Flat Scatterer.................................................................................... 126 5.1.2 Contoured Scatterer........................................................................ 127 5.1.3 Dual-Ring Scatterer........................................................................ 130 5.1.4 Occluding Rings.............................................................................. 130 5.2 Range Modulation Techniques................................................................. 130 5.2.1 Range Modulation Principles........................................................ 131 5.2.2 Energy Stacking.............................................................................. 133 5.2.3 RM Wheels....................................................................................... 134 5.2.4 Ridge Filters..................................................................................... 140 5.3 Conforming Techniques............................................................................ 142 5.3.1 Aperture........................................................................................... 142 5.3.2 Multileaf Collimator....................................................................... 143 5.3.3 Range Compensator....................................................................... 144 5.4 Scattering Systems...................................................................................... 146 5.4.1 Large-Field Double-Scattering Systems....................................... 147 5.4.2 Single-Scattering System for Eye Treatments............................. 151 5.5 Conclusion................................................................................................... 152 References.............................................................................................................. 153

Passive scattering is a delivery technique in which scattering and rangeshifting materials spread the proton beam. After the protons are accelerated, either by a cyclotron or synchrotron, they are transported into the treatment room through the beam line (see Chapter 3). The proton beam that reaches the treatment room is mono-energetic and has a lateral spread of only a few millimeters. Without modification this beam would give a dose distribution that is clinically not very useful. Along the beam axis the dose is initially fairly constant, but peaks sharply toward the end of travel of the protons (Bragg peak). In the lateral direction the profile would be a Gaussian with a spread on the order of a centimeter. Clinical use of the proton beam requires both spreading the beam to a useful uniform area in the lateral direction as well as creating a uniform dose distribution in the depth direction. The 125

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main function of the treatment head, or nozzle, is shaping the proton beam into a clinically useful three-dimensional (3D) dose distribution. In general two methods of lateral beam spreading are applied: passive scattering, in which high-Z materials scatter the proton beam to the desired dimension, and magnetic beam scanning, in which magnetic fields sweep the proton beam over a desired area. Scattering systems are described in this chapter; scanning systems are the topic of Chapter 6. In the depth direction a uniform dose region is created by adding Bragg peaks that are shifted in depth and given an appropriate weight to obtain a flat dose region called the spreadout Bragg peak (SOBP). This method of adding pristine peaks is called range modulation. The number of peaks that is added proximally can be varied, varying the extent of the uniform region in depth. Combining scattering and range modulation gives a uniform dose distribution shaped like a cylinder. Field-specific apertures and range compensators conform the dose to the target. The aperture blocks the beam outside the target and conforms the beam laterally. The range compensator is a variable range shifter that conforms the beam to the distal end of the target. In this chapter we will first describe the basic techniques of scattering and range modulation. Next the design and application of apertures and range compensators is discussed. In the final section several complete scattering systems are discussed, combining scattering technique, range modulation method, and conforming devices.

5.1  Scattering Techniques 5.1.1  Flat Scatterer The simplest scattering system is a single, flat scatterer that spreads a small proton beam into a Gaussian-like profile (Figure 5.1A). A collimator (aperture) blocks the beam outside the central high dose region. To keep the dose variation over the profile within clinically acceptable limits, most of the beam will need to be blocked. For a Gaussian beam profile with spread, σ, the efficiency, η, defined as the proportion of protons inside a useful radius, R, is given by the following (1):

η = 1− e

1 − ( R/σ )2 2

(5.1)

It follows that the fraction of protons outside the useful radius is equal to the relative dose at the useful radius (when normalizing to the central axis). Allowing for a dose variation of ±2.5% over the profile and setting the useful radius at the 95% dose level, results in an efficiency of only 100% − 95% = 5%. Because of this low efficiency, requiring relatively large beam currents and

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A. Single Scattering with flat scatterer

B. Double Scattering with contoured scatterer

C. Double Scattering with dual ring

D. Double Scattering with occluding ring

FIGURE 5.1 Schematic representation of the single-scattering technique using a flat scatterer (A) and double-scattering techniques using a contoured scatterer (B), dual ring (C), and occluding ring (D). Dashed lines, lateral profile without aperture; solid lines, with aperture.

generating high production of secondary neutrons, spreading using a flat scatterer (single scattering) is limited to small fields with a diameter typically not exceeding ~7 cm. Besides its simplicity, the advantage of a single flat scatterer over more complex scattering techniques is the potential for a very sharp lateral penumbra. Most of the scattering occurs in a single location limiting the angular diffusion of the beam. Especially if the scatterer is placed far upstream of the final collimator, a very sharp lateral penumbra can be achieved. The field size limitation and sharp dose falloff make single scattering ideal for eye treatments (2–8) and intracranial radiosurgery (9). Typically the scatters are made of high-Z materials, such as lead or tantalum, providing the largest amount of scattering for the lowest energy (range) loss. A scattering system that allows variation of the thickness of the scattering material can be used to maintain scattering power for varying proton energy. An example of such a system has a binary set of scatterers (with each scattering foil double the thickness of the previous) that can be independently moved in or out of the beam path. 5.1.2  Contoured Scatterer A better efficiency can be achieved by scattering more of the central protons to the outside and creating a flat profile (Figure 5.1B). The shape of a contoured scatterer, thick in the center and thin on the outside, has been optimized to do this (10, 11). Typically a flat scatterer (first scatterer) spreads the beam onto the contoured scatterer (second scatterer) that flattens out the

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profile at some distance. This type of system is called a double-scattering system. Mathematically the lateral dose distribution Φ(r) created by a double-scattering system can be described as follows: Φ(r ) =

(2π z

1 FS

2π

θFS )

2

∫ 0

  1 r '2   exp − ∫0  z θ 2  ⋅ ( z θ ( r '))2  ( FS FS )  CS CS R

   (r − r ')2    × exp −  2   ⋅r ' dr ' dφ,  ( zCS θCS ( r ') ) 

(5.2)

where zFS and zCS are the distance from the first and second scatterer to the plane of interest; θFS is the characteristic scattering angle of the first flat scatterer (which is constant), θCS is the characteristic scattering angle of the contoured scatterer that depends on radial position r′. R is the radius of the contoured scatterer assuming all protons outside R are blocked. The radial coordinates r′ and R of the contoured scatterer are projected from the first scatterer onto the plane of interest. The first exponential in the equation gives the fluence of the beam hitting the contoured scatterer at position r′. Without the contoured scatterer the dose distribution would be equal to this term. The second exponential describes the operation of the contoured scatterer. It describes the proportion of protons hitting the second scatterer at position r′ and ending up in position r. This depends on the distance between r′ and r and the angular spread added by contoured scatterer, which is a function of the characteristic scattering angle (i.e., thickness) at location r′. By integrating over all positions, r′, the dose in point r is found. (Note that we have made some simplifications here such as Gaussian scattering, rotational symmetry, thin scatterers, and a small parallel entrance beam. More realistic properties will complicate the formulation, but can typically still be described analytically.) Given a desired flat dose distribution Φ(r), it is not possible to analytically solve Equation 5.2 and find the required shape of the contoured scatterer θCS(r′). Instead the shape of the contoured scatterer is determined using numerical methods. The scattering shape is described by a parameterized function such as a cubic spline through a limited number of points whose thickness is optimized (11) or a modified cosine with four independent variables (10). The variables of the contoured scatterer are optimized in combination with the scattering power of the first scatterer to obtain a dose distribution of desired size and acceptable uniformity. Efficiency can be made an additional objective in the optimization. Efficiencies of up to 45% can be obtained, significantly larger than in single scattering. Protons hitting the center of the contoured scatterer lose more energy than those going through the thinner parts at the periphery. To avoid a concave distortion of the distal isodose plane, with the range increasing away from the beam axis, energy compensation is applied to the contoured

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scatterer. A high-Z scattering material (lead, brass) is combined with a low-Z compensation material (plastic). The thickness of the two materials is designed to provide constant energy loss, while maintaining the appropriate scattering power variation. The thickness of the high-Z material decreases with distance from the axis, whereas the thickness of the compensating low-Z material increases. Figure 5.2 shows a schematic of an energy-compensated scatterer. Note that energy compensation will increase the total water equivalent thickness of the scatterer because the compensation material increases the scattering power on the outside of the scatterer, which needs to be compensated for by adding additional scattering material in the center. The energy of the protons entering the nozzle needs to be increased to achieve the same range in the patient as with an uncompensated scatterer. The dose distribution is sensitive to misalignments of the beam with respect to the second scatterer. A displacement of the beam increases the fluence on one side of the second scatterer and reduces it on the other side, causing a tilt in the dose profile at isocenter. To keep the symmetry within clinical tolerance, the alignment of the beam typically needs to be better than ~1 mm. The large distance between the final steering magnet of the beam line and the second scatterer makes this difficult to achieve without a feedback mechanism. By monitoring the profile symmetry downstream of the second scatterer (e.g., using strip ionization chambers), the final steering magnets can be controlled maintaining a flat profile (12). In addition to misalignment, the profile is sensitive to variations in beam size at the second scatterer level. If the profile is too large, the dose profile will have “horns”; if the profile is too small the dose profile will be “domed.” If the second scatterer is placed far enough downstream, meaning that its physical size is large enough, the width of the beam onto it will be dominated by the scattering of the first scatterer and variations in beam spot size at the nozzle entrance will not play a role.

lead

0.6 cm

Lexan 3 cm

16 cm FIGURE 5.2 Schematic cross section of an energy-compensated contoured scatterer in the IBA universal nozzle.

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5.1.3  Dual-Ring Scatterer An alternative to the contoured scatterer is the dual-ring scatterer (13). It consists of a central disk made of a high-Z material (lead, tungsten) and a surrounding ring of a lower-Z material (aluminum, Lucite). The physical thickness of the outer ring is chosen such that the energy loss is equal (or close) to the energy loss in the central disk. A first, the flat scatterer spreads the beam onto the dual-ring scatterer. The central disk produces a Gaussianlike profile, and the ring produces an annulus-shaped profile, which combine to produce a uniform profile at the isocenter (Figure 5.1C). In the design the projected scattering radius of the first scatterer and of the two dual-ring materials, together with the diameter of the central disk, are optimized to generate a flat dose profile of the desired size (14). Because of the binary nature of the dual-ring, the dose distribution is not perfectly flat. A small cold spot is allowed at the level of the interface between the two materials. Like the contoured scatterer, the dual-ring system is sensitive to both beam alignment and phase-space changes. 5.1.4  Occluding Rings Most double-scattering systems today use a contoured or dual-ring scatterer, but occluding rings combined with a flat second scatterer can also flatten the profile (15). Instead of scattering the central protons outward they are blocked (Figure 5.1D). The “hole” created in the fluence distribution is filled in by scattering through a flat, second scatterer. Larger-field sizes can be obtained by not just blocking the center but by adding one or more occluding rings. Optimization of the ring diameters and the first scatterer power results in a flat dose distribution. Because the protons are not redistributed but blocked, the efficiency of an occluding ring system drops significantly as the number of rings and maximum field size are increased. It is significantly lower than for the contoured scatterers. The energy loss is smaller though, because a relatively thin second scatterer foil is needed to spread out  the beam. The geometry of the occluding rings makes them just as sensitive to beam misalignment as the contoured scatterers.

5.2  Range Modulation Techniques When looking at the depth–dose curve of a mono-energetic proton beam, it is obvious that the Bragg peak is too sharp to cover a target of any reasonable size. By combining proton beams of decreasing energy, range modulation transforms the pristine Bragg peak into a uniform depth–dose region called the SOBP. Addition of Bragg peaks shifted in depth and weighted

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Relative dose [%]

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A

100

B

85%

50

36% 25% 20% 13% 17% 11%12% 15% 7%7% 7% 8% 8% 9%10%

Relative dose [%]

5

16 peaks: full mod, 95% skin dose 12 peaks: 7.6 cm mod, 79% skin dose 8 peaks: 4.8 cm mod, 65% skin dose 4 peaks: 2.1 cm mod, 47% skin dose

10

5 C

90

103%

100

100

10 D

50 sigma = 3% sigma = 2% sigma = 4%

5 Depth [g/cm2]

Maximal uniformity Smallest fall-off

10

8

Depth [g/cm2]

10

FIGURE 5.3 Creation of the SOBP with a range of 10 g/cm2. (A) Subplot of the weights of the pristine peaks when creating a full modulation SOBP. (B) Subplot of the SOBP of various modulation width are shown. (C) Subplot of the effect of a change in pristine peak energy spread on the SOBP. (D) Subplot of the alternative methods of optimization at the distal end of the SOBP are shown.

appropriately yields a uniform dose. Depending on the size of the target to be covered, the extent of the uniform region can be adjusted by changing the number of added peaks (Figure 5.3). Several range modulation techniques are applied in proton therapy: energy stacking, range modulator (RM) wheels, and ridge filters. After exploring some of the general principles of range modulation and SOBP construction, we discuss each of these techniques in detail. 5.2.1  Range Modulation Principles Using a power-law approximation of proton stopping power, it is possible to analytically describe the Bragg peaks and calculate the optimal weights for an SOBP (16). In reality the shape of the Bragg peak is complex and depends on the energy spread and scattering properties of the delivery system. Measured Bragg curves are used and the weights are determined numerically using simple optimization algorithm (17–19). Mathematically the problem can be described as follows: N



SOBP(R, d) = ∑ wi ⋅ PP(Ri , d), i =1



(5.3)

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where PP(Ri, d) is the pristine peak depth–dose curve with range Ri, wi is the relative contribution of peak i to the SOBP given by the ratio between the maximum dose in the peak and the SOBP plateau dose, N is the number of peaks summed, and SOBP(R, d) is the resulting spread-out depth–dose curve with range R. The weights wi are optimized, minimizing the difference between SOBP(R, d) and an ideal, presumably uniform, dose distribution. Figure 5.3A shows the optimization of an SOBP with a range of 10 g/cm2 and full dose up to skin. The range shift between the pristine peaks is fixed at 6 mm, and 16 pristine peaks are required to obtain a full skin dose. The peak weights drop exponentially from 85% of the plateau dose for the distal layer, to 36% for the second layer, down to 7% for the most proximal layers. The increasing contribution of dose from the more distal layers reduces the dose required for more proximal layers to reach the plateau. The extent of the uniform dose region can be varied by changing the number of pristine peaks delivered. Figure 5.3B shows the SOBP when the distal 12, 8, or 4 layers are delivered, resulting in a 90%–90% modulation width of 7.6, 4.8, and 2.1 g/cm2. All peaks add dose to the skin. The distal peaks have a small skin dose due to the rising shape of the Bragg curve but have a large weight. Proximal peaks have larger skin-to-peak dose ratio, but their contribution to the SOBP is less. These competing effects result in a relationship between modulation width and skin dose that is not far from linear. The skin dose also depends on the SOBP range decreasing with increasing range. Although the range of the individual pristine peaks can be made a variable in the SOBP optimization process, good results are obtained by keeping the range shift (pullback) between the peaks constant and setting it equal to the 80% width of the individual peaks (11). A larger pullback between the peaks results in a ripple in the dose distribution, but a smaller pullback does not improve uniformity. In Figure 5.3C the SOBP is shown when the width of the peaks is set to 5 or 7 mm, but the pullback is kept at 6 mm. The sharper peaks generate a strong ripple in the SOBP, whereas the wider peaks do not change the uniformity of the plateau, they just deteriorate the sharpness of the corners. It is interesting to consider that we have not reoptimized the weights here. The sharper peaks generate a ripple but not a tilt in the plateau, suggesting that the weights are still optimal. This effect has also been observed experimentally when changing the energy spread of the proton beam entering the nozzle (20). A choice needs to be made at the distal end of the SOBP when optimizing the weights. One can either make the dose as flat as possible or make the distal falloff as sharp as possible (Figure 5.3D). If the extent of the desired uniform dose region is limited to a point halfway between the distal two peaks, the dose distribution can be made completely flat, but the distal dose falloff exhibits a fairly large shoulder and distal falloff. The falloff can be made sharper by increasing the weight of the distal peak while decreasing the weight of the second peak. The resulting dose distribution acquires a hot

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133

spot at the distal end of the uniform region and a cold spot more proximally. For the SOBP in Figure 5.3D the 95%–20% distal falloff is decreased from 6.8 to 5.5 mm when limiting the hot spot to 103%. An additional consideration here is the biological effect. Several studies have shown that the radiological bioeffectiveness (RBE) increases in the shoulder and distal falloff of the SOBP (see Chapter 19). Optimizing for the sharpest falloff might result in even larger hot spots in biological effect. Whichever approach is taken, it should be mimicked in the treatment-planning algorithm (21). 5.2.2  Energy Stacking Changing the energy of the protons entering the nozzle is conceptually the easiest method of range modulation because it requires no dedicated nozzle elements. Between layers the energy is changed at the accelerator level, either by changing the extracted synchrotron energy or the energy-selection system setting at the exit of the cyclotron (Chapter 3). By accurately controlling the number of protons delivered for a given energy, for example, by terminating the beam once a preset number of monitor units in the reference ionization chamber is reached, the appropriate SOBP weighting is realized. A major advantage of this form of range modulation is that the protons do not need to interact with a range shifter inside the nozzle. Range-shifting material scatters the protons increasing the lateral penumbra, straggles the protons increasing the energy spread and distal falloff, and generates neutrons  (22). However, energy stacking with range shifting upstream is not applied in current clinical scattering systems. The first reason for this is the technological challenge of quickly switching energy between layers. Not only the accelerator energy needs to change, but also the beam transport magnets need to be adjusted to account for the change in proton energy of protons transported into the room. Current (cyclotron-based) systems have difficulty switching the energy in less than about 5 s. For a field with a modulation width of 10 g/cm2 delivered in 16 layers, the switching overhead would be more than a minute. (In pencil beam scanning [Chapter 6], range shifting in the nozzle is not a viable alternative because of beam spot size requirements. So, it looks like there is no escaping this challenge.) The second issue with energy stacking is the potential of interplay effects with organ motion (Chapter 14). Dose uniformity is only achieved if every point in the SOBP gets exactly the contribution from each of the pristine peaks as determined during optimization. Intrafraction motion can cause the depth of a voxel to vary over time. (Note that the depth can change when the voxel itself moves with respect to upstream nonhomogeneous target tissue, including range compensator, or when upstream tissue moves with respect to the stationary voxel.) If the depth of a voxel changes between two energy layers contributing to that voxel, the dose contribution of each of the pristine peaks will no longer match the optimized layer weighting. Hot and cold spots in the depth–dose curve will be the result of motioninduced depth changes during energy stacking.

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The problem of changing accelerator energy and beam-transport settings can be avoided by applying range shifting inside the nozzle, although the issue of interplay effects remains. The accelerator energy is set to the appropriate energy for the distal pristine peak. After delivering the dose for the distal layer, an absorber with a water equivalent thickness equal to the desired pullback is inserted in the beam path, and the next layer is delivered. The absorber thickness is increased sequentially while stepping through the energy layers. Low-Z materials, such as plastic or water, are the preferred range-shifter materials because they provide the least amount of scattering per unit of range shift. Several types of variable range shifters have been implemented, including a variable water column that uses a moveable piston to accurately adjust the amount of water in a cylinder, a binary set of plastic plates that can be moved independently into the beam path, and a doublewedge variable absorber (23). Like the upstream method, energy stacking in the nozzle also is not used much in clinical scattering systems. 5.2.3  RM Wheels In his original article on proton therapy, Wilson proposed an RM wheel as a method to spread the dose: “This can easily be accomplished by interposing a rotating wheel of variable thickness, corresponding to the tumor thickness, between the source and the patient” (24). Koehler, Schneider, and Sisterson were the first to report implementation of an RM wheel (25). The RM wheel has been and continues to be the method of range modulation in most clinical proton-scattering systems. An RM wheel has steps of varying thickness, each step corresponding to a pristine peak in the SOBP. When the wheel rotates in the beam, the steps are sequentially irradiated. The thickness of a step determines the range shift of that pristine peak; the angular width of the step determines the number of protons hitting the step, and thus the weight of the pristine peak. By progressively increasing the step thickness while making the angular width smaller, a flat SOBP can be constructed. Like the range shifters used in energy stacking, modulator wheels are preferentially made of low-Z materials to limit scattering. Plastics (Plexiglas, Lexan) are often used, but for wheels that need to provide large range shifts and that are mounted in nozzles where space is limited, carbon (26) and aluminum (27) have been applied. Figure 5.4 shows a range modulator used at the Harvard Cyclotron Laboratory. Symmetrically cut fan-shaped sheets of Plexiglas are stacked together, repeating the modulation pattern four times per wheel revolution. Because the wheel is mounted close to the patient where the beam is already spread out, the dimension of the wheel is relatively large (~85-cm diameter). The size of the RM wheel can be made smaller by moving it further upstream. A smaller RM wheel allows higher rotational speeds and for easier, even automatic, exchange of wheels. Figure 5.5 shows an example of such an “upstream propeller” from the Ion Beam Application (IBA) universal

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FIGURE 5.4 Range modulator wheel used at the Harvard Cyclotron Laboratory. (Courtesy of B. Gottschalk.)

nozzle (26). It is located 2.8 m from isocenter where the size of the beam is in the order of 8-mm FWHM (full-width at half-maximum). Here the range modulator pattern can be made small enough that three separate 3-cm range modulator tracks are combined on one 34-cm-diameter wheel. On this wheel the range modulation pattern is not repeated. The high rotational speed (10 Hz) requires that the wheel is accurately balanced, and counterweights

FIGURE 5.5 Range modulator wheel combining three range modulation tracks as installed in the IBA universal nozzle. (Note that the outer track is used in range shifting for uniform scanning.)

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are mounted on the outside of the wheel to compensate the uneven weight distribution in the tracks. (Note that the angular width of the steps in the outer track is constant. This track is used as a variable range shifter with the wheel in stationary position when energy stacking in uniform scanning mode.) The drawback of an upstream propeller is a larger dependence on energy. The steps of an RM wheel are optimized to give a flat dose distribution for a specific energy. When the incident energy (i.e., the range of the SOBP) is changed, the weights are no longer optimal, and the SOBP no longer flat. The main reason for the change in SOBP is the change in scattering power of the RM wheel steps with energy. (Change in energy spread and source-toskin distance [SSD] also play a role but are less important.) Combined with the large drift distance to the isocenter, small changes in range modulator scattering power can cause large changes in fluence at the isocenter. When the energy of the proton beam increases, the scattering in the RM steps will decrease. For the thinnest step the scattering in the RM wheel will not contribute much to the total spread at the isocenter, which is dominated by scattering in other nozzle elements (such as the second scatterer) and the target. With increasing step thickness, range modulator scattering will contribute progressively more to the spread at the isocenter. A change in scattering power will affect the spread of the proximal layers more than the distal layers. Consequently, the increase in fluence on the beam axis associated with the decreased spread will be larger for the thicker than for the thinner steps. The increased relative weight of the proximal layers tilts the SOBP, which acquires a negative slope. The spread of the beam at the isocenter is not only proportional to the scattering angle of the range modulator steps, but to the drift space between range modulator and isocenter. For large downstream propellers, the energy dependence is less because of the shorter drift space between the RM wheel and the patient. The way to avoid this problem is using a scatter-compensated RM wheel. By combining a low-Z (plastic, carbon, aluminum) and a high-Z material (lead, tungsten) each step is given the appropriate range shift but with constant scattering power. Starting with only high-Z material for the thinnest step, the thickness of high-Z is progressively reduced, whereas the thickness of low-Z material is increased for thicker steps. As with the energycompensated contoured scatterer the scatter-compensated RM wheel has larger water equivalent thickness than an uncompensated wheel. Even with scatter compensation an upstream RM wheel is useable within a limited range span. The ability of cyclotrons to accurately and quickly vary the beam current (by manipulating the ion source current) allows for a further extension of the range over which an RM wheel can be used. By changing the beam current as function of RM wheel position, the number of protons hitting a step can be adjusted, and the intrinsic weight of the step, defined by its angular width, can be adjusted (28). Figure 5.6 shows how an SOBP with a negative slope (~1.3%/cm) is made flat by a beam current modulation profile

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Current intensity (%)

80

(a)

70 60 50 40 30

20

40 60 Time (ms)

100

80

(b)

No beam current modulation

Dose (%)

110 108 106 104 102 100 98 96 94 92 90 88 86

0

Optimized BCM measured

0

2

4

Optimized BCM calculated

6

8 10 Depth (cm)

12

14

16

FIGURE 5.6 By varying the beam current (top) synchronized with the RM wheel position a tilted SOBP can be made flat (bottom). (Reproduced from Lu and Kooy, Med. Phys., 33, 1281, 2006. With permission.)

that decreases the beam current by a factor of 2 when moving from the thin to the thick RM steps. Beam current modulation involves a complex feedback control system that needs to be closely monitored during irradiation. Drifts in ion source output, feedback ionization chamber response, and RM wheel timings can cause large dose deviations (29). We have seen that the range span an RM wheel can cover varies from a single range for an upstream wheel that is not scatter-compensated and covers a large modulation, up to a significant range span for a scatter-compensated wheel with beam current modulation. How many different modulation widths can an RM wheel deliver? The thickest step determines the maximum shift in range between the most distal and proximal Bragg peaks and defines the maximum modulation width of a wheel. If the whole track is irradiated, the maximum modulation width is always delivered, and a library of

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wheels is required to cover different target sizes. Alternatively the beam can be turned on and off (gated) synchronized with wheel position. Every wheel revolution the beam is turned on at the first step and off at the step corresponding to the most proximal layer needed to cover the target. By varying the number of steps irradiated the modulation width can be varied, up to the maximum modulation width for which a wheel is designed when all steps are irradiated. Modulation width control using beam gating is applied in both cyclotron and synchrotron systems. In cyclotron systems beam gating is performed by cutting the ion source current (26) and in synchrotron systems by turning off the extraction RF power (30). Instead of switching on and off the beam, a block can be used to cover the part of the modulator wheel that should not be irradiated. Figure 5.7 shows an example of two modulator blocks from an ocular scattering system. The same blocks can be used on different RM wheels and each wheel-block combination corresponds to a specific range and modulation width. The limited overall range and modulation span required for eye treatments result in a manageable wheel and block library. For every revolution of the RM wheel the SOBP is delivered. If the rotational speed is high enough, the delivery can be considered quasi-instantaneous, and the issues related to interplay effects with organ motion disappear. Typical rotational speeds of 6–10 Hz are larger than organ motion frequencies. Repetition of the range modulation pattern as seen before (Figure 5.4) increases the frequency of SOBP delivery even more. Synchrotron systems have an additional speed requirement because the beam spill structure is generally not synchronized with the wheel rotation. The start and end of each spill occur at random wheel positions (within the gating window). Enough complete SOBPs need to be delivered per beam spill to avoid unacceptable perturbations by partial SOBPs delivered at the start and end of each spill (23). The dose variation, ε, for a wheel with n repetitions spinning

FIGURE 5.7 Two modulator wheel blocks (left) determining the modulation width for an RM wheel (right) in the IBA eyeline.

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at f Hz in a beam with a spill time of τ s, is equal to 1/(nfτ) (23). Limiting the dose variation to 1% for a rotational speed of 10 Hz and a spill time of 2.5 s requires four repetitions. Making the range modulation pattern smaller, by moving the wheel upstream and repeating the pattern, will start to affect the delivered dose distribution once the size of the steps becomes smaller than the beam spot (31). When the beam is gated, the beam spot not only covers the gating step but spills onto neighboring steps. The steps thicker than the gating step receive some protons, and thinner steps receive less than their full weight, resulting in a softening of the shoulder at the proximal end of the uniform region. Figure 5.8 shows the effect of “partial shining” for a RM wheel designed for a range of 15 g/cm2 and full modulation width (30 steps). The track radius is 12.5 cm, and the beam spot is Gaussian with a sigma of 0.7 cm. The beam is gated on step 20, which has an arc length of 1.1 cm when there is no repetition. Repeating the pattern one, four, or six times reduces the extent of the 100% dose region by 0.2, 1.8, or 2.8 cm compared to an infinitesimally small beam. Note that proximal to the 90% dose level the dose hardly varies and that the integral dose decreases. This can be explained by the fact that although the protons not delivered on the thinner steps are all delivered on the thicker steps, these steps contribute less dose because they are pulled back and deposit more dose in the RM wheel.

Relative dose [-]

1

0.9

no spread 1 repetition 4 repetitions 6 repetitions

0.8

5 Depth [g/cm2]

10

FIGURE 5.8 The effect of the beam spilling onto multiple steps of the RM wheel when it is gated off. Proximal region of the SOBP is shown for an infinitesimal small beam and for a beam with a 7-mm sigma and one, four, or six repetitions of the modulation pattern on a 25-cm-diameter wheel.

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5.2.4  Ridge Filters Ridge filters have been applied in proton therapy for at least as long as modulator wheels (32, 33), and although less wide spread than RM wheels, they are used in several clinical scattering systems today (34–36). The principle of the ridge filter is the same as the modulator wheel: the thickness of the ridge filter steps determines the pullback of the peaks, and the width of the steps sets the weight of the peaks. Figure 5.9 shows a ridge filter designed for a modulation width of 6 cm. Protons hitting the tip of the ridge will form the most proximal peak in the SOBP; protons passing outside the ridge will form the distal peak. The thickness and width of steps in-between is optimized to provide a flat SOBP. The energy lost depends on the location where the protons hit the filter. To avoid a dependence of the SOBP shape on lateral position, the ridge is made small enough that the incident proton angular diffusion and scattering in the ridge filter smooth out any positional dependence. In the optimization of the ridge shape the scattering can be taken into account (37, 38). The width of the ridges is typically 5 mm in systems that have the ridge filter downstream of the second scatterer. By arranging many bar-shape ridges in parallel, a large beam area can be covered. Spiral ridge filters rely on the same principles as bar ridge filters, but the ridges are arranged in a circular pattern (39). Manufacturing constraints need to be taken into account when designing ridge filters. The total height needs to be limited to avoid ridges that are too sharp to be accurately machined. This limits the maximum modulation width that can be achieved. Traditionally ridge filters are made of high-Z materials, like brass, that can be machined accurately. The large stopping power of brass limits the height and gradient of the ridges, but its scattering power has a negative effect on the lateral penumbra. With improvement of machining technology, lower-Z materials like aluminum (37) and even plastics have been used. A Height of ridge (cm)

2.5

B

2.0 1.5 1.0 0.5 0 0.25

0 Ridge base (cm)

0.25

FIGURE 5.9 (A) Bar ridge filter designed to modulate the beam to a 6-cm SOBP. (B) The cross section of a ridge. (Reproduced from Akagi et al., Phys. Med. Biol., 48, N301, 2003. With permission.)

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As we have seen, energy stacking delivers the pristine peaks sequentially in time. Spinning modulator wheels deliver them sequentially as well, but are repeated every cycle of the wheel, delivering the SOBP quasi-­ instantaneously. The ridge filter delivers all pristine peaks at the same time, making SOBP delivery truly instantaneous. This makes ridge filters suitable for range modulation in systems in which the beam itself has a time structure, like synchrotron-based scattering systems with a pulsed beam of low duty cycle or uniform scanning systems in which the beam is scanned over a ridge filter (40, 41). The main drawback of ridge filters is the fact that they can only be used for a single modulation width. A possible solution is tilting the bar ridge filter (41 and references within). Rotating the ridge filter θ degrees in the plane of the beam axis and the long axis of the ridges increases the thickness of all ridge steps by 1/cos(θ). Unlike the gated modulator wheel that increases modulation by adding more pristine peaks, the tilted ridge filter keeps the same number of peaks but increases the pullback between the peaks. The number of steps in the ridge needs to be large enough to avoid a ripple in the SOBP at maximum tilt. Feasibility has been shown experimentally for a ridge filter increasing modulation width from 10 to 14.5 cm when tilting 45° (41). The miniature ridge filter is designed to be used in combination with energy stacking (42). It spreads the mono-energetic Bragg peak into a wider peak; energy stacking combines multiple range-shifted wide peaks into an SOBP. In this hybrid delivery technique the number of energy layers is reduced compared to pure energy stacking. The delivery efficiency is increased, whereas interplay effects with respect to organ motion are reduced. The modulation width can be varied although with a worse resolution than can be obtained with pure energy stacking or gated RM wheels. On the downside, the broadening of the peaks deteriorates the distal falloff of the SOBP. In another method of combining the ridge filter and energy stacking, the miniature ridge filter is used to combine the distal pristine peaks into a small-modulation SOBP width, and energy stacking is used to vary the modulation by adding mono-energetic pristine peaks proximally (N. Schreuder and G. Mathot, private communication, December 2010). Application of these forms of range modulation has only been reported in uniform scanning systems, but could in principle be applied in scattering systems as well. A miniature ridge filter can also extend the energy range over which a ridge filter can be applied (43). If the beam energy is decreased below the energy for which a ridge filter is designed, the width of the peaks will become sharper (specifically for synchrotron systems that have a small energy spread at low energies), the pullback between peaks is no longer optimal, and a ripple appears in the SOBP. To counter the sharpening of the peaks, a miniature ripple filter increases the energy spread of the protons and widens the peaks. A library of a few ridge filters and mini-ridge filters can cover the complete clinical range span.

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5.3  Conforming Techniques The second scatterer spreads the beam to a uniform lateral distribution; the RM wheel spreads the dose to a uniform depth–dose distribution. Clearly something is needed to conform the dose to the target. As in conventional external radiotherapy, a block, called an aperture in proton therapy, shapes the dose laterally. Alternatively, a multileaf collimator (MLC) can be used. Unlike conventional radiotherapy, the sharp distal falloff of the proton beam allows conforming the beam to the distal end of the target. A range compensator is designed to perform this function. 5.3.1  Aperture The shape of the aperture is defined by the shape of the target projected along the beam axis with added margins accounting for penumbra width and setup uncertainty. Because of the large geometric source size of a protonscattering system, it is important to bring the aperture close to the patient. Large air gaps inflate the lateral penumbra undesirably. The aperture and range compensator are mounted together on a snout. The snout travels along the beam axis and brings the aperture close to patient skin. Based on the snout position, the virtual source-to-axis distance (SAD) of the scattering system, and the projection of the target onto the isocenter plane, a simple back projection gives the physical shape of the aperture. The primary physical consideration in selecting aperture material is stopping power. High-Z materials are the obvious choice as they stop the protons in the shortest physical distance. From a practical point of view we want a material that can be manufactured easily and cheaply. The two materials that are commonly used are brass and cerrobend. Brass apertures are cut with a milling machine; cerroband apertures are poured into a mold. It should be pointed out that such an aperture will completely stop the beam. Because of the finite range of the protons the chance is zero that a primary proton will traverse the complete aperture. Unlike x-ray therapy, leakage of primary protons through the aperture does not exist. This does not mean that all protons hitting the aperture will be absorbed. Protons hitting the upstream face close to the aperture opening can escape through the inner surface of the opening; protons hitting the inner surface can scatter out of the aperture through the inner surface or escape through the downstream face. These slit-scattered protons perturb the dose distribution specifically at shallow depth and near the field boundary (44, 45). The aperture and snout are the largest contributors of neutrons to the patient (46) (see Chapter 18). Not only do they completely absorb highenergy protons in material with a large cross section for neutron production, they do it close to the patient. Several approaches to reduce neutrons have been investigated. Changing the aperture material would not reduce

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the neutron dose dramatically. Stopping 235-MeV protons in nickel instead of brass reduces the neutron dose by about 15% (47). A bigger reduction can be obtained by using a precollimator, limiting the number of protons hitting the aperture (47–49). A related radiation safety issue is the activation of the apertures (50, 51). Activation levels are low enough to avoid special procedures in the daily handling of the apertures by staff. For disposal of the apertures, activation levels need to be below the background. Irradiation of brass yields several isotopes with relevant activation and half-lives (58Co − T1/2 = 71 d, 57Co − T1/2 = 271 d). In typical clinical practice apertures are stored for about two weeks when activation has reached background levels. 5.3.2  Multileaf Collimator In conventional radiotherapy the MLC has become the standard field-­ shaping device. Perhaps surprisingly MLCs are currently not applied much in proton therapy. The vast majority of proton treatments today use custommade apertures. A possible explanation might be that scattering systems with their apertures and range compensators are expected to be replaced by pencil beam scanning systems that do not need field-shaping hardware (Chapter 6). Implementation of an MLC could be seen as an unnecessary intermediate step. Related is the fact that even if an MLC replaces the aperture block, the field-specific range compensators still need to be manufactured and installed in-between treatment fields. Still, the MLC is receiving more attention of late, and several centers have successfully implemented an MLC in their proton-scattering system (9; McDonough J., private communication, December 2010). The main issues when considering an MLC for proton therapy are not different from conventional radiotherapy: penumbra and conformity, leakage, neutron production, and activation. An additional concern is clearance: given the large source size of many proton-scattering systems, it is important to bring the final collimator as close as possible to the patient, which might be difficult with bulky MLCs. In collaboration with Varian, the University of Pennsylvania has developed a proton MLC to be used with their IBA universal nozzle (McDonough J., private communication, December 2010). It consists of two banks of 50 tungsten leaves. Leaf width is 4.4 mm; leaf height 6 cm. The parallel and abutting sides have steps of 0.45 and 0.30 mm, respectively, to limit leakage. For a 30-cm snout position the maximum projected opening is 25 × 18 cm 2. Preliminary results show that the scalloping effect of the leaves on the dose distribution is clinically acceptable. Multiple scattering of the protons in the target smear out the leaf effects with depth. Although tungsten has a higher neutron yield than brass, maximum neutron dose levels for a 230-MeV proton beam are about 20% lower for the MLC compared to a 6.5-cm brass aperture. This is presumably because of the self-shielding effect of the additional tungsten on top of the 3.5 cm required to stop a 230-MeV proton beam (about 6-cm

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brass is required). This self-shielding also limits the measured activation on the downstream face to levels far below regulatory limits. In addition to the MLC a “range compensator loader” has been installed that can hold up to two compensators and eliminates the need to go into the room between fields. Massachusetts General Hospital has implemented a mini-MLC in its radiosurgery beam line (9). Although this MLC was designed for stereotactic treatments on a linear accelerator, it behaves well in the proton beam. For a typical field, agreement between an MLC-shaped and a custom aperture– shaped field is within 1.5 mm or 2%. The leakage dose is below the measurement threshold (0.3%). The neutron dose for the MLC is 1.5–1.8 times higher than for the brass aperture. Alternative applications of the MLC in proton therapy have been considered. Tayama et al. have described the MLC as a precollimator to a custommade aperture (48). By reducing the proton flux onto the final aperture, the neutron dose to the patient is significantly reduced. Bues et al. has proposed the MLC as a method to sharpen the penumbra in low-energy, spot-scanning treatments (52). Full-blown, intensity-modulated proton therapy (IMPT) using MLCs, equivalent to intensity-modulated radiotherapy with photons, might conceptually seem appealing. However, the large inefficiency of such an approach, resulting in high neutron doses and activation, makes it hard to see it as a reasonable alternative to IMPT using scanned proton pencil beams (Chapter 6). On the other hand, the flexibility of the MLC can be used to improve dose conformity compared to a single-aperture field. In systems that apply energy stacking to create the SOBP, the MLC opening can be optimized per energy layer (53). Because each point of the target needs to get the dose contributions of all upstream layers to achieve full dose, the collimator opening for a layer can never be larger than the opening of the previous layers. The collimator can only be progressively closed while stepping from the distal to the proximal layers. Improved proximal conformity will only be achieved in convex targets. 5.3.3  Range Compensator The range compensator conforms the dose to the distal end of the target. Figure 5.10 shows a schematic representation of the application of range compensation. The water-equivalent depth of the distal end of the target varies with lateral position. It is a function of the shape of both external body contour and target, as well as of the composition of the tissue in-between. The range compensator is designed to remove the depth variation by adding more absorbing material in areas where the depth is small and less where it is large. For example, the energy loss in the high-density structure in Figure 5.10 is compensated for by removing more material from the compensator. It is obvious that each treatment field has a unique compensator. Designing the range compensator is an important part of the treatment-planning

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A

B

C range compensator skin

high-density heterogeneity target

FIGURE 5.10 Schematic representation of the application of a range compensator that compensates for the shape of the body entrance, the distal target shape, and inhomogeneities.

process. Most algorithms use a ray-tracing algorithm to determine the water-­ equivalent depth of selected points on the distal surface of the target (54–56). The deepest point will determine the required proton range. For each of the other points, the difference in depth with the deepest point determines required pullback. The matrix of pullbacks is divided by the compensator’s relative stopping power to obtain physical thickness. To accurately model the effect of the real compensator, the milling pattern as described below can be applied to the compensator model before the final dose calculation. Correct compensation is only achieved if the range compensator is exactly aligned to the geometry and heterogeneities for which it compensates. Misalignment causes the dose to fall short, resulting in underdosage of the target, and/or to overshoot, resulting in dose to normal tissue distal to the target. Smearing is a geometrical operation applied to the range compensator to account for uncertainties (Chapter 10). Ideally the range compensator provides pullback with as little scattering as possible. Scattering decreases the compensator’s conforming ability and generates undesirable cold and hot spots inside the target. Low-Z, highdensity materials give the least scattering per energy loss. Lucite and wax are the two materials most commonly used. Proponents of wax favor it because it is easier (faster) to mill, has lower cost, and can be recycled. Lucite users value its transparency, which allows for visual screening for air pockets and validation of the iso-height lines by placing it on a paper printout during quality assurance. A standard milling machine mills the desired profile into a blank compensator. Resolution needs to be weighed against speed when selecting drill bit size and spacing. The smallest drill provides the best lateral resolution in conforming the dose, but it takes the longest to drill. Because of scattering there is a lower limit below which reduction of the drill bit

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size does not significantly improve conformity anymore. A typical drilling pattern will use a 5-mm-diameter drill bit and a spacing of 5 mm. For such a pattern, machining times (for Lucite) range from 10 min for a small brain lesion, 45 min for a prostate, and up to 4 h for a 2-L sarcoma field. The tapering (angle) of the drill bit affects the magnitude of the dose perturbation created by large range compensator gradients (57). A gradient in the range compensator will scatter more protons from the thick part to the thin part than vice versa, creating a cold spot beyond the thicker part and a hot spot beyond the thinner part. If the gradient is exactly parallel to the beam axis the magnitude of the dose perturbation is maximal. When irradiating a 4-cm-deep, 0.5-cm-diameter hole in acrylic with 160-MeV protons, ±20% dose perturbations are observed 1 cm downstream. By applying a tapered drill bit, the gradient becomes less steep, reducing the dose perturbation to ±15%/±5% for a 1.5º/3º tapering, respectively. A 3º tapering is common because it reduces the scattering to an acceptable level without compromising the lateral resolution too much in most clinical situations. An interesting approach to limit the compensator scattering perturbations is the bi-material range compensator (58). By combining the low-Z compensating material with a high-Z scattering material a compensator can be designed with the desired range compensation pattern but also with constant scattering power. (This is similar to the approach taken with the scatter-compensated RM wheel described above.) The drawback of such an approach, besides added complexity in design, fabrication, and quality assurance, is that it increases the overall compensator thickness. As result a bi-material compensator requires larger proton range and has worse lateral penumbra because of increased scattering.

5.4  Scattering Systems In the previous sections we discussed the individual elements of passive scattering systems. In this section we will focus on integrated scattering systems. The number of different scattering systems is almost as big as the number of proton therapy centers. This makes a general description of scattering systems complicated. The approach taken here is to discuss a few representative scattering systems in more or less detail. We will describe the scattering systems and refer to Gottschalk (11) for a detailed discussion of the design methods and tools. First we will discuss several “general purpose” scattering systems. These large-field double-scattering systems can be seen as the proton equivalent to the standard x-ray linear accelerators. They have been designed to treat a large variety of target sizes and depths and are gantry mounted. Next we will discuss a single-scattering system that has been designed to treat a specific target, the eye. This system is mounted at the

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end of a fixed beam line. It should be emphasized that the choice of scattering systems discussed is purely based on their familiarity to the author and availability in the literature, not on presumed superiority over other systems. 5.4.1  Large-Field Double-Scattering Systems Table 5.1 gives an overview of three commercially available, turnkey proton therapy systems that use double scattering on a gantry (26, 30, 59). Two of the systems have a synchrotron, and the third a cyclotron. The three systems are similar in design, all applying RM wheels to create the SOBP and a contoured second scatterer to flatten the lateral profile. The Optivus system has the RM wheel downstream of the second scatterer, and both the Hitachi and IBA systems have an upstream range modulator. Figure 5.11 shows the layout of the IBA universal nozzle in detail. It is called universal because it permits irradiations not only in double-scattering mode, but also in single-scattering, uniform-scanning, and pencil beam–scanning modes. The Hitachi nozzle, which has only the double-scattering delivery mode, is shown in Figure 5.12. The IBA nozzle uses two contoured scatterers to spread the beam to a uniform field diameter of 24 cm for ranges from 4.6 to 23.9 g/cm2 in water. The amount of scattering material (first and second scatterer) needed to scatter the beam to this field size reduces the maximum cyclotron range (~34 g/cm2) significantly. To treat deeper seated targets a third, thinner second scatterer is added that allows treatments up to 28.4 g/cm2 depth, but with a limited field diameter of up to 14 cm. All three contoured scatterers are energy compensated, combining Lexan and lead. They are mounted together on a large wheel that is located 178 cm from the isocenter. Before the start of irradiation TABLE 5.1 Commercially Available Turnkey Proton Therapy Systems with Double Scattering Manufacturer Optivus

Installations

Loma Linda University Medical Center (1991) Ion Beam Massachusetts General Applications Hospital (2001) Wanjie Hospital, Wanjie, China (2004) University of Florida (2006) National Cancer Center, Ilsan, South Korea (2006) University of Pennsylvania (2009) Institute Curie, Paris, France (2010) Hitachi M.D. Anderson Cancer Center (2006)

Accelerator

Range Modulation

Lateral Spreading

Synchrotron (250MeV) Cyclotron (235MeV)

RM Wheel Downstream RM Wheel Upstream

Contoured scatterer Contoured scatterer

Synchrotron (250MeV)

RM Wheel Upstream

Contoured scatterer

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Range modulator wheels Magnet 2 IC1 Jaws (X and Y) (and range verifier) Snout retraction area Water phantom

Snout

First scatterers Magnet 1 Second scatterers IC2 and IC3

FIGURE 5.11 Schematic layout of the IBA universal nozzle. (Reproduced from Paganetti et al., Med. Phys., 31, 2107, 2004. With permission.)

the appropriate scatterer is rotated into the beam path. The variable collimators are set to block the beam outside the aperture opening. Unlike the IBA nozzle that always spreads the beam to the maximum field diameter, the Hitachi nozzle has contoured scatterers optimized for different field sizes. By scattering the beam less for smaller targets the efficiency of the system is improved, increasing maximum dose rate and range and reducing production of secondary neutrons in the nozzle. In addition, the lateral penumbra is improved for small fields. The system provides three field sizes: 25 × 25, Beam

Profile Monitor Reference Dose Monitor X-Ray Tube Range Shifters Laser Marker

Range Modulation Wheel Second Scatterers

Main Dose Monitor Sub Dose Monitor

Block Collimator

Square Collimator Multi Layer Faraday Cup

Snout

Isocenter

FIGURE 5.12 Schematic layout of the Hitachi large-field scattering nozzle. (Reproduced from Smith et al., Med. Phys., 36, 4068, 2009. With permission.)

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18 × 18, and 10 × 10 cm2. For each field size, three second scatterers cover the whole range span, resulting in a total of nine second scatterers. The maximum range for each of the field sizes is 25.0, 28.5, and 32.4 g/cm 2, respectively. It is interesting to see that the maximum range for the 10 × 10-cm2 field size is 4.0 g/cm2 larger than the maximum range for the equivalent field size ( 2 ⋅ 10 = 14-cm diameter) in the IBA nozzle. This is equal to the difference in maximum accelerator range. (The synchrotron energy of 250 MeV corresponds to a range in water of 38 g/cm2 and the cyclotron energy of 235 MeV to a range of 34 g/cm2.) The thickness of the scattering material required is similar because of the similar position of the scattering elements inside both nozzles. The Hitachi system extracts eight energies from the synchrotron. An RM wheel has been designed for each of the 24 energy and field-size combinations. The steps of the RM wheel are scatter compensated resulting in a constant scattering power over the steps. As range-shifting material plastic or aluminum is used and for scattering compensation tungsten. The wheel not only acts as a modulator, but also as the first scatterer in the double-­scattering system. Additional tungsten is added to provide, combined with the second scatterer, the desired uniform field size at the isocenter. The fine range adjustment in the Hitachi nozzle is done with a variable range shifter located downstream of the second scatterer. In the IBA nozzle the range adjustment is done by changing the energy of the protons entering the nozzle (using the energy-selection system at the exit of the cyclotron). As a result the RM wheels are not used at a single energy, but for a range of energies. As the beam energy increases the scattering power of both the RM wheel and second scatterer decreases, resulting in a nonflat lateral profile at the isocenter. This can be compensated for by adding additional scattering material to the first scatterer. In the IBA nozzle adjustment of scattering is done by the fixed scatterer, a binary set of lead foils that can be inserted independently into the beam path and that is located upstream of the RM wheel. The RM wheel and first scatterer combine to form a first scatterer with variable scattering power. The RM steps are scatter compensated, limiting the effect of change in scattering power on the pristine peak weights and increasing the range of energies over which a flat depth–dose curve is generated. Still, an RM wheel track can only be used for a range span of 0.4 g/cm 2 for the lowest ranges and up to 2.0 g/cm2 for the highest ranges. By applying beam current modulation, adjusting the beam current as a function of modulator wheel position, the number of modulator wheels can be limited. A total of five modulator wheel tracks covers the complete energy range. Unlike the Hitachi system where the RM wheels are loaded manually, the IBA nozzle has an automated system. Three range modulator tracks are combined on a single wheel (Figure 5.5), and three wheels are mounted on a large wheel whose position determines which track is in the beam path. (The four remaining tracks are used in single scattering and uniform scanning.) Because the cyclotron generates a continuous beam, the speed requirements are not very stringent for

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the IBA RM wheels. They spin at 600 rpm, and the modulation pattern is not repeated. The Hitachi RM wheels spin at 400 rpm, and the modulation pattern is repeated six times per revolution, washing out the effects of the beam pulse structure on the SOBP shape. In both systems the beam’s turning on and off is synchronized with the wheel rotation, allowing for variation of the modulation width. The repetition of the pattern on the Hitachi wheel causes more beam spilling over the steps and a softer shoulder on the proximal side of the SOBP compared to the single pattern of the IBA track. Both nozzles have ionization chambers at the entrance and exit of the nozzle to monitor the beam properties and terminate the beam once the prescribed dose has been reached. A snout that can move along the beam axis holds the aperture and range compensator and collimates the beam outside the aperture. Both systems have a library of three snouts. Depending on the field size, the appropriate snout is installed before treatment. The dosimetric properties of the delivery system depend mostly on the design of the scattering system. Figure 5.13 shows the virtual SAD of the IBA nozzle, determined by back-projecting the 50% field width in air as measured in several planes along the beam axis. For all ranges the source position falls between the range modulator (270 cm) and the second scatterer (178 cm) as expected. For options that use the same second scatterer, the SAD increases continuously with range. Given all that has been said before, it is not that difficult to explain the observed behavior. The scattering power of the second scatterer decreases as the range increases. To compensate, the scattering power of the first scatterer is increased either by adding additional scattering material to the RM wheel (between options) or by increasing the fixed scatterer thickness (within an option). (An option is a combination of

Virtual SAD [cm]

260

SS1 SS2 SS3

240

220

10

Range [g/cm2]

20

30

FIGURE 5.13 Virtual SAD as function of range in patient for the double-scattering options of the IBA universal nozzle.

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Source size [cm]

4

2

option 1 - step 1 option 2 - step 1 option 3 - step 1 option 4 - step 1 option 5 - step 1 option 6 - step 1 option 7 - step 1 option 8 - step 1 option 5 - steps 1, 6, 13 option 8 - steps 1, 3, 5

10

Range [g/cm2]

20

30

FIGURE 5.14 Effective source size as function of range in patient for the double-scattering options in the IBA universal nozzle.

an RM wheel track and second scatterer.) The increased scattering power of the first scatterer pulls the source toward it, increasing the SAD. The smallfield second scatterer is thinner than the two large-field second scatterers, resulting in a source position closer to the first scatterer and a larger SAD. Figure  5.14 shows the source size as function of range. The source size is determined by measuring the lateral penumbra in air at several distances from a square aperture. The measured 80%–20% penumbra is back-projected to a nominal source position of 230 cm. The source size of the large-field options (options 1–7) is significantly smaller than the small-field option (option 8). The additional scattering to spread the beam to a larger diameter increases the angular confusion of the beam. Within the large-field options the source size decreases continuously with range. 5.4.2  Single-Scattering System for Eye Treatments Ocular tumors have been successfully treated with protons for decades. Most eye lines spread the beam with single scattering (2, 4, 5, 7, 8) or an occluding beam stopper (3, 6), although contoured second scatterers (30) have been applied as well. Figure 5.15 shows the IBA eye line whose design is based on the eye line at the Centre de Protonthérapie Orsay in France. The beam is brought into the room at a fixed energy of 105 MeV. After passing through a beam monitor, the protons hit the RM wheel spinning at 1200 rpm. The RM wheels are not scatter-compensated and can be used within a very small range span (0.2–0.4 g/cm2). Eleven wheels are required to cover ranges from 0.3 to 3.4 g/cm2. The wheels are designed for full modulation, and blocks are used to vary the modulation width (Figure 5.7). The blocks are made of brass

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Fixed range shifter

Range Variable modulator range wheel shifter

Aperture

105 MeV protons Vacuum window

Ionization chambers

Collimator & neutron shield 180 cm

FIGURE 5.15 Schematic representation of the IBA eye line that applies single scattering to spread the beam.

and are 1.2 cm thick. Both the RM wheel and block are loaded manually. Next the beam passes through a variable range shifter and scatterer system. For a given range and field size the appropriate Lucite range shifter plates and lead scattering foils are selected. A brass collimator blocks the majority of protons. The neutron shield downstream of the collimator is intended to absorb most of the neutrons generated in this collimation. The virtual source position of this system is located between the RM wheel and the variable range shifter system where most of the scattering takes place. The resulting SAD is about 150 cm. Because the distance between the RM wheel and variable range shifter is small, the angular diffusion of the beam and thus the effective source size are small. Given the large SAD and small source size, the penumbra of this system is very sharp. The 80%–20% penumbra in air at 7 cm from the final aperture is 1.2 mm.

5.5  Conclusion Proton-scattering systems have some major drawbacks compared to scanning systems. The protons interact with the scattering and range modulation material in the nozzle. They lose energy, decreasing the maximum penetration depth of the beam, and gain angular diffusion, increasing lateral penumbra. Nuclear interactions will cause activation and create unwanted secondary particles such as neutrons. Apertures and range compensators need to be made for every treatment field requiring an expensive and labor-intensive fabrication and quality assurance process. In a state-of-theart proton scanning system no field-specific hardware is required, and no

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interaction of the proton beam with nozzle material occurs. Depending on the size and shape of the target, a scanning system also allows for better dose conformity, reducing the integral nontarget dose. Still, the vast majority of proton therapy treatments worldwide has been and continues to be delivered with scattering systems (60). The main reason for this is the robustness of typical scattering systems. As long as the correct nozzle elements are placed in the beam path (either stationary or rotating), the delivered dose will be correct. No sophisticated beam control and feedback systems are required as in a pencil beam–scanning system. Also the dose delivery itself is more robust in that it is less sensitive to organ motion. In a scattering delivery the whole target will be irradiated (quasi) instantaneously; in a scanning delivery, different parts of the target will be irradiated sequentially. With the development and implementation of more scanning-based proton therapy systems in the coming years, it will become clear if scanning will become the prevalent mode of delivery or if scattering will remain the dominant technology.

References

1. Preston WM, Koehler AM. The effects of scattering on small proton beams. [Online]. 1968 [cited 2010 December 10]; available from http://huhepl.harvard. edu/˜gottschalk/BGDocs.zip. 2. Montelius A, Blomquist E, Naeser P, Brahme A, Carlsson J, Carlsson AC, et al. The narrow proton beam therapy unit at the Svedberg Laboratory in Uppsala. Acta Oncol. 1991;30(6):739–45. 3. Bonnett DE, Kacperek A, Sheen MA, Goodall R, Saxton TE. The 62 MeV proton beam for the treatment of ocular melanoma at Clatterbridge. Br J Radiol. 1993 Oct;66(790):907–14. 4. Moyers MF, Galindo RA, Yonemoto LT, Loredo L, Friedrichsen EJ, Kirby MA, et al. Treatment of macular degeneration with proton beams. Med Phys. 1999 May;26(5):777–82. 5. Newhauser WD, Burns J, Smith AR. Dosimetry for ocular proton beam therapy at the Harvard Cyclotron Laboratory based on the ICRU Report 59. Med Phys. 2002 Sep;29(9):1953–61. 6. Cirrone GAP, Cuttone G, Lojacono PA, Lo Nigro S, Mongelli V, Patti IV, et al. A 62-MeV proton beam for the treatment of ocular melanoma at Laboratori Nazionali del Sud-INFN. IEEE Trans Nucl Sci. 2004;51(3):860–65. 7. Hérault J, Iborra N, Serrano B, Chauvel P. Monte Carlo simulation of a protontherapy platform devoted to ocular melanoma. Med Phys. 2005 Apr;32(4):910–19. 8. Michalec B, Swakon´ J, Sowa U, Ptaszkiewicz M, Cywicka-Jakiel T, Olko P. Proton radiotherapy facility for ocular tumors at the IFJ PAN in Kraków Poland. Appl Radiat Isot. 2010 Apr-May;68(4-5):738–42. 9. Daartz J, Bangert M, Bussière MR, Engelsman M, Kooy HM. Characterization of a mini-multileaf collimator in a proton beamline. Med Phys. 2009 May;36(5):1886–94.

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29. Lu HM, Brett R, Engelsman M, Slopsema R, Kooy H, Flanz J. Sensitivities in the production of spread-out Bragg peak dose distributions by passive scattering with beam current modulation. Med Phys. 2007 Oct;34(10):3844–53. 30. Smith A, Gillin M, Bues M, Zhu RX, Suzuki K, Mohawk R, et al. The M. D. Anderson proton therapy system. Med Phys. 2009 Sep;36(9):4068–83. 31. Li Y, Zhang X, Lii M, Sahoon N, Zhu RX, Gillin M, et al. Incorporating partial shining effects in proton pencil-beam dose calculation. Phys Med Biol. 2008 Feb 7;53(3):605–16. 32. Larsson B. Pre-therapeutic physical experiments with high energy protons. Br J Radiol. 1961 Mar;34:143–51. 33. Lomanov M. The Bragg curve transformation into a prescribed depth dose distribution. Med Radiol. 1975;11:64–69. 34. Inada T, Hayakawa Y, Tada J, Takada Y, Maruhashi A. Characteristics of proton beams after field shaping at PMRC. Med Biol Eng Comput. 1993 Jul;31 Suppl:S44–S48. 35. Kostjuchenko V, Nichiporov D, Luckjashin V. A compact ridge filter for spread out Bragg peak production in pulsed proton clinical beams. Med Phys. 2001 Jul;28(7):1427–30. 36. Ando K, Furusawa Y, Suzuki M, Nojima K, Majima H, Koike S, et al. Relative biological effectiveness of the 235 MeV proton beams at the National Cancer Center Hospital East. J Radiat Res (Tokyo). 2001 Mar;42(1):79–89. 37. Akagi T, Higashi A, Tsugami H, Sakamoto H, Masuda Y, Hishikawa Y. Ridge filter design for proton therapy at Hyogo Ion Beam Medical Center. Phys Med Biol. 2003 Nov 21;48(22):N301–12. 38. Fujimoto R, Takayanagi T, Fujitaka S. Design of a ridge filter structure based on the analysis of dose distributions. Phys Med Biol. 2009 Jul 7;54(13):N273–82. 39. Khoroshkov VS, Breev VM, Zolotov VA, Luk’iashin VE, Shimchuk GG. Spiral comb filter. Med Radiol (Mosk). 1987 Aug;32(8):76–80. 40. Akagi T, Higashi A, Tsugami H, Sakamoto H, Masuda Y, Hishikawa Y. Ridge filter design for proton therapy at Hyogo Ion Beam Medical Center. Phys Med Biol. 2003 Nov 21;48(22):N301–12. 41. Nakagawa T, Yoda K. A method for achieving variable widths of the spread-out Bragg peak using a ridge filter. Med Phys. 2000 Apr;27(4):712–15. 42. Fujitaka S, Takayanagi T, Fujimoto R, Fujii Y, Nishiuchi H, Ebina F, et al. Reduction of the number of stacking layers in proton uniform scanning. Phys Med Biol. 2009 May 21;54(10):3101–11. 43. Takada Y, Kobayashi, Y Yasuoka K, Terunuma T. A miniature ripple filter for filtering a ripple found in the distal part of a proton SOBP. Nucl. Instrum. Methods Phys Res A. 2004 Ajn 29;524:366–73. 44. van Luijk P, van t, Veld AA, Zelle HD, Schippers JM. Collimator scatter and 2D dosimetry in small proton beams. Phys Med Biol. 2001 Mar;46(3):653–70. 45. Titt U, Zheng Y, Vassiliev ON, Newhauser WD. Monte Carlo investigation of collimator scatter of proton-therapy beams produced using the passive scattering method. Phys Med Biol. 2008 Jan 21;53(2):487–504. 46. Pérez-Andújar A, Newhauser WD, Deluca PM. Neutron production from beammodifying devices in a modern double scattering proton therapy beam delivery system. Phys Med Biol. 2009 Feb 21;54(4):993–1008. 47. Brenner DJ, Elliston CD, Hall EJ, Paganetti H. Reduction of the secondary neutron dose in passively scattered proton radiotherapy, using an optimized precollimator/collimator. Phys Med Biol. 2009 Oct 21;54(20):6065–78.

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48. Tayama R, Fujita Y, Tadokoro M, Fujimaki H, Sakae T, Terunuma T. Measurement of neutron dose distribution for a passive scattering nozzle at the Proton Medical Research Center (PMRC). Nucl Instrum Methods Phys Res A. 2006; 564:532–36. 49. Taddei PJ, Fontenot JD, Zheng Y, Mirkovic D, Lee AK, Titt U, et al. Reducing stray radiation dose to patients receiving passively scattered proton radiotherapy for prostate cancer. Phys Med Biol. 2008 Apr 21;53(8):2131–47. 50. Faßbender M, Shubin YN, Lunev VP, Qaim SM. Experimental studies and nuclear model calculations on the formation of radioactive products in interactions of medium energy protons with copper, zinc and brass: Estimation of collimator activation in proton therapy facilities. Appl Radiat Isot. 1997; 9:1221–30. 51. Sisterson JM. Selected radiation safety issues at proton therapy facilities. 12th Biennial Topical Meeting of the Radiation Protection and Shielding Division of the American Nuclear Society (Santa Fe, NM) [Online]. 2002 [cited 2010 Dec 5]; available from http://gray.mgh.harvard.edu/content/dmdocuments/ Janet2002.pdf. 52. Bues M, Newhauser WD, Titt U, Smith AR. Therapeutic step and shoot proton beam spot-scanning with a multi-leaf collimator: a Monte Carlo study. Radiat Prot Dosimetry. 2005;115(1-4):164–69. 53. Kanai T, Kawachi K, Matsuzawa H, Inada T. Broad beam three-dimensional irradiation for proton radiotherapy. Med Phys. 1983 May-Jun;10(3):344–46. 54. Goitein M. Compensation for inhomogeneities in charged particle radiotherapy using computed tomography. Int J Radiat Oncol Biol Phys. 1978 May-Jun;4(5-6):499–508. 55. Urie M, Goitein M, Wagner M. Compensating for heterogeneities in proton radiation therapy. Phys Med Biol. 1984 May;29(5):553–66. 56. Petti PL. New compensator design options for charged-particle radiotherapy. Phys Med Biol. 1997 Jul;42(7):1289–300. 57. Wagner MS. Automated range compensation for proton therapy. Med Phys. 1982 Sep-Oct;9(5):749–52. 58. Takada Y, Himukai T, Takizawa K, Terashita Y, Kamimura S, Matsuda H, et al. The basic study of a bi-material range compensator for improving dose uniformity for proton therapy. Phys Med Biol. 2008 Oct 7;53(19):5555–69. 59. Moyers MF. Proton Therapy. In: The Modern Technology of Radiation Oncology, Van Dyk J, editor. Madison (WI): Medical Physics Publishing; 1999, 823–69. 60. Jermann M. Hadron Therapy Patient Statistics. [Online]. March 2010 [cited 2010 Dec 10]; available from http://ptcog.web.psi.ch/Archive/PatientenzahlenupdateMar2010.pdf.

6 Particle Beam Scanning Jacob Flanz CONTENTS 6.1 Introduction................................................................................................. 158 6.1.1 General Description of Scanning................................................. 159 6.1.2 Limits of Scanning Implementations........................................... 160 6.1.3 Safety................................................................................................ 162 6.2 Parameters That Affect the Beam and Dose Delivery........................... 162 6.2.1 Static Beam Parameters.................................................................. 162 6.2.1.1 Depth–Dose Distribution................................................ 162 6.2.1.2 Transverse Dose Distribution and Modulation........... 163 6.2.2 Motion Beam Parameters.............................................................. 167 6.2.2.1 Motion Effects................................................................... 167 6.3 Time Sequence of Beam Scanning Tasks................................................. 169 6.3.1 Scanning Techniques..................................................................... 170 6.3.2 Contributions to Time.................................................................... 172 6.4 Scanning Hardware................................................................................... 174 6.4.1 Adjust the Beam Properties........................................................... 175 6.4.1.1 Energy................................................................................ 175 6.4.1.2 Size..................................................................................... 175 6.4.1.3 Position on the Target...................................................... 176 6.4.1.4 Scan Patterns..................................................................... 177 6.4.2 Dose Rate......................................................................................... 177 6.5 Scanning Instrumentation and Calibration............................................ 177 6.5.1 Calibration....................................................................................... 178 6.5.2 Calibration of the Beam Position at the Isocenter...................... 178 6.5.3 Calibration of the Beam Size at the Isocenter............................. 179 6.5.4 Calibration of the Dose Delivery at the Isocenter...................... 179 6.5.5 On-line Verification of Beam Position.......................................... 180 6.5.6 Beam Steering Corrections............................................................ 180 6.6 Scanning Gantries...................................................................................... 181 6.7 Beam Property Quality Assurance (QA)................................................. 183 6.8 Safety............................................................................................................ 184 6.8.1 Safety Strategy................................................................................. 185 6.8.2 Beyond Safety.................................................................................. 185 6.9 Summary...................................................................................................... 187 157

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Acknowledgments............................................................................................... 188 References.............................................................................................................. 188

6.1  Introduction The dimensions of a clinical target are typically different from the dimensions of an unmodified particle beam. The beam extracted and transported from a typical accelerator will have dimensions on the order of millimeters and will have a narrow energy spectrum that results in a narrow spread of ranges in a target. Therefore that beam has to be spread out in three dimensions to match the target volume. In this chapter the method of spreading called beam scanning will be described. Beam scanning is quite a general technique, and although it has acquired many acronyms such as PBS (particle beam scanning or pencil beam scanning), IMPT (intensity-modulated proton therapy), and SS (spot scanning), coming from specific implementations of the technology and limitations of accelerator beam properties. These acronyms only serve to minimize the power and generality of this beam spreading approach. Particle beam scanning (hereafter abbreviated as PBS) can be defined as the act of moving a charged particle beam of particular properties and perhaps changing one or more of the properties of that beam for the purpose of spreading the dose deposited by a beam throughout the target volume. Some examples (nonexhaustive) of these properties include position, size, range, and intensity, which are all adjusted in such a way as to deposit the appropriate dose at the correct location and time. Physical equipment in the system is used to control these properties. For example, the beam position on target can be controlled using magnetic fields or other mechanical motion techniques. Other properties are modified using other equipment. When a beam penetrates the target, it delivers dose to the intercepting volume along the beam trajectory. The goal of this beam delivery is to deliver dose according to a prescription. This prescription provides a map of the dose that is necessary to deliver at each region in the target. The beam parameters can and should be able to change on a location-by-location basis; for example, two locations can have different ranges or beam size. In the transverse dimension, there are a variety of ways of moving the beam across the target. Some of these methods include the following: • Scanning by mechanical motions • Physically moving the target with respect to a fixed beam position • Mechanically moving a bending magnet to change the position of the transported beam • Using an adjustable collimator to effectively adjust the location/ region of the beam

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• Scanning by magnetic field variation to bend the beam trajectory • Scanning an unmodified beam (sometimes called a pencil beam) • Scanning a slightly scattered beam, so that the beam scanned on the target is a larger size. This is called “wobbling.” • Combinations of the above • Two-dimensional (2D) “ribbon” scanning of a beam wide in the dimension perpendicular to the direction of motion, with the beam extent adjusted by a variable collimator • Scanning the beam magnetically in one dimension and moving the target mechanically in the other dimension • Other combinations are possible In fact, the first implementation of a scanning beam was demonstrated in Japan using a novel system including a range modulator wheel to modulate the beam range while scanning the beam transversely with magnetic dipoles (1). As implied by the above, the beam size used in scanning can be varied. An unmodified (nonscattered or tightly focused) beam is sometimes called a pencil beam, although sometimes this term is used for a beam that has a dimension on the order of a few millimeters. It is possible to obtain a raw, unmodified (unscattered and uncollimated) beam that is on the order of several millimeters or even a centimeter, in which case, one can consider using the term “crayon beam,” owing to the larger size. In any case, it is more important to define the terms and understand the regime being considered than to rely on ill-defined acronyms. The longest implementations of the scanning modality have been ongoing at the Paul Scherrer Institute (PSI) (2) and at the Gesellschaft fur Schwerionenforschung (GSI) (3). The most recent implementations were in commercial and academic hospital collaborations at the University of Texas MD Anderson Cancer Treatment Center and Massachusetts General Hospital (MGH) in the earlier and latter part of 2009, respectively. 6.1.1  General Description of Scanning Beam scanning is the process of spreading the beam over the target volume by moving the beam throughout the target. Pictorially, Figure 6.1 describes the scanning process. It is important to understand that true beam scanning could involve the variation of many parameters of the beam while it is being scanned. A beam at position A, can be characterized by a variety of parameters including the vector transverse coordinate XA (xA , yA), its energy EA, which determines its depth (the third dimension), the beam current IA, the beam size (a vector since it may be different in x and y) σA, and others. The beam deposits a dose DA in the voxel around A. After that dose is deposited, having stayed at A for a time tA, the beam is moved to location B. The time it takes to move from

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A

(xA, yA, EA, σA, IA, DA, tA) IAB, DAB, tAB, vAB

(xB, yB, EB, σB, IB, DB, tB) B FIGURE 6.1 Parameters useful in describing the scanning process. Beam A with the indicated parameters is modified to beam B, with modified parameters.

location A to location B is tAB. The beam current during that movement is IAB, which could be a function of position. The velocity that the beam moves from position A to B is vAB = (XB − XA)/tAB, and the average beam current change rate between A and B is dI/dt = (IB − IA)/tAB. In this way we have defined all the variables that are necessary in the delivery of beam scanning. 6.1.2  Limits of Scanning Implementations The above description appears intrinsically discrete or digital. Usually there are two interpretations of this description related to one extreme or the other. This has unfortunately caused confusion in the specification of the system and in the terminology. In one extreme when tA = 0, the beam does not stop at a particular location, and its motion is characterized by vAB. Also, in such a case, the concept of IA is undefined, but rather the quantity IAB is relevant. This extreme has been called continuous or raster or line scanning. It is the equivalent beam motion as that used in the old CRT (cathode ray tube) televisions. In the other extreme, when tA>0, it has been called spot scanning or sometimes also raster scanning. However the distinction between these extremes in the case when tA is sufficiently small and/or xB − xA << σA is not relevant. Whether or not the tA = 0 limit is reached is an implementation decision or is based on physically realizable quantities. Thus the level of discreteness of motion, measurement limitations, and control will all lead to the method that will be used to control the beam and contribute to the implementation. In the case when the beam fully stops at a given point A, it may be necessary to measure DA at that location, if the integrated current is not reliable; however, even when the beam does not “stop” at a given point, it is necessary to measure some form of the quantity DA at places on a three-dimensional (3D) grid in the target volume in order to compare with the desired dose distribution. A simplified way of looking at this is to identify two different extremes of implementation that we will call dose- and time-driven scanning as depicted in Figure 6.2 (left and right, respectively). These more

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Time Current

Time Current

Dose

Dose

Position

Position Raster or line or continuous scanning

Dose driven “spot” scanning

Time driven (can also be achieved by dose driven methods)

FIGURE 6.2 Graphs of beam current, position, and dose delivered in the dose- (left) and time-driven (right) techniques, during a one-line scan.

adequately describe the type of implementation and the properties required of the accelerator. In dose-driven scanning, the beam motion is controlled by whether the desired dose has been achieved at each location. The requirements on beam current control are light. In time-driven scanning, the beam motion is determined by the time the beam spends in any given region and is very dependent upon the beam current and/or beam velocity. Note that so-called spot scanning can be implemented in either a dose- or time-driven mode. Even the case in which the beam is not stopped (moving continuously, sometimes called line or raster scanning) can be approximated by a series of small moves and can be implemented both in the time- and dose-driven modes. Also note that the implementation chosen normally depends on the ability of the accelerator to deliver well-controlled beams and whether the beam is continuous or pulsed. The control of these quantities, whether open loop or closed loop, is a subject of importance. In an ideal world, all quantities would be perfect. In another idealistic world all parameters would be controlled in a closed-loop mode and verified. In the physical world, when measurements are made in finite times, open-loop delivery and correction or feed-forward processes are needed. In the case when tA ≠ 0, such as in Figure 6.2 (left), the dose is delivered in quantized doses and that there might be a correction for the next quantum of dose. This allows the beam delivery to be independent of the quantity (below the desired dose) and the quality of the beam current. The beam is stopped (or moved) when the desired dose is reached independent of its time dependence. However, if tA = 0, then the position of the beam at any given time is not known (due to the Heisenberg uncertainty principle), and the fact that it takes time to make the dose measurement may necessitate an analysis and dose distribution correction after the fact. In any case, one will have to identify the time scale for measurement and control for each parameter and/or device and define the control strategy to obtain the appropriate dose distribution.

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6.1.3  Safety The highest importance must be given to a safe and accurate delivery of dose to the patient. The scanning system must ensure that the correct dose fidelity is achieved, which includes giving the right dose to the right place and not giving the wrong dose to any place. The methods used to ensure this will place severe constraints on the implementation of the scanning system. This will impact the control strategy mentioned earlier given the time constants built into the system. Also, a safety plan should contain the definitions of the required types of redundancy and sensors to be used and therefore help define the interfaces with which the scanning system will interact.

6.2  Parameters That Affect the Beam and Dose Delivery The goal of radiotherapy implementation is to deliver the prescribed dose to the target with the prescribed dose distribution. In general, the dose fidelity (conformality to the prescription) is given by properly controlling and checking the beam properties at any given time or integrated over any given time interval. Each of the devices affecting or measuring the beam properties can be controlled and/or measured in a finite time period or continuously, depending on the measuring device (e.g., power supply current vs. beam position). The scanning system will control equipment parameters, read back instrumentation parameters, and make decisions about the settings of the equipment parameters based on the instrumentation parameters. It is useful to separate the discussion of beam parameters into the static and motion regimes. The former refers to the unperturbed property of the beam when it is not in motion, and the latter includes effects arising from the motion. 6.2.1  Static Beam Parameters 6.2.1.1  Depth–Dose Distribution The depth–dose distribution will be determined by the superposition of the Bragg peaks used in the delivery of the dose volume. Unlike a spread-out Bragg peak (SOBP) as used in the scattering technique (see Chapter 5), the delivery of a scanned beam can be general. An example of a nonuniform depth (single field) dose distribution required for a prostate carcinoma is shown in the top curve of Figure 6.3. However, without any scatterers, the width and distal falloff of a Bragg peak for shallower depth is smaller, and creating a smooth dose distribution by superposition of these depth doses

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60 50

Dose (Gy)

40 30 20 10 0

0

50 100 150 200 250 Depth dose in water (mm)

300

FIGURE 6.3 Two nonuniform, but realistic longitudinal dose distributions. The one at shallower range (bottom curve) suffers from the narrower Bragg peak and is less smooth when the Bragg peak spacing is too far apart compared to the deeper top curve.

is difficult, as shown in the bottom curve for a base of skull ependymoma of Figure 6.3 (J. Hubeau, Private communication). A range shifter or ridge filter is generally used for this situation; thus, even the scanning beam may be modified. It should be added that although scanning is sometimes considered beam delivery without modifying devices, use of a range compensator can provide advantages in some situations. This would allow one beam range to be used to irradiate an irregular shape distally and thus reduce the number of energy levels required for the dose delivery. 6.2.1.2  Transverse Dose Distribution and Modulation The transverse dose distribution is given by a superposition of the transverse raw beam profiles. Much depends on the shape of that raw beam. A beam is a collection of particles. The distribution of particles in a beam is typically statistical, and owing to the physics of the source of ions and the accelerator, the 2D (position and angle) phase space, in each plane, results in a distribution as shown in Figure 6.4, top left. An integrated projection along either the position (horizontal) or angular (vertical) axis results in a Gaussian distribution as shown in the darker curve in the histogram projections. The lighter curve is the distribution with limited statistics. The properly spaced Gaussian has a special shape with magic properties. A superposition of Gaussians results in a flat distribution. There is also considerable tolerance to the relative positions of these beams before their spacing affects the overall distribution. On the other hand, an asymmetric beam, or one that has a transverse falloff with a different shape than a Gaussian, will lead to much tighter beam-positioning tolerances.

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4

y

4 3

3 Transverse angle

2

–4 –3

3 4 5

1 0 –1 –2 –3

–3 Transverse position –4 #particles

–4

#particles

–5

–5 –4 –3 –2 –1

0

1

2

3

4

5

FIGURE 6.4 Statistical coordinates of particles in a beam defined by position and angle. The side and bottom graphs are histogram projections of the two dimensions (bottom, position; side, angle), showing the Gaussian distribution.

The sharpness of the Gaussian beam falloff will determine the sharpest dose falloff possible with a clinical beam. Figure 6.5 shows some of the features of a Gaussian beam, which is characterized by the following: y=e

1

0.8 0.6

Target region

Intensity of beam (relative)



0.4

1 x  −   2 σ 

2

(6.1)

.

Half width half max

Organ at risk

0.2 0

0

1 2 3 4 5 Distance from center of Gaussian (relative dimension)

6

FIGURE 6.5 A graph of the intensity versus distance of a Gaussian beam. An example of regions of target (left dashed box) and organ at risk (right dashed box) are shown to relate that spacing to the Gaussian parameters.

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A) CTV 50

0 60

Relative volume (%)

100

80 70 Dose (Gy) C) Brainstem

50

0

0

20 40 Dose (Gy-RBE)

IMRT IMPT σ = 8 mm IMPT σ = 5 mm IMPT σ = 3 mm

90

50

0

20 40 Dose (Gy-RBE)

60

D) Nasopharynx

IMRT IMPT σ = 8 mm IMPT σ = 5 mm IMPT σ = 3 mm

60

100

B) Left parotid

0 100

50

0

20 40 60 Dose (Gy-RBE)

0 80

Relative volume (%)

Relative volume (%)

100

Relative volume (%)

The beam sigma (σ) is the single parameter characterizing the Gaussian shape. The full-width at half-maximum (FWHM) is given by 2.35σ. In particular, if the Gaussian is unmodified (no collimator to produce sharper edges) and one wants to separate the target (Figure 6.5, left dashed box) from a critical structure in such a way that the critical structure does not receive more than, say, 50% of the target dose (Figure 6.5, right dashed box), the distance between the target and this critical structure has to be at least 0.85σ. This sets the scale of the beam size needed for different treatment sites. For example, if the target and organ at risk are separated by 5 mm, then the beam sigma should be smaller than approximately 6 mm. Alternatively, one might modify the beam or apply an aperture to sharpen an edge. Apertures are generally thought of as an inconvenience and expense when confused with the type used in scattering systems which are built to collimate a large beam and installed near the patient. However, one can conceive of a beam optics solution that allows a sharper edge to be created upstream of the target, and the beam on target is imaged from this aperture so that the beam that is scanned has a sharper edge at the target, the solution first proposed by Flanz at PTCOG in 2002 and subsequently implemented by Pedroni et al. (4). Of course, if the beam traverses too much material on the way to the target, the multiple scattering in this material will broaden the beam again. The clinical utility of smaller beams has yet to be determined. Some initial treatmentplanning studies have been conducted in order to evaluate the dose volume histograms and dose to critical structures as a function of the size of the beam (5). Examples of these comparisons are shown in Figure 6.6. Note the

FIGURE 6.6 Dose volume histograms for one treatment site planned with different size Gaussian beams and intensity-modulated photons. (A) CTV; (B) left parotid; (C) brainstem; (D) nasopharynx. The clinical impact of these differences is not yet known, but the relative quantitative importance of these parameters can be seen (Courtesy of Alex Trofimov).

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relative values of the dose-volume histograms for various beam sizes and for comparison purposes also for a highly conformal photon plan. Because some of these types of plans are a bit subjective, in that different planners may achieve different results, one has to be careful comparing them; however, there the curves show an interesting indication of the relative importance of the beam sigma in this particular case. If one is scanning the unmodified Gaussian beam, the scanning method affects the falloff at the edge of the field, as shown in Figure 6.7A. The addition of spaced Gaussians results in a larger-than-optimal edge falloff distance. However, in much the same way that one sharpens the edge of an SOBP by emphasizing the Bragg peak at the distal edge, it is possible to achieve similar results by modifying the distribution of the number of protons across the field as shown in Figure 6.7B (2, 6). Thus, to achieve a flat distribution with optimal edges, it is necessary to modulate the dose delivered across the target even for a single-field delivery. Finally, it is important to realize that the transverse dose delivered at any given depth will depend on the overall depth dose. Consider, for example, a dose distribution that is desired to be uniform after the delivery of a single field, which is called a single-field uniform dose (SFUD) (see Chapter 10). Figure 6.8 (left) shows an actual example of a treated field under such conditions (7). Figure 6.8 (right, bottom) shows the 2D transverse dose distribution along the transverse section A at this depth. Looking, now at a shallower depth B, one has to account for the proximal tail of the depth–dose distribution that was delivered to A and thus a lower dose is delivered in the center of B. The resulting transverse dose distribution in the transverse section B is shown in Figure 6.8 (right, top), and one can see a typical “island-of-dose” pattern for these fields. Thus, the dose across the shallower depth is also a highly modulated distribution, in order to obtain an optimized uniform field throughout the volume.

1.2

Uniform intensity profile

1.2

1.0

Relative dose

Relative dose

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2 0.0 0 A)

Nonuniform intensity profile

0.2 50 100 150 Position (arbitrary units)

200

0.0 0 B)

50 100 150 Position (arbitrary units)

200

FIGURE 6.7 (A) A superposition of equal space and equal amplitude Gaussian beams. (B) A nonuniformly spaced and modulated dose distribution also resulting in an acceptable uniform overall dose with a sharper penumbra.

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[cm]Y 10 50 96 98 100 102 105

–10.0 –8.0 –6.0 –4.0 –2.0 0.0 2.0 4.0 6.0 8.0 10.0

B

100% = 35.5875 cGy

11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 –1.0 –2.0 –3.0 –4.0 –5.0 –6.0 –7.0 –8.0 –9.0 –10.0 –11.0

[cm]X

A

20 40 60 80

20

40

60

FIGURE 6.8 (See color insert.) Left: an actual treatment plan for a SFUD delivery. Right: cross sections of the dose distribution required to achieve the overall uniform dose, at the two depths indicated by the magenta arrows labeled as A (deeper depth, bottom) and B (more proximal depth, top).

These last two examples highlight the fact that the dose distribution for most fields delivered will naturally be characterized by a dose modulation pattern. In common usage today, the term IMPT is used in contrast to SFUD to indicate a single-field delivery that is not uniform vs. a single-field delivery that is uniform. In the former, subsequent fields are delivered to finish the desired dose pattern, and, for example, results in a dose-uniform overall volume. However, in the IMPT mode, especially in the dose-driven case, the intensity is not normally modulated. Furthermore, in the case of the SFUD delivery, the dose is modulated, just as it is in what has been called IMPT. Therefore, the beam delivery methods are NOT different and are just particle beam scanning (PBS). Understanding these distinctions and care to not use an incorrect term such as IMPT, is vital in properly specifying a scanning beam system. 6.2.2  Motion Beam Parameters 6.2.2.1  Motion Effects It is useful to note that the dose delivered to the target can be affected by motion. This includes the motion of the beam and the motion of the target (8, 9), The latter will be covered in Chapter 14, and the former will be mentioned here. In the case of dose-driven spot scanning, the dose delivered is what one would expect from a static beam. Indeed, in the extreme example,

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the beam is only turned on when it is at the correct location. If, however, the beam is not turned off before moving to the next spot, the dose delivered during the motion must be accounted for and the final dose will depend on the stability and predictability of the current delivered. In the other extreme example, wherein the beam is continuously moving, there are a variety of effects to consider. One may desire to change the dose from one location to another, and this change can be as extreme as turning off the beam. If one does not stop the motion of the beam (which is possible, but also takes time), one has to account for the distance that the beam travels while the intensity is changing. This is illustrated in Figure 6.9 (top), where there are several Gaussians, each one displaced a given distance (as time evolves and the beam moves) and each one with a smaller amplitude as the beam is being turned off. Integrating these Gaussians results in the overall dose distribution, or the effective penumbra. For example, a moderate scanning dipole with an effective 30-Hz frequency that sweeps over 30 cm results in an effective sweep speed of 18 m/s. If one wants to effect the desired intensity change before the beam moves 1 mm, this requires that

Relative amplitude

Snapshot of Gaussian beams at different positions as the beam moves.

0

0

1

2

3

Scaled Gaussian

Relative amplitude

Ramped beam

4

0

1

2 3 Transverse distance (relative)

4

FIGURE 6.9 Top: reducing amplitude of a Gaussian beam at specific locations (multiexposure snapshots) along its path as the beam intensity is being reduced. Bottom: difference between the effective penumbra (top curve) and the unmodified pure Gaussian (bottom curve) penumbra for this case.

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Particle Beam Scanning

change to be done within 55 μs. Figure 6.9 (bottom) shows an example of the effective increase in beam size owing to the motion shown in the upper curve. At 20 m/s, with a 3-mm sigma, beam off in 500 μs produces a penumbra growth, from the undisturbed Gaussian of the lower curve to the ramped beam above, of 70% (3–5-mm sigma). Similarly the effect is only 10% for a beam with a 1-cm sigma, because the absolute distance traveled does not change and the relative distance is smaller.

6.3  Time Sequence of Beam Scanning Tasks The events that take place during a scanning sequence will determine the time required to deliver the treatment plan, and depending on motion effects, will determine the actually delivered dose distribution. One can consider that the treatment plan is a 3D map (it will probably grow into four-­dimensional maps as adaptive therapy evolves). How this map is to be delivered can have nothing to do with the treatment plan, other than delivering the correct dose to the correct voxel within tolerance, but it is related to the scanning implementation. For example, in some situations it is advantageous to vary the beam energy first and the position second or to mix the two. Figure 6.10 illustrates these different sequences. In the top panel, the ellipsoidal volume is scanned first in the transverse direction, as indicated by the transverse planes shown, and then the beam energy is modified to move the beam in the third dimension. Scanning may be used to conform to a distal layer without a range compensator by adjusting the field size as a function of the distal depth. Alternatively, the depth direction can be combined with

Beam

Beam

Transverse 

Depth 

FIGURE 6.10 Two styles of scanning with different time sequence. Top: sketch showing the beam painting the transverse cross section first (left, right, up and down) and then changing the range. Bottom: sketch shows changing the range and one coordinate (left and right) before changing the third coordinate (up or down).

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one transverse direction first, followed by a motion to the other transverse direction. Scanning can also be used to deliver dose to each of these layers, but less than the total required dose, so that the layers may be repainted ([10] or see Chapter 14) repeatedly to compensate for organ motion or just to deliver a time-dependent field position with a variation of range. Focusing on the transverse positions, the pattern delivered can be optimized and will be based on the implementation specifics. All of the variations can be independent of the treatment plan. Therefore there will be the equivalent of an intensity-modulated x-ray therapy sequencer (a series of multileaf collimator settings), or more accurately, for scanning, a trajectory manipulator that converts the treatment plan into something closer to what should be delivered. Of course, it should be possible for the treatment-planning software to read this manipulated map to be sure that the treatment plan is unaffected (especially if interpolation is required). Although some accelerators have certain beam delivery limitations with respect to the time-optimized order of the steps described above, new accelerators being developed may not and will be able to vary quickly the beam energy, spot size and position, and current. 6.3.1  Scanning Techniques Various types of scanning have been identified. For example, there is the dose-driven spot scanning technique used at PSI (2), a variation on that one used at GSI (11) in which the beam is not turned off between spots and there is, time-driven continuous scanning, which is still, to this day, a research and development area. There is the general feeling that the main advantage of a continuous raster technique would be that of speed, not necessarily speed in delivering all the dose in a field, but speed in covering a dose layer with a fraction of the dose and the possibility to repeat it several times. One type of continuous scanning method can be characterized by a constant beam deflection speed on the target. The beam intensity is modulated to adjust the dose per voxel. The constant beam deflection rate translates into very benign requirements for the deflection magnet power supply (essentially a constant voltage). In time-driven spot scanning, the beam intensity is attempted to be held constant. The dose per voxel is controlled by the time the beam spends on each spot. Between spots, the beam is deflected as fast as possible by applying the maximum power supply voltage to the deflection magnet. This method requires a high-compliance power supply and more sophisticated control circuitry. Assuming the motion is similar (same average speed) in both situations, it is clear that the shortest time to deliver the dose is by a method that can deliver the beam with a maximum dose rate. In fact, the velocity of the scan can be used to control the dose deposited during continuous scanning, instead of modulating the beam intensity and possibly allowing

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Particle Beam Scanning

Speed (x) x direction

Dose rate (x) Amplitude

Amplitude

Dose rate (x)

Speed (x) x direction

FIGURE 6.11 Graphs of the amplitudes of either dose rate or speed as a function of position during a transverse scan. This shows an example of two extremes of scanning dose delivery. Left: a constant speed scan with an irregular desired dose distribution; right: a constant dose scan, with the same desired irregular dose distribution.

the maximum dose rate to continue, or using a spot-by-spot approach can always allow the maximum dose rate. There are different limitations to each of these approaches. Figure 6.11 contains two graphs in which the top curve is dose rate and the bottom curve is scan speed. The left panel represents a constant velocity scan, and the right panel shows a constant dose rate scan, whereby the dose in a voxel is modulated by the scan speed. Both deliver the same modulated dose to the target. It is instructive to compare these two cases. In the case of constant speed, one can examine several scenarios. Let us assume, in arbitrary units, that we have a dose rate less than 1. If the velocity (in arbitrary units) is 1, then the time to deliver this scan is, say, t1. If we increase the speed by a factor of 2, but do not increase the dose rate, for each scan—because the time it took to cover the area was reduced by onehalf—the dose delivered is also one-half. Therefore one would have to rescan twice, and the overall time is not affected. If we double the dose rate, then we must increase the scan speed by a factor of 2, or the dose delivered during time t1 would be twice the required dose. In this way we can reduce the time by one-half. Again, increasing the scan speed without increasing the dose rate does not gain any time. In the case of constant dose rate one can examine similar scenarios. Using a scan speed of 1 is not good, because, as seen in the graphs of Figure 6.11, it was desired to reduce the dose in the center of the scan; therefore, the speed has to be increased in the center of the scan. If for example, the ratio of maximum to minimum dose during the scan is a factor of 2, we can consider a solution with the speed starting at 1 and rising to 2 in the middle of the scan. This will take approximately 1.5 times the original time. However increasing the dose rate will further reduce the time. Conclusion: Although it may seem trivial, the dose rate limitation is the main issue. Given a dose rate, faster speed only buys you repainting, not time. However if you have higher dose rate, you need scan speed to use it.

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This brings up one of the safety issues. In the process of radiotherapy one can “not” prevent an overdose; one can only react in sufficient time to stop the overdose from becoming relevant. Therefore, depending on the system parameters, including dose readout time and beam control time, one is limited in dose rate by these instrumentation time constants. 6.3.2  Contributions to Time It is helpful to consider, within safety limits, how to best deliver an efficient scanned beam. One can identify the contributions to the scanning time per layer: • Beam control • Time to change beam intensity or to turn it on and off. An example of this is shown in the current-modulated scope trace shown in Figure 6.12A. • Time to irradiate a location (dose rate) • As discussed earlier with respect to the dose rate—the faster the better, but for safety reasons the maximum dose rate will be inversely proportional to the time to measure and stop the beam. • Time to move from spot to spot • Note that in time-driven scanning mode, the maximum dose rate depends on maximum scan speed; the instrumentation time constants and the maximum scanning speed depends on the time it takes for a beam current change and the desired effective penumbra. • Scanning magnets • Time to change the magnetic field is a balance between speed and accuracy. Some practical limitations such as the voltage available also come into play. An example of a moving beam is shown in Figure 6.12B. Also important is the time to detect that the magnets are settled. • Instrumentation • As in all the above contributions, instrumentation plays a crucial role. For example, the time to read the dose is determined by a number of factors including the ion drift time in the ionization chambers (ICs) and the speed of the electronics readout. The graph in Figure 6.12C shows multiple rise times as the resistors of an IC electronic unit were modified to achieve faster response times. It is useful to separate the timing information into that required to deposit the dose, the time needed by the scanning magnets to move the beam between adjacent locations, and the time taken by other equipment such as the dosimetry system. Once this is done, there are a variety of parameters that can be explored. Among these are the relative time of the extreme of

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1

Sum of the IC2 strip Mean of Ictydo over 2 msec

0.8 0.6 0.4 0.2 0

B)

12.0 10.0 8.0 6.0 4.0 2.0 0.0 –2.0 –4.0 –6.0 –8.0 –10.0 –12.0

Transverse y position

Normalized signal

A)

50

100 150 200 250 Time in m sec

Normalized response of IC2 + ICEEU (a.u.)

C)

300

–12.0 –8.0 –4.0 0.0 4.0 8.0 12.0 Transverse x position

1

0.8 0.6 0.4 0.2 0

20 30 40 50 Acquisition time (msec)

60

FIGURE 6.12 (A) A graph of beam intensity (signal) versus time showing an example of beam current modulation. (B) A scintillator screen image of a beam position change requiring a finite time (and distance). (C) The time response of an IC for different electronic configurations.

spot scanning compared with continuous scanning, as a function of dose rate (or beam current) as shown in Figure 6.13. For the very specific conditions explored here and for one energy layer, the top curve in Figure 6.13A includes five repaintings of spot scanning with 2 cm sigma (5 Spot 2); the middle curve is spot scanning for one repainting (1 Spot 0.5), and the bottom curve is raster scanning (Raster 0.5), which, because of the high speed used, requires multiple repaintings anyway. Owing to the extra steps in a spot scanning method in which the beam is turned on and off (not all dosedriven methods require this!), there is indeed some increase in irradiation time. However, for some realistic parameters, for a given layer the difference may only be a fraction of a second; when considering the overall time of the irradiation (including the time to change the energy, which is normally a few seconds, but can be as low as fractions of a second), the difference can be less than half a minute, assuming repainting with both methods, as shown in Figure 6.13B. This plot is typical for the case in which the time to change the energy is relatively significant (e.g., seconds).

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A)

3

1 Spot 2 1 Spot 0.5

Time (min)

2.5

5 Spot 2 5 Spot 0.5

Raster 2 Raster 0.5

2

1.5 1

0.5 0 B)

0

5

2500

10 Current (nA) 5 Spot

15

Raster

20

1 Spot

Time (msec)

2000 1500 1000 500 0

0

5

10 Current (nA)

15

20

FIGURE 6.13 (A) The time to irradiate one layer as a function of beam current. (Safety issues are not included, or there would be a hard cutoff with an upper limit of beam current.) (B) Curves includes the time for energy change for a full volumetric delivery with different currents and different beam sizes (e.g., 5 Spot 0.5 = 5 repaintings of spot scanning with a beam size sigma of 0.5 cm). The raster beam is scanned as many times as needed to deliver the appropriate dose, as fast as allowed.

6.4  Scanning Hardware The unmodified accelerator beam must be spread out throughout the target volume, and the appropriate dose must be delivered. The hardware required to do this can be divided into two main categories: (1) equipment to adjust the beam properties and (2) instrumentation to measure the beam properties. The equipment used for these manipulations at the MGH system developed jointly by Ion Beam Applications (IBA) and MGH is summarized in

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Particle Beam Scanning

Quadrupole magnets

Dipole magnets

Proton beam Quadrupole vacuum chamber

Dipole vacuum chamber

Ion chambers

Brass snout

Isocenter

p

FIGURE 6.14 The equipment used to deflect and measure the beam for the MGH/IBA system is diagrammed at the top and the beam deflections resulting from the magnetic fields at the botttom.

Figure 6.14. The equipment in these figures, from left to right, includes a quadrupole doublet to control the beam size, a pair of scanning dipoles to deflect the beam to the desired position, and ICs to measure the dose, position, and beam profiles. Other commercial scanning systems are depicted in Figure 6.15. 6.4.1  Adjust the Beam Properties The equipment that is used to deliver the dose introduces physical constraints and therefore limits the types of patterns that can be applied and the timing that is possible. The scanning patterns that will be allowed are determined by the ability to adjust the relevant beam properties.

6.4.1.1  Energy In the case of scanning the beam range is normally given by the accelerated beam energy or the beam energy resulting from a degrader system and perhaps is slightly further modified by a minimum of material in the beam path. Any material in the beam path will scatter the beam (see Chapter 2) and increase the beam emittance which is related to the beam size. 6.4.1.2  Size The beam size is determined by the intrinsic emittance of the beam as modified by the beam-focusing elements in the beam line. Sometimes a set of final quadrupoles can be used to fine-tune the beam size in the nozzle.

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A)

B) Beam Profile monitor Scanning magnets Helium chamber Spot position monitor Dose monitor 1, 2

Iso center

C)

Ionization chamber Scanning quadrupoles Scanning dipoles X-ray equipment Beam modifying equipment (when needed) FIGURE 6.15 (A) The scanning nozzle of Hitachi as implemented at MD Anderson. (Courtesy of Hitachi.) (B) The IBA scanning nozzle. (Courtesy of IBA.) (C) The dedicated PBS nozzle vertical. (Courtesy of IBA.)

6.4.1.3  Position on the Target It takes two parameters to define a trajectory. One must control the position and angle of the beam. Assuming one already knows the position and angle of the beam entering the scanning dipoles (Figure 6.14, left side), the excitation of the magnetic field in the scanning dipoles will determine the final beam path angle and thus the location of the beam in the target as shown at the bottom of Figure 6.14. The overall system of power supply and dipole will determine the speed of the scan. The relation, V = L di/dt, indicates that the faster the scan (di/dt) the higher the voltage (V) requirements, which also depend on the magnet design such as the inductance (L).

Particle Beam Scanning

177

6.4.1.4  Scan Patterns We can call “field area” the area in which we expect the beam to be delivered according to a particular pattern of scan lines with a certain distance between scan lines. If one chooses a pattern with constant frequencies along the x and y axes ( fx and fy, respectively) a Lissijoux pattern results with a spacing between the painted lines. To reach the required line spacing (δ), which depends on the beam size and desired overlap, the frequency ratios could be adjusted. If you change the frequency ratio, a = fy/fx, while keeping nearly the same sizes for the scanning area, one can theoretically adapt the pattern to reach any required line spacing with a repeating pattern. However, the limitations on frequencies and speeds along both axes due to the hardware inherent to any power supply will limit the lowest reachable spacing between scan lines. One way to solve this is to work around those hardware limitations and modify the relative phasing of the frequencies. This will reduce the distance between the scanning lines because the scan will not repeat for a to-be-defined number of cycles. In the ideal case, the beam trajectory is arbitrary and one is not dependent on a set of fixed frequencies; however, there will always be a dependence on the hardware constraints of the system. 6.4.2  Dose Rate The highest dose rate available is almost completely determined by the extracted current from the accelerator, assuming that there are no losses in the beam path or in the case of a degraded energy beam that the beam intensity will be reduced by the scattering resulting from a degrader system (see Chapter 3) and the collimation system that contains a fixed amount of beam losses. The highest dose rate allowable will be determined by the parameters of the instrumentation and beam control.

6.5  Scanning Instrumentation and Calibration We can divide the situation for which we must measure the beam properties into on-line (during Treatment) measurements and off-line (during nontreatment times) measurements. The latter includes calibration and quality assurance (QA). It is important to decide how to verify that the beam is entering the target with the correct parameters. Introducing a monitor that intercepts the beam will affect the beam profile in a potentially adverse way. Weighing the optimized beam parameters with the impact of measurements on safety is a complicated process. For example, there can be an IC to determine the beam position entering the scanning dipoles or not. One can argue that downstream ICs that measure the position of the beam before the patient

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is sufficient; however, this can depend on the distance of these chambers to the patient. If they are close, then the beam angle will not play a significant role, but if they are far, the angle could be cause for consideration. The overall system design is important in determining the optimum configuration of instrumentation. 6.5.1  Calibration A significant amount of measurements is necessary to both characterize the system performance and to calibrate the system settings so that the desired performances can be achieved. Some of the tools that can be used are depicted in Figure 6.16. Depending on the system, some of these devices might be embedded in the system, and some might require external implementation, for example, at the isocenter. 6.5.2  Calibration of the Beam Position at the Isocenter It is necessary to ensure that the scanning dipoles can position the beam on the target at the desired location. Given the safety impact of this quantity, multiple levels of redundancy should be used to monitor the status of the scanning dipole, including redundant current measurements, voltage measurements, and magnetic field measurements as well as the status of the power supply. This, together with input trajectory information fully characterizes the deflection of the beam. Providing a functional redundancy with IC strips can be used to further augment the redundancy in beam position; however, this is usually installed upstream of the isocenter. Thus a device Devices embeded in the system IC23

Hall probe

Devices used at the isocenter

10 mm

BPC

MLFC

FC

Matrix DCCT

MC

MLIC BIS

FIGURE 6.16 Some instrumentation used includes the following: MLFC (multilayer Faraday cup), DCCT (DC current transformer), FC (Faraday cup), MC (monitor chamber), BIS (beam imaging scintillator), BPC (Bragg peak chamber), and IC23 (ionization chambers in the MGH system).

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–15 –10 –5 0 5 10 15 –15 –10 –5

0

5

10

15

FIGURE 6.17 Beam spots at the Isocenter using a MatriXX (11) IC system. The lower axis is the horizontal position, and the abscissa is the vertical beam position.

mounted at the isocenter is useful for calibration. In Figure 6.17, the MatriXX (12) was used at the isocenter to measure the deflection as a function of set point voltage and to calibrate the magnet settings as well as the upstream IC. These calibrations result in position accuracy of ±0.7 mm, under the conditions of this measurement. 6.5.3  Calibration of the Beam Size at the Isocenter The beam size performance was discussed previously in the section on beam performance. Measurements can been made using the BIS and the MatriXX. Figure 6.17 shows some MatriXX results. 6.5.4  Calibration of the Dose Delivery at the Isocenter There is a series of steps that are necessary to perform all the calibrations required to enable accurate dose delivery, including • Calibration from charge to the monitor unit (MU) • Characterization of the beam turn-off time • IC effects With respect to the beam turn-off time, a plot of the difference between the expected dose and actual dose as a function of dose rate will help determine this time. The slope of this curve is related to the beam turn-off time. Measurements of this sort may result in a parameter that requires the beam to be shut off in advance of reaching the desired dose at a spot. The signal from the IC itself can depend on the beam current due to recombination effects. The maximum beam current will be limited by the IC response.

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SMPS X [V]

2 1 0

X plot Expected slews Expected spots LOW threshold HIGH threshold Measured Measured spots

–1

3

Y plot

2 SMPS X [V]

3

1 0

–1

–2

–2

–3 0

–3 0

2000 4000 6000 8000 10000 Element ID [-]

2000 4000 6000 8000 10000 Element ID [-]

FIGURE 6.18 An example of an on-line data analysis system monitoring each of the axes of the scanning dipole power supply (left and right) as a function of an element of the treatment plan. Also contained is the actual measured x and y power supply current behavior. (Courtesy of Pyramid Technical Systems and IBA)

6.5.5  On-line Verification of Beam Position The tolerances applied to the beam properties during a treatment are dictated by the clinical tolerance. However, a beam position cannot be measured with sufficient accuracy, by an IC, until sufficient charge is collected. Therefore the beam position (and size) measurement may have to be delayed. Other measurements may be quicker. A good scanning system will record the on-line measurement data and compare it with the expected values within the specified tolerances. An example of this is shown in Figure 6.18. These are plots of the scanning magnet current values as a function of spot positions. Included on these plots are the measured spots, the expected values, and the high and low thresholds. Similar plots can be made of the scanning magnet field and power supply parameters. It is a fact that much calibration must been done in order to optimize the speed when it is important and to focus on the accuracy when it is important. Adjustment of the tolerances is a very important and time consuming part of the calibration process. 6.5.6  Beam Steering Corrections Although significant time can be spent on calibrating the position and in trying to understand all the effects that contribute to mispositioning, not all the effects may be understood; so it is necessary to consider how to best deliver an irradiation if not all parameters are, a priori, perfect. Given the desire to reduce the time for an irradiation and to continue an irradiation once started, assuming all the parameters are within tolerances, it is possible to apply some robust techniques in correcting the beam position if deviations occur. Four methods have been developed:

1. Deck reckoning via the algorithmic tables or formulas 2. Beam tuning on the first layer (if an energy layer approach is used)

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Deviation from desired position (mm)

14 12 10 8 6 4 2 0 0 –2

After turning (middle curve) After turning and SM steering (lower curve) No turning, no SM steering

(SM = Scanning magnet) 5 10 15 20 25 Depth layer number

30

FIGURE 6.19 Data (offset vs. time) obtained from a simulated beam position correction process. The top curve shows the raw data (purposely misaligned position both during the first and third depth layers). The middle curve is corrected from the first position (but purposely modified subsequently). The bottom curve is corrected each time the beam exceeds the maximum offset.



3. Adaptive beam tuning, which applies the position offset corrected in the first energy layer to all subsequent layers 4. Adaptive scanning magnet correction, which corrects the beam position within a scan

Together, these approaches significantly enhance the precision of the absolute beam position and provide a degree of robustness so that the irradiation is less sensitive to potential beam positioning fluctuations. Figure 6.19 shows an example of the beam position correction processes. The vertical axis is the beam position in millimeters, and the horizontal axis is the layer number for a 3D irradiation. The top curve is the measured position of the beam without corrections, for a contrived case. (Note in particular the discontinuity between layers 2 and 3.) The middle (just below the top) curve shows the result from adaptive beam tuning, which was implemented during the first layer. Thus all subsequent layers are corrected by the same amount; however, there was a discontinuity between the second and third layers. Finally, the bottom curve shows the result of the adaptive scanning magnet correction. In this example the threshold is set at 1.6 mm. Note that in layers 3, 7, etc., the measured beam position exceeds the threshold and the scanning magnet is used for correction. This correction is applied to the entire map. The mispositioning is measured and reacted to before a dose of any clinical significance is delivered with the beam out of tolerance.

6.6  Scanning Gantries The delivery of any beam will be characterized by the relative orientation of the beam and the patient target. Although, in general, either the patient

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or the beam orientation can be manipulated, for the most part, nonplanar beams are delivered by rotating gantries that manipulate the beam from the horizontal orientation to an orientation perpendicular to a patient in a prone or supine, horizontal, position. Although the subject of gantry design and implementation is large, the beam delivery modality can have a significant impact on their design. For the most part, a gantry that contains a scattering beam delivery system will have that scattering system immediately after the last bending dipole of the gantry. The scattered beam becomes very large and uniform, and further transport by magnets will require very large magnet apertures and may negatively affect the particle distribution. However, in the case of PBS, with an unmodified beam, the potential geometries expand since there is no scattering system. The first gantry to take advantage of this possibility is shown in Figure 6.20A (13). This gantry is also compact in the vertical dimension by setting the patient position away from the gantry rotation axis. Inserting the scanning dipoles before the last gantry dipole allows one to minimize the space between the last gantry dipole and the target, at a cost of a large aperture in the gantry dipole to accept the diverging scanned beam. It is possible to obtain a variety of optical solutions that will control the angle of the scanned beam at the target. For example, the beam angle can be anything from parallel to the actual angle the beam was bent by the scanning dipole and magnified beyond that. Additional geometries include A)

S S

GD

C)

S

GD

I T

S

B) GD S S

I

I

T

T FIGURE 6.20 Depictions of three types of gantry geometries capable of providing scanning beams. (A)  Geometry of the first scanning proton gantry with both scanning dipoles upstream of the last gantry bending dipole. (Courtesy of E. Pedroni.) (B) Geometry of the Hitachi scanning gantry with scanning dipoles downstream of the last gantry dipole. A drawing of the physical gantries are in the left of each box, and the line drawing to the right shows the scanning dipole(s) (lighter colored blocks with S inscribed), gantry dipole (darker wedge with GD), the instrumentation (I), and an ellipse representing the target (T). (Courtesy of Hitachi.) (C) Geometry of the scanning dipoles split upstream and downstream of the gantry dipole.

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positioning the scanning dipoles before or after the last gantry dipoles as well as the inclusion of focusing elements, which will affect both the beam size and effective scanning beam angle (or effective source-to-axis distance [SAD]). Some of these geometries are shown in the sketches of Figure 6.20B, as implemented by Hitachi, for example, and the one in Figure 6.20C in which the scanning dipoles are split before and after the gantry dipole with the appropriate beam optics in between. In cases where the dipoles are together, they can be replaced by a single combined dipole (14), if there is sufficient distance to achieve the desired field size. Many more combinations are possible.

6.7  Beam Property Quality Assurance (QA) One can have a friendly, long, discussion about all the aspects of the beam that have to be correct in order to achieve the desired dose within a 3D field that contains nonuniform field distributions. However, one way to cut that discussion short is to find a way to measure some of the important beam properties explicitly and to do so in a very short time. One such method is a test pattern that can measure many important properties of the beam in a very short time. It takes a few seconds to deliver that pattern, and the dose delivered is displayed on a MatriXX or BIS monitor. This pattern has the capability, with analysis, to give the beam position, size, and dose. An example of this with an automated analysis tool is shown in Figure 6.21A and B. The grayscale in Figure 6.21A shows the pattern assuming perfect A)

position (x, y)

B) 15 10

sigmaX y (cm)

5 0

–5 dose

–10 –15 –15 –10 –5

0 5 x (cm)

10

15

2000 1800 1600 1400 1200 1000 800 600 400 200 0

sigmaY FIGURE 6.21 (See color insert.) (A) A theoretically designed scan test pattern. (B) A result of a measurement with a larger beam size and some of the parameters that can be obtained through analysis using this pattern.

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beam resolution. Figure 6.21B, in living color, shows the results when this pattern is delivered with the MGH scanning beam. In this case, an unfocused beam with a sigma of about 1 cm was used. Also indicated are some of the regions in the pattern that can be used to analyze beam position, dose, and beam size. It is envisioned to repeat this test pattern daily, after the scanning system hardware is configured and to use this data as QA testing. Finally, it is necessary to determine the correspondence of the beam position and the imaging fiducials. One way to do this is to generate an exposure with the x-ray tube and produce an image of the x-ray crosshairs on the same screen as that which is measuring the QA pattern. This completes the correlation between the beam and the patient setup data.

6.8  Safety Particle beam scanning is a modality to deliver a particle beam while achieving a high degree of irradiation conformality to the desired target. As a form of radiation, it is desired to minimize the radiation delivered outside the target. Underdosing the target can also have undesirable results. The dose outside the target may be acceptable as defined by the medical prescription. The equipment must be capable of ensuring that target dose is delivered and unwanted dose is not delivered by detecting both the target and unwanted dose and stopping the irradiation in sufficient time to prevent too high a quantity of undesirable dose. Thus the accuracy in some cases will in part be determined by the specifications of the instrumentation used to detect beam properties. One must ensure that

1. The appropriate dose is delivered 2. The dose distribution is correctly delivered 3. The dose is delivered to the correct location

One way to help ensure that a system can operate in a safe manner is to evaluate the failure modes and develop a strategy that leads to a safe and consistent mitigation of all conceived failures. For the PBS, a comprehensive failure mode and effects analysis (FMEA) and hazard analysis should be done. Elements of the process include the following: • Possible hazards/effect on the beam • Risk mitigation method • Hardware detection • Software safety • Functional redundancy (measurement of delivery beam properties)

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• Clinical protocol • What has to be done for QA? • What should a therapist/physicist do? 6.8.1  Safety Strategy To develop an appropriate strategy, a philosophy of risk mitigation is needed. The following questions should be posed: • What needs to be set to determine a property (e.g., magnets and scattering for beam size)? • Are there other factors (that we do not control) that can determine a property (e.g., accelerator-extracted beam trajectory)? • What can be monitored to determine that the setting of the device is correct? Are there redundant ways to monitor it (e.g., limit switches or current transformers)? • Is there a direct way to measure that beam property (e.g., ICs or range verifiers)? • What can be done with software, and what can be done with hardware? • What additional QA can or should be done? 6.8.2  Beyond Safety An old adage says that “the safest system is one that does not work.” We cannot always expect everything to be perfect, and therefore we look for some ways to be insensitive to errors or to correct errors in a fast and accurate way that allows treatment to continue. For example, the system should accept a “pause, stop, and resume” command. If the beam has been paused or stopped before the irradiation has completed and it is desired to complete that irradiation, this process must account for all the dose that has been previously delivered. Unlike scattering, where the entire volume is irradiated almost simultaneously, in the case of scanning there is a time dependence to the beam delivery. In the case of recovering a treatment after it has been stopped or paused, the measurement of the dose already delivered is crucial. Figure 6.22 shows the case irradiation of a particular layer. The numbered sections are voxels, and by the time of the pause, the gray filled-in boxes have been irradiated, whereas box 11 is only partially irradiated. The rightmost panel represents the desired irradiation of the remaining voxels upon resuming the irradiation. Treatment-planning simulations have been carried out to understand the effect on different types of fields. For example, in a plan (Figure 6.23) with a 34-Gy highly modulated field, a scenario could be created in

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1

2

3

4

5

6

7

8

9

10 12 13 14

11

Starting map

Irradiation interrupted

Irradiation resumed

FIGURE 6.22 Illustration of an interrupted scanning map and the recovery and continuation.

which there are localized changes of ~6 Gy =  ~16%. This does not show up in the dose-volume histogram, but does contribute to the desired accuracy of the already delivered dose. Note that in this case, if thousands of spots are used, 0.1% can result in missing 10 spots. If those 10 spots are in a highly nonuniform distribution, the results are a bit unpredictable or at least nonintuitive. At MGH it has been determined that 0.7-MU accuracy or limitation on the noise that contributes to the dose

100

5 10 15 20 25 30 35 Dose [Gy] CTV

10

Nominal 1MU repainted 1MU skipped

60

60

40

40

20 0 30

80 % Volume 

% Volume 

80

100

20 30 40 Dose [Gy] Spinal cord

20 32

34 36 38 40 Dose (Gv) 

42

0 20

22

24 26 28 30 Dose (Gv) 

32

FIGURE 6.23 (See color insert.) Treatment-planning example of an interrupted scanning beam delivery to determine the accuracy required of knowing the actually delivered monitor units, in order to accurately resume the treatment. The left treatment plan shows a local under dose, CTV, clinical target volume. Right: spinal cord.

Particle Beam Scanning

187

measurement is required. This gives an acceptable dose distribution for the cases examined.

6.9  Summary PBS represents a technical improvement in obtaining the most conformal dose distributions possible with particles. Additionally it allows for dose delivery without patient-specific hardware. This allows for the most efficient beam delivery modality. One can envision multiple-field irradiations being delivered without entering the treatment room between fields. The depth–dose distribution together with the conformality of this approach leads to a minimization of beam fields necessary for an excellent dose distribution. The overall system is in fact simpler in the number of elements required than a scattering system; however, the implementation of the system with respect to timing and tolerances is more challenging. Given the fact that for a scanned beam it is not normally necessary to prepare, in advance, elements that will control the beam delivery, it is ideally suited for adaptive radiotherapy. Adaptation is not only relevant for intrafraction effects, but can also be important for interfraction effects. Indeed the largest obstacle to widespread use of scanning in all body sites is the factor of organ motion. In general the scanning technique contains flexibility to compensate for all types of organ motion effects: if the treatment planning can be adapted to account for these effects and if the accelerator system is nimble enough to compensate. As is the case in all particle beam–spreading methods, the tolerances associated with the delivery of the particle beam are more stringent than those associated with photon beam delivery; however, the gains in dose conformality, efficiency, and compensatory power are all significant with the use of the beam scanning modality. Accelerator, beam line, and scanning systems have previously been built for scattering beam delivery; however, newer systems can be optimized for scanning and provide more flexibility for adaptive and fast beam delivery. On the whole, the cost of delivering a beam using scanning can be lower than other alternatives and the treatment more efficient, thus positively contributing to the cost effectiveness of particle therapy. The beam scanning modality is now integrated into hospital-based clinical treatment facilities and is not just in the laboratory environment anymore. This represents a new phase in the evolution of accessible particle beam therapy and research.

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Acknowledgments The author recognizes the tireless efforts invested by Dr. Claise, who has devoted considerable time and energy in the commissioning of the MGH scanning system. This has been augmented with the help of Dr. Bentefour of IBA. In addition, the works of Drs. Dowdell, Kooy, and Trofimov have been instrumental to the MGH portion of the work reported in this chapter. The author also acknowledges Ion Beam Applications s.a. (IBA) and the National Cancer Institute for their support of some of the work reported herein. The author thanks the editor, Dr. Paganetti, for the invitation to prepare this chapter and for providing help in editing. Finally, thanks are owed to the author’s wife, Nancy and children, Adam and Scott, for their patience during the nights and weekends (yes this took more than one night) spent in the preparation of this chapter.

References

1. Kanai T, Kawachi K, Kumamoto Y, Ogawa H, Yamada T, Matsuzawa H, et al. Spot scanning system for proton radiotherapy. Med Phys. 1980;7:365–9. 2. Pedroni E, Bacher R, Blattmann H, Bohringer T, Coray A, Lomax A, et al. The 200-MeV proton therapy project at the Paul Scherrer Institute: conceptual design and practical realization. Med Phys. 1995;22:37–53. 3. Haberer T, Becher W, Schardt D, Kraft G. Magnetic scanning system for heavy ion therapy. Nucl Instrum Methods Phys Res A. 1993;330:296–305. 4. Pedroni E, Bearpark R, Bohringer T, Coray A, Duppich J, Forss S, et al. The PSI Gantry 2: a second generation proton scanning gantry. Z Med Phys. 2004;14(1):25–34. 5. Trofimov A, Bortfeld T. Optimization of beam parameters and treatment planning for intensity modulated proton therapy. Technol Cancer Res Treat. 2003 Oct;2(5);437–44. 6. Staples JW, Ludewigt BA. 1993 Proceedings Particle Accelerator Conference: 1759–61. 7. Kooy HM, Clasie BM, Lu HM, Madden TM, Bentefour H, Depauw N, et al. A case study in proton pencil-beam scanning delivery, Int J Radiat Oncol Biol Phys. 2010 Feb 1;76(2):624–30. 8. Saito N, Bert C, Chaudhri N, Gemmel A, Schardt D, Durante M, et al. Speed and accuracy of a beam tracking system for treatment of moving targets with scanned ion beams. Phys Med Biol. 2009 Aug 21;54(16):4849–62. 9. Haberer et al. N.I.M. 1993;A;330:296–305. 10. Seco J, Robertson D, Trofimov A, Paganetti H. Breathing interplay effects during proton beam scanning: simulation and statistical analysis. Phys Med Biol. 2009 Jul 21;54(14):N283–94. 11. Eickhoff H, Haberer T, Kraft G, Krause U, Richter M, Steiner R, et al. The GSI Cancer Therapy Project. Strahlenther Onkol. 1999 Jun;175 Suppl2:21–24.

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12. Herzen J, Todorovic M, Cremers F, Platz V, Alvers D, Bartels A, et al. Dosimetric evaluation of a 2D pixel ionization chamber for implementation in clinical routine. Phys Med Biol. 2007 Feb 21;52(4):1197–208. 13. Peroni E, Enge H. Beam optics design of compact gantry for proton therapy, Med Biol Eng Comput. 1995 May;33(3):271–77. 14. Anferov V. Combined x-y scanning magnet for conformal proton radiation therapy. Med Phys. 2005;32(3):815–18.

7 Dosimetry Hugo Palmans CONTENTS 7.1 Detectors...................................................................................................... 191 7.1.1 Calorimeters.................................................................................... 192 7.1.2 Fluence-Based Measurements....................................................... 197 7.1.3 Ionization Chambers...................................................................... 198 7.1.4 Detectors for Profile Measurements............................................. 202 7.2 Reference Dosimetry.................................................................................. 207 7.2.1 History of Reference Dosimetry for Protons.............................. 207 7.2.2 Recommendations of IAEA TRS-398 and ICRU Report 78....... 209 7.3 Microdosimetry.......................................................................................... 211 7.3.1 Microdosimetric Quantities.......................................................... 212 7.3.2 Experimental Microdosimetry..................................................... 212 References.............................................................................................................. 215 The accuracy needed in dosimetry should be considered in view of the requirement for the dose delivered to the target volume for which, in general, required relative standard uncertainty levels between 3% and 5% have been quoted (1). Reference dosimetry, which is only one step in a chain of procedures leading to dose delivery, should thus be done with uncertainties well below that, typically better than 1%. For relative dosimetry, the uncertainty requirements are usually a bit more relaxed. The first section of this chapter discusses the detectors used for proton beam dosimetry and their particular characteristics in protons compared with photons, the second one discusses their application to reference and relative dosimetry, and the chapter ends with a section on microdosimetry.

7.1  Detectors An up-to-date review of clinical high-energy photon and electron dosimetry can be found in Reference 2. The main issues that complicate proton beam 191

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dosimetry compared with photon and electron dosimetry are the poorer knowledge of stopping powers and other electronic interaction quantities, the increased ionization density characterized by a larger linear energy transfer (LET), and the occurrence of nonelastic nuclear interactions. These are all of concern related to detector response, and the latter two effects contribute to the energy-dependent dose response that all detectors exhibit in proton beams. The first three detectors that will be discussed are the main instruments used for absolute dosimetry: calorimeters, Faraday cups, and ionization chambers. Those three subsections are then followed by a subsection on detectors for relative dose distributions. 7.1.1  Calorimeters Calorimeters provide the most direct method to measure the quantity of interest in reference dosimetry for radiotherapy, which is the absorbed dose-to-water. Relevant quantities such as biological response and isoeffective dose are also defined with reference to the absorbed dose-to-water. The most direct way of measuring this quantity is by use of water calorimeters, but calorimeters using different absorbed media such as graphite or the tissue-equivalent plastic A-150 have been used for the same purpose as well. The latter require in addition to the measurement of dose to the calorimeter medium, a conversion procedure to derive the absorbed dose-to-water. In calorimetry, the temperature increase in the medium, ∆Tmed, as a result of the energy deposited by ionizing radiation, is measured with high precision. Absorbed dose to the medium, Dmed, is then obtained by multiplying with the specific heat capacity of the medium, cmed, and the necessary correction factors:

Dmed = cmed ⋅ Tmed ⋅

1 ⋅ Πki 1− h

(7.1)

where h is the physicochemical heat defect that represents the (fractional) energy that has been deposited by ionizing radiation but is taken away from the medium by any changes of its physical or chemical state and Πki is the product of correction factors for heat transported away or toward the measurement point, field nonuniformity and changed scatter and attenuation due to the presence of nonmedium-equivalent materials. The specific heat capacity is normally obtained from measuring the temperature rise in the medium due to electrical energy dissipation, either in a separate experiment or within the calorimeter setup. The operation of calorimeters in photon and electron beams has been described extensively (1, 4) and for proton beams operating and understanding calorimeter response is very similar. The main additional issues that

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need to be considered are the chemical heat defect, thermal heat conduction, and dose conversions between different media. The heat defect is defined as follows:

h=

Ea − Eh Ea

(7.2)

where Ea is the energy from ionizing radiation absorbed locally and Eh is the energy appearing as heat, and thus as a temperature rise when no latent heat absorption is involved. If no change of the physicochemical state of the medium takes place then the heat defect is zero. If the net heat balance of processes after the absorption of energy is endothermic the heat defect is positive, whereas it will be negative when the net heat balance is exothermic. In water calorimeters, the main source of a heat defect is the chain of chemical reactions after the radiolysis of water. The reactions after the production of so-called primary species (which are present about 10−7 s after passage of the ionizing particle) are well known and documented (5, 6), and together with values of the chemical yields of primary species and the heats of formation of the six stable chemical species after irradiation (7), the chemical heat defect can be calculated by solving the coupled set of linear differential equations describing all chemical reactions. The production of primary species, however, is LET dependent, and this dependence is not very well known. The most comprehensive information comes from References 7 and 8, and based on this, calculations of the chemical heat defect for proton beams have been performed and discussed in various publications (9–15), leading to the following observations: • For high-energy (low-LET) protons, pure water saturated with a chemically inert gas like argon or nitrogen (the argon or nitrogen system) exhibit a small (<0.1%) initial heat defect, reaching a steady state after a modest irradiation just as it does in photon beams. For high-LET protons, however, a steady increase of the chemical energy in the aqueous system is observed because of a higher production of hydrogen peroxide than what is decomposed, resulting in a nonzero endothermic heat defect. • Pure water saturated with hydrogen (the hydrogen system) exhibits a zero heat defect over the entire LET range, which can be explained by an enhanced decomposition of hydrogen peroxide compared with the nitrogen system. • When initial oxygen concentrations are present, the hydrogen system exhibits an initial exothermic heat defect that increases until depletion of oxygen after which the heat defect drops abruptly to zero. This is an attractive system because this phenomenon offers a way of monitoring when the steady-state, zero-heat-defect condition is reached.

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• For water with a known quantity of sodium formate as a deliberate impurity saturated with oxygen (the formate system), the exothermic heat defect in a modulated beam is only about half of that in a 60Co beam with the same dose rate. This was explained by the lower chemical yields for certain species at high LET as well as the time structure of the formation of chemical species due to the beam modulation. Two types of experiments can be distinguished that provide support for the theoretical observations above:

1. Comparison of the heat defect of water with that of a metal for which the heat defect is assumed to be zero (e.g., aluminium or copper). The experiment consists of measuring the thermal heating of a dual water/metal absorber, which forms one thermal body, by totally absorbing the same number of protons in either the water component or the metal component. Using such a setup, it was experimentally confirmed that the endothermic heat defect in pure water increases with LET from a value close to zero for protons to a value of about +4% for 100 keV μm−1 helium ions (16). A weighted least-squares fit of an exponential function to the data including an uncertainty of 0.3% for the assumption that the heat defect is zero at low-LET (3) gives the following:

(

)

h = ( 4.1 ± 0.4 ) ⋅ e −( 0.035±0.010)⋅LET − ( 1.000 ± 0.001) .

(7.3)

Figure 7.1 shows the experimental data points as well as the fit with the standard uncertainty as a function of LET. 2. Relative comparison of the heat defect of different aqueous systems by comparing their relative response to the same dose. This way the initial exothermicity of the hydrogen system in the presence of trace oxygen concentrations was demonstrated for protons as well as the relative agreement of the hydrogen system with the nitrogen or argon system after a steady state was reached (9, 10, 14). Also the lower heat defect of the formate system in protons compared with photons in a modulated proton beam was demonstrated experimentally (9, 10, 14). A chemical heat defect can also occur in solid calorimeters. In graphite as well as plastic calorimeters (A150 tissue equivalent plastic and polystyrene), reaction of the medium with dissolved oxygen may result in an exothermic heat defect. This has been suggested to explain the initial overresponse of calorimeters made of A150 and graphite (more than 10% and 2%, respectively), which disappears after sufficient preirradiation (17, 18). Another suggested

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Chemical heat defect / %

7 6 5 4 3 2

H-1 H-2 C-12 He-4

1 0

–1

0

20

40

60

80

LET / keV µm–1

100

120

140

FIGURE 7.1 Chemical heat defect of pure water as a function of LET measured for various ions (16). The middle line represents an exponential fit and the two outer lines the one standard deviation interval based on the uncertainties from the least-square fit parameters and a standard uncertainty of 0.3% for the assumption that the heat defect is zero at low-LET. (From Brede et al., Phys Med Biol, 51(15), 3667, 2006. With permission.)

mechanism for a chemical heat defect is the dissociation of polymers, which explains the endothermic heat defect of about 4% for A150 obtained from similar total absorption experiments as described above using a dual A150/ aluminium absorber (19–21). In solid calorimeters made of a crystalline or polycrystalline material such as graphite, a physical heat defect is also possible due to the creation and annihilation of interstitial lattice defects. This is generally assumed to be small but may be larger in proton beams than in photon beams because of the higher probability of a sufficient energy transfer to a recoil nucleus. Only at extremely high doses (order 109 Gy) received in nuclear reactors has a heat defect been demonstrated by measuring the release of the Wigner energy when annealing the graphite samples by heating it above 250°C (22). It is not clear if and how these results would translate to radiotherapeutic dose levels. In a proton total absorption experiment using a graphite/aluminium absorber, an endothermic heat defect of 0.4% with a standard uncertainty of 0.3% was observed (21), indicating that the physical heat defect in graphite must be limited to a few tenths of a percent. The second issue of concern with calorimeters in proton beams is that of heat conduction, potentially leading away heat from the measurement point or adding heat from the irradiated surroundings of the measurement point. For water calorimeters, where the thermal diffusivity is relatively low, thermal conduction is manageable when the steep gradients are kept a sufficient distance away from the point of measurement. The same criterion as in photon beams could be used that corrections for heat losses are negligibly small when the distance from the measurement point to steep edges such as the penumbrae and the Bragg peak or to the distal edge of the spread-out Bragg

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Proton Therapy Physics

peak is at least 3 cm (23). In scanned proton beams, an additional complication is that when a pencil beam hits the measurement point the instantaneous gradients are always substantial, but it has been demonstrated theoretically (11) and experimentally confirmed (24) that if the painting of a target volume takes not more than 2–3 min, the correction for heat conduction and its uncertainty are very similar to that of passively scattered broad proton beam irradiation of the same duration. Also the excess heat due to the presence of nonwater materials (the glass vessels to contain the high-purity water and the thermistors probes) has been found to cause only minor differences compared with that of photon beams (24). In solid calorimeters and in particular graphite calorimeters, the phenomenon of heat conduction is very different given the higher thermal diffusivity. In graphite the thermal diffusivity is three orders of magnitude higher than in water, meaning that temperature profiles within an irradiated sample redistribute within a time interval much shorter than the irradiation time itself. This is traditionally dealt with by introducing gaps and so-called jackets around the core, a graphite sample with known mass over which the average dose is measured by comparing the temperature increase during irradiation with the temperature increase resulting from known electrical energy dissipation. In photon beams advantage is taken from the almost linear attenuation curve; by thermally connecting equal-sized parts of the jackets in front and to the back of the core, the average heating of the jackets is almost equal to that of the core, thus minimizing radiative heat transfer. In proton beams, because of the Bragg peak or the distal edge this is more difficult to achieve, and the steep gradients need to be either shielded by inducing more thermal barriers or by matching the size of graphite parts beyond the core such that the energy per unit mass of those parts equals the dose in the core (25). For scanned proton beams, the only option is to work in isothermal operation mode, in which all graphite parts are kept to a constant temperature and the changes in electrical energy dissipation required during irradiation provide a way of measuring of how much energy is deposited in the core. Finally, for nonwater calorimeters there is the issue of converting dose to the calorimeter medium to the quantity of interest: dose-to-water. For graphite calorimeters, the conversion from dose-to-graphite to dose-to-water is one of the main uncertainties on the dose-to-water determination in a proton beam (14). If the charged particle spectra at equivalent depths in water and graphite (related by the CSDA [continuous slowing down approximation] ranges) are identical, then the dose conversion is adequately described by the mass stopping power ratio water-to-graphite for the charged particle spectrum. However, differences in the absorption of primary protons in nonelastic nuclear interactions and differences in the production of secondary charged particles in both target materials are likely to result in unequal charged particle spectra at equivalent depths. The absorption of primary protons can be approximated by a simple analytical calculation. Using

197

Dosimetry

nuclear interaction data from the International Commission on Radiation Units and Measurements (ICRU) Report 63 (26), it is found that the number of primary protons absorbed over the entire range in graphite is different from that in water by 2% for 60-MeV protons and 8% for 200-MeV protons (27). MCNPX (Monte Carlo N-Particle eXtended) Monte Carlo simulations, on the other hand, indicate that this is largely compensated by the difference in secondary particle production leading to dose conversion corrections that are limited to 0.4% at 60 MeV and 0.6% at 200 MeV. 7.1.2  Fluence-Based Measurements In a broad proton beam, dose-to-water at a shallow depth, z, can in principle be derived from the proton fluence at the surface, Φ, as follows:



Dw ( z) = φ ⋅

Sw ( z) ⋅ Πki ρw

(7.4)

where Sw(z) is the stopping power of the proton spectrum at depth z and Πki is the product of correction factors for beam divergence, scatter, field nonuniformity, beam contamination, and secondary particle build-up. It is obvious that this method relies on accurate values of the proton stopping power in water for which the uncertainty is estimated to be 1–2% according to ICRU Report 49 (28). The main instrument in use to measure the incident particle fluence is the Faraday cup, which enables an accurate measurement of the number of protons, provided it is well designed (Figure 7.2). For broad beams an additional major uncertainty is due to the determination of the field area. For pencil beams this uncertainty vanishes when the derived quantity is a laterally integrated dose. A major concern is the influence of electrons generated in the entrance window that reach the collecting electrode (and thus reduce the signal) as well as electrons liberated in and escaping from the collecting electrode (which enhance the signal). Both sources of perturbation to the measurement are usually suppressed by a guard electrode with a negative potential with respect to the electrode and casing, and sometimes with addition of a magnetic field. An alternative method for determining the fluence is to measure the induced activation of a sample (29). If the number, N, of 12C atoms in a sample is known as well as the cross section of the 12C(p,pn)11C reaction, the measurement of 11C activity, A0, immediately after an irradiation time τ can be used to derive the proton fluence in the center of the broad beam that hits the sample using the following equation:



φ=

A0 ⋅ e λ⋅τ 2 σ ⋅ N ⋅λ

(7.5)

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Proton Therapy Physics

Protons

Housing

Entrance window

Collecting electrode

B

Guard

Winding

FIGURE 7.2 Schematic diagram of a reference dosimetry level Faraday cup with internal vacuum. Shown are the collecting electrode, the guard electrode (which is at negative potential with respect to the collecting electrode), the entrance window, and the windings creating a magnetic field, B, to suppress the loss of electrons generated in the collecting electrode. (Reproduced from Palmans et al., Hadron Dosimetry. In: Clinical Dosimetry Measurements in Radiotherapy (Rogers and Cygler eds.), Medical Physics Publishing, Madison WI, 2009, previously printed in Palmans and Vynckier, Reference Dosimetry for Clinical Proton Beams, In: Recent Developments in Accurate Radiation Dosimetry (Seuntjens and Mobit eds.) Medical Physics Publishing, Madison WI, 2002. With permission.)

where λ is the decay constant of 11C. The activity is usually measured using 4π βγ-coincidence counting, and it is estimated that the fluence can be derived with a standard uncertainty of 3%. Advantages of this method are that no determination of the beam area is needed and that it can be used without much loss of accuracy in high dose-per-pulse beams such as from synchrotrons or laser-induced beams. 7.1.3  Ionization Chambers Ionization chambers are the backbone for reference dosimetry in radiotherapy. With an ionization chamber, dose-to-water, Dw,Q, in a proton beam of beam quality, Q, is related to the average dose-to-air in the air cavity volume, Dair,Q, via Bragg-Gray cavity theory:

Dw,Q = Dair ,Q ⋅ ( sw ,air )Q ⋅ pQ ,

(7.6)

where (sw,air)Q is the Bragg-Gray or Spencer-Attix mass collision stopping power ratio water-over-air for the charged particle spectrum at the measurement point in water and pQ is a correction factor to account for any deviation from the conditions under which Bragg-Gray cavity theory is valid. The average dose-to-air can in principle be obtained from the measured ionization in the cavity, MQ, and knowledge of the mass of air in the cavity (mair = ρair·Vcav) and the mean energy required to produce an ion pair in air, (Wair/e)Q

Dair , Q =

MQ ⋅ (Wair e)Q ρair ⋅ Vcav

.

(7.7)

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Dosimetry

In practice, however, the volume of commercial ionization chambers is not known with the required precision, and one has to rely on a calibration in a reference beam to estimate the volume or bypass the requirement of knowing the volume. It is worthwhile to mention, however, that if an accurate estimate of the volume is available independently of a calibration, for example, from the manufacturer’s blueprints or measured dimensions (as in primary standards of air kerma), dosimetry using an ionization chamber could be based on first principles using Equations 7.6 and 7.7. It has been shown that this can provide a reliable way of a monitor unit calibration for a transmission ionization chamber to link with a Monte Carlo–based planning system (30). To facilitate later the discussion of contributions to differences in dosimetry protocols, the overall expression to derive dose-to-water from the ionization measurements can be split into three factors as follows:



  1 Dw ,Q =  MQ  ⋅   ⋅ (Wair e)Q ⋅ ( sw ,air )Q ⋅ pQ  .  ρair ⋅ Vcav 

(7.8)

All protocols for dosimetry of proton beams using ionization chambers and calculated data can be reduced to this factorization in which the second factor, representing an estimate of the ionization chamber volume, is solely related to the calibration conditions, whereas the third factor is solely related to the proton beam. For example, with the formalism from the International Atomic Energy Agency (IAEA) TRS-398 (1) using calculated kQ values the second factor is given by



 N D , w , Q0    1   =   ρair ⋅ Vcav   (Wair e)Q0 ⋅ ( sw , air )Q0 ⋅ pQ 0 

(7.9)

where N D , w ,Q 0 is the absorbed dose-to-water calibration coefficient in the calibration beam with quality, Q 0, and the quantities in the denominator have the same meaning as quoted above but now for the calibration beam quality. The third factor is identical to the one in Equation 7.8 given that the notations used are consistent with those in IAEA TRS-398. If we take the European Charged Heavy Particle Dosimetry (ECHED) protocol (31, 32) as an example, then the second factor becomes



   N K ⋅ (1 − g ) ⋅ Awall ⋅ km  1   =  (Wair e )c   ρair ⋅ Vcav  

(7.10)

where NK is the air kerma calibration coefficient in 60Co, g is the correction for radiative losses, Awall is the correction factor for absorption and scatter in

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Proton Therapy Physics

the chamber wall and build-up cap in 60Co, km is the correction factor for the nonair equivalence of the chamber’s construction materials, and (Wair/e)c is the mean energy required to produce an ion pair in dry air in the calibration beam quality. The third factor is very similar as in IAEA TRS-398 with the exception that there is no explicit mention of an ionization chamber perturbation correction factor. This is not a de facto difference because in IAEA TRS-398 the assumption is made that pQ equals unity. Interesting to note is that there may not be a great difference in uncertainty on the chamber volume as derived by this factor from air kerma or absorbed dose calibrations. However, in the absorbed dose–based protocols, the quantities occurring in the denominator of Equation 7.9 and those in the third factor in Equation 7.8 are the same except for the difference in beam quality and thus are expected to be more strongly correlated than those in the air kerma–based approach where the factors Awall and km refer to very different conditions as well as to the build-up cap, which is not present with in-phantom measurements. This shows that this factorization is only for illustrative purposes but that the factors two and three cannot be considered independently. Although it is interesting and necessary to study the influence of the second factor in Equation 7.8 on dosimetry using different dosimetry formalisms, it is not related to the proton beam. Differences in dosimetry related to that factor have been reviewed at length in Huq and Andreo (33 and references therein) and will not be further discussed. Concerning the third factor, each of the constituting quantities deserves separate attention: • Mean energy required to produce an ion pair in dry air, (Wair/e)Q: Although often denoted with a capital W, sometimes a small w is used to clarify that it should be the differential value for the local charged particle spectrum because protons lose only a fraction of their energy in the ionization chamber cavity (as opposed to photon and electron beams, where the integral value accounts for all energy losses during the complete slowing down of secondary electrons). The Wair/e value for protons has been the subject of controversy since the ICRU Report 31 (34) recommended a value of 35.18 J C−1, adopted by the ECHED (31, 32), whereas the American Association of Physicists in Medicine (AAPM) Task Group 20 (35) recommended a value of 34.3 J C−1. This discrepancy of 2.6% remained the source of differences in dosimetry recommendations until the publication of ICRU Report 78 (36), which adopted the same value as IAEA TRS-398. There are essentially two ways of measuring this quantity: (1) a simultaneous measurement of the energy loss over an air column and the ionization produced per proton and (2) by comparing the dose response of an ionization chamber and a calorimeter. The first method is cumbersome and requires a correction for electron losses, which is difficult to determine. The second method has the

201

Dosimetry

disadvantage that it provides not a direct measurement of Wair/e, but the pragmatic advantage is that if ionization chamber dosimetry is based on a value derived from calorimetry, it provides consistency with the dosimetry in high-energy photon beams. Noteworthy is also that the Wair/e value in protons is energy dependent but that this energy dependence is not very well known (37). • Water-to-air mass collision stopping power ratio, (sw,air)Q: The stopping power for protons is governed by the same physics as for electrons and positrons, and the theoretical models for calculations at high energies are based on the same Bethe-Bloch formulas with a series of correction terms. For consistency with photon and electron dosimetry, ICRU Report 49 (38) recommended proton stopping powers using the same values for the mean excitation energy, I, as used in the electron and positron stopping power tables of ICRU Report 37 (39). An important difference is that, compared with electrons, the clinically relevant range of proton energies is at much lower (nonrelativistic) velocities where the density effect is of no importance but where there is a strong energy (v−2) dependence of the stopping powers (14). The result is that the water-to-air collision stopping power ratios is fairly constant over the entire clinical energy range. The most recent recommended values of sw,air are Spencer-Attix stopping power ratios, including the contributions of secondary protons and electrons (40), and are given as a function of the residual range Rres by the following (1):









sw ,air = a + b Rres +

c Rres

(7.11)

where a = 1.137, b = −4.3 × 10−5, and c = 1.84 × 10−3. • Ionization chamber perturbation factor, pQ: The ionization chamber perturbation factor corrects for deviations from Bragg-Gray conditions and can according to IAEA TRS-398 be described as the product of four factors: (i) a displacement correction factor, pdis, for the deviation of the effective point of measurement from reference point of the ionization chamber (ii) a cavity perturbation correction factor, pcav, for the perturbation of the charged particle fluence distribution due to the presence of the air cavity (iii) a wall perturbation factor, pwall, for the nonwater equivalence of the ionization chamber’s wall, and (iv) a central electrode correction factor for the presence of the central electrode

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Proton Therapy Physics

The first one can alternatively be dealt with by positioning the effective point of measurement at the required measurement depth. For proton beams it is slightly easier to determine an effective point of measurement than for photon beams given the small lateral deflections that protons undergo. A reasonable approximation is thus to regard protons as traveling along straight lines once they enter the ionization chamber geometry and integrate their dose contributions over the cavity volume. For a cylindrical air cavity with radius Rcyl in water, it is easy to show that this results in an effective point of measurement that is relative to the center of the cavity positioned a distance Δzcyl = 8Rcyl/3π ≈ 0.85·Rcyl closer to the phantom surface (41). For Farmer-type chambers, the higher density of the wall and central electrode materials brings this slightly toward the center of the chamber and closer to the value of Δzcyl = 0.75·Rcyl recommended in IAEA TRS-398 for ion beams (42) but this is not the case for other cylindrical chambers with a thick wall or central electrode for which substantial deviations from this rule may occur. Regarding the other perturbation factors, all the evidence points to corrections of less than 1% (14, 15), and relative correction factors of 1.005 have been demonstrated both experimentally, by cavity theory and by Monte Carlo simulation for A150 walled ionization chambers compared with graphite walled chambers (43, 44, 45). 7.1.4  Detectors for Profile Measurements A range of detectors can be used for lateral or depth–dose profile measurements in proton beams and as for photon beams one can distinguish small, point-like detectors that are used for scanning one-dimensional profiles and continuous or matrix detectors that form rigid structures and that can measure two- (2D) or three-dimensional (3D) profiles in one exposure with a high or relevant resolution. Lateral profiles are usually not problematic given that the spectral variations over the field area are modest. Volume averaging may be of concern in steep penumbrae and small-field profiles occurring in stereotactic treatments and scanned beams. For the measurement of depth–dose profiles, the main issue is that many detectors exhibit a pronounced LET dependence often resulting in a substantial underresponse in the Bragg peak. As we have seen, even water calorimeters exhibit an LET-dependent dose response due to the chemical heat defect, apart from the fact that they are impractical instruments for measuring depth–dose data. Ionization chambers remain the instrument of choice for depth–dose measurements because they exhibit a rather modest LET-dependent dose response that is usually ignored. The third factor in Equation 7.7 clarifies the reasons for this LET dependence.

203

Dosimetry

First, the water-to-air mass collision stopping power ratio, sw,air, is energy dependent, resulting in the beam quality dependence of Equation 7.11. For mono-energetic protons of energy E, sw,air can be calculated as follows: sw ,air =

(S (E) ρ) (S (E) ρ) c

w

c

air

(7.12)

where ( Sc (E) ρ )med is the restricted mass collision stopping power in the medium, med, for protons of energy, E. For protons with a spectral energy distribution, the numerator and denominator in Equation 7.12 become a convolution of proton fluence and restricted stopping powers. The restricted mass collision stopping power can be calculated from the unrestricted mass collision stopping power ( Sc ρ ) med for example, as tabulated in ICRU Report 49, by (44):



(S

c

ρ )med = ( Sc ρ )med −

K Z W ⋅ ⋅ ln  maxx  2  2 ⋅ β  A  med 

  

(7.13)

where the constant K = 0.307075 MeV cm2 g−1 and Wmax is the maximum energy that a secondary electron can obtain from a proton-electron collision. For energies from 1 to 300 MeV, restricted mass collision stopping power ratios water-to-air with cutoff energy Δ = 10 keV, derived from ICRU Report 49 using Equations 7.12 and 7.13, can be approximated by the following:



sw ,air (E) =

a ⋅E (E − b)1+n

(7.14)

where the constants are a = 1.1425, b = 0.025, and n = 0.0012. Second, the mean energy required to produce an ion pair in dry air depends on proton energy (37, 46, 47), and a model for energies above 1 MeV, based on the assumption that for high-energy protons the value should evolve asymptotically to the value for high-energy electrons, is given by the following (46):



(Wair (E) e )p =

(We e ) ⋅ E E−k



(7.15)

where We/e = 33.97 J C−1 is the mean energy required to produce an ion pair in high-energy electron and photon beams and k is a constant that equals k = 0.08513 derived from Dennis’ data (46, 47), whereas a fit to the data from Grosswendt (37) results in k = 0.05264. These two values for k represent quite a large difference in the variation of (Wair/e)p with energy (9.3% and 5.5% from 1 to 300 MeV, respectively), mainly due to the structure of the functional dependence at lower energies; however, this variation is mainly of significance for proton energies under 10 MeV (hence the last couple of millimeters of the proton range).

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Proton Therapy Physics

Third, the wall perturbation factor for ionization chambers has equally been demonstrated to be energy dependent (44, 45) and can be calculated based on cavity theory as follows (44): pwall =



SA swBG, wall ⋅ swall , air

swSA, air

(7.16)



Relative quantity normalized at 100 MeV

where the super indices BG and SA have been introduced to indicate BraggGray stopping power ratios (using unrestricted stopping powers in Equation 7.12) and Spencer-Attix stopping power ratios, respectively. The energy dependence of the three contributions is illustrated in Figure 7.3 for graphite- and A150-walled ionization chambers using the Wair/e variation from the Dennis data. All contributions were normalized to unity at 100 MeV. Convolving this with proton spectra and dose contributions as a function of depth, this leads to a reduction of the peak to entrance ratio of about 1.5% to 2% for air-filled ionization chambers in high-energy proton beams and 3% to 4% for low-energy beams typically used for the treatment of eye melanoma, where the lower numbers are obtained using the Grosswendt data and the higher numbers using the Dennis data. If no variation of the Wair/e value for protons with energy is assumed, the reduction of the peak to entrance ratio is about 0.7% for high-energy beams and 1.2% for lowenergy beams. For other devices typically used for measuring depth–dose curves, the underresponse in the Bragg peak is usually worse than for ionization

1.05 Total A150-walled

1.04

Total graphite-walled

1.03

Wair/e

1.02

sw,air

1.01 1.00 0.99

pwall-graphite pwall-A150 1

10

E / MeV

100

1000

FIGURE 7.3 Relative variation as a function of proton energy of the mean energy required to produce and ion pair in dry air, the mass collision stopping power ratio water-to-air, and the ionization chamber wall perturbation correction factor due to secondary electron effects for two wall materials according to the data and expressions discussed in the text as well as the product of the three.

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Dosimetry

Normalized detector signal

6.0

Markus ionization chamber

5.0

GafChromic EBT film

4.0

GafChromic MD-55 film

3.0 2.0

Alanine

1.0 0.0

24

26

28 Depth / mm

30

32

FIGURE 7.4 Underresponse of two types of radiochromic film and alanine compared with an ionization chamber in the Bragg peak of a 60-MeV proton beam as expected from model functions derived from experimental data.

chambers. Figure 7.4 shows the underresponse compared with the response of an ionization chamber in a 60-MeV proton beam for two types of radiochromic film using a model based on experimental data (48) and for alanine using a model based on experimental data from the literature (49). Note that only the last couple of millimeters of the Bragg curve is shown. Other dosimeters such as diamond detectors, silicon diodes, MOSFETs (metal-oxide-semiconductor field-effect transistors), thermoluminescent devices, optically stimulated luminescence devices, scintillators, gel dosimeters, radiochromic plastics, and photographic film usually show this Bragg peak quenching (14), often to a much worse level than in Figure 7.4. Various explanations have been given for this energy-dependent response such as single-hit theory (saturation of the sensitive site with one ionization) in, for example, alanine and radiochromic film; interradical recombination in, for example, gel dosimeters; and charge recombination in, for example, diamond and more complex theoretical models including charge transport and trapping such as in thermoluminescent devices. In addition, several of these devices are less water equivalent in terms of stopping power variation with energy as can be seen in Figure 7.5. On the other hand, some have reported about diodes that over-respond or highly doped p-type diodes that give good agreement with ionization chambers (50), but given the variability of the response of diodes of the same types, this needs to be verified for each individual diode. A gel dosimeter that is less prone to Bragg peak quenching has also been reported recently, the improvement being explained by the mixing in of a compound that results in smaller radiation-induced polymers and a higher viscosity of the gel (51). A gas electron multiplication detector, mainly used

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Proton Therapy Physics

1.70

1.20 Photographic emulsion

Air

1.15

Diamond

sw, med

1.50

Si

1.05

Al2O3 LiF

Alanine EBT MD-V2-55

1.00 0.95

1

10

E / MeV

100

1.40

sw, med

1.10

1.60

1.30 1.20 1000

FIGURE 7.5 Mass collision stopping power ratios water-to-medium for a variety of detector materials. The black curves for air, diamond, alanine, GafChromic EBT film, and GafChromic MD-V2-55 film are represented on the left-hand side vertical axis; the gray curves for silicon, aluminium oxide, lithium fluoride, and photographic emulsion are represented on the right-hand side vertical axis.

for 2D lateral profile measurements, has also been demonstrated to exhibit only a small quenching effect in the Bragg peak (52). Another interesting method to overcome this energy dependence was reported on scintillating plastics after observing that some scintillating mixtures exhibit an underresponse, whereas others exhibit an overresponse. By choosing an appropriate mixture, a scintillator giving the same depth-dependent dose response as an ionization chamber was established (53), the disadvantage still being that the result applies only to the one particular energy where it was matched. Although with any of the above-mentioned detectors dose distributions can be obtained by scanning, efficient systems exist that allow measurement of distributions in a single exposure. Multilayer ionization chambers have been developed (54) containing absorbing material between neighboring chambers, enabling the measurement of a depth–dose distribution and range in a single exposure. For 2D and 3D dose distributions ionization chambers have been configured in pixel arrays, strips, and multiple-layer strip arrays extending these possibilities. A multilayer Faraday cup can also be used for range verification (55). Further devices for 2D and 3D measurements to mention are radiochromic film (48), radiographic film (56), gel dosimeters (51), radiochromic plastics (57), scintillating screens (58), scintillating liquids (59), gas electron multiplication detectors (52), and amorphous silicon flat-panel detectors (60). A more extensive review is given in Karger et al. (15).

Dosimetry

207

7.2  Reference Dosimetry Reference dosimetry in clinical beams is usually based on national or international reports providing protocols or codes of practice. This section gives first a historical view followed by a subsection on the most recent recommendation. 7.2.1  History of Reference Dosimetry for Protons The first codes of practice for heavy charged particle dosimetry emerged in the 1980s and early 1990s from the AAPM (AAPM Report 16 [35]) and by the ECHED group (31, 32). They all had in common that the first recommendation was to use a calorimeter for reference dosimetry. If not available, a Faraday cup could be used as reference instrument (35) or calibrated against a calorimeter (31, 32), or an ionization chamber calibrated in terms of exposure in air or air kerma in a 60Co calibration beam could be used. In AAPM Report 16 (35) and the original ECHED code of practice (31), the quantity of interest was defined as dose-to-tissue so that in the third factor of Equation 7.8, a stopping power ratio tissue-to-air (tissue-to-gas in AAPM Report 16 because ionization chambers filled with other gasses than air were considered) would occur rather than a stopping power ratio water-to-air. For those two protocols, the second factor in Equation 7.8 was, apart from a few details, similar to that used in AAPM TG-21 for photon and electron dosimetry (61), although no consideration was given to the fact that in the 60Co calibration beam, part of the electron spectrum in the air cavity is not generated in the wall. Both also used the stopping power tables of Janni (62). In the Supplement to the ECHED protocol (32) dose-to-water was defined as the quantity of interest and in addition, the stopping powers of ICRU Report 49 (38) were recommended, which was a step in bringing proton dosimetry in better harmony with high-energy photon and electron dosimetry. One of the more substantial differences between the recommendations of the AAPM and the ECHED was, as discussed before, the substantial discrepancy of about 2.6% in the Wair/e value for proton beams. ICRU Report 59 (63) provided a new recommendation that covered both the air kerma and the absorbed dose routes for dosimetry, but in the latter a number of deficiencies of the procedures and data were pointed out (65), including the undocumented derivation of the Wair/e value for proton beams based on published data, the recommendation of using a Wair/e in ambient air rather than dry air, and the omission of a perturbation factor for the ionization chamber in the calibration beam (as in the denominator on the right-hand side of Equation 7.9). IAEA TRS-398 improved on this and provided a recommendation covering ionization chamber dosimetry based on absorbed dose-to-water calibrations for all external beams except neutrons.

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Proton Therapy Physics

For protons, the value of Wair/e was obtained from a robust statistical analysis of the available data and Spencer-Attix mass collision stopping power water-to-air ratios (40) were used for the first time. Other advantages were better estimates of the uncertainties and better consistency with other external beam modalities regarding the measurement of influence quantities such as recombination and polarity effects. The most recent recommendation in ICRU Report 78 (36) integrally adopts the concepts and data from TRS-398. One of the achievements of ICRU Report 78 was to readdress all the published Wair/e data, correcting a few inconsistencies in earlier used data by ICRU Report 59 and IAEA TRS-398, and to add new data published since 2000. It was decided that for consistency with calorimetry-based data in high-energy photon and electron beams, only the data obtained by calorimetry would be used for a reevaluation (64), resulting in a weighted mean value of 34.15 ± 0.13 J C−1 and a weighted median value of 34.23 ± 0.13 J C−1, both consistent with the value recommended in IAEA TRS-398. All the calorimetric data and the quoted mean and median values are shown in Figure 7.6. With the latter three protocols mentioned, the idea of recommending calorimeters in a clinical environment was abandoned given that calorimeters are too cumbersome and time consuming to operate for routine dosimetry. Nevertheless, the first recommendation of IAEA TRS-398 remains that kQ values are measured for each individual ionization chamber in each individual beam they are used. A number of published articles have reported kQ values in proton beams by comparing ionization chambers with water calorimeters both in passively scattered proton beams as in scanned proton 36.0

Schulz et al. 1992 Palmans et al. 1996 Brede et al. 1999 Palmans et al. 2004

(Wair/e)p / eV

35.5 35.0

Siebers et al. 1995 Delacroix et al. 1997 Hashemian et al. 2003 Medins et al. 2006

34.5 34.0 33.5 33.0

Weighted mean 0

50

Weighted median

100 Energy / MeV

150

200

FIGURE 7.6 Calorimetric determinations of the mean energy required to produce an ion pair in dry air and weighted mean and median values as determined in Jones (64). (From Palmans et al., Hadron Dosimetry. In: Clinical Dosimetry Measurements in Radiotherapy (Rogers and Cygler eds.), Medical Physics Publishing, Madison WI, 2009, and Jones, Rad Phys Chem, 75(5), 541, 2006. With permission.)

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Dosimetry

1.08 1.06 1.04 kQ

1.02 1.00

Sarfehnia 2010 Exradin T1 235 MeV

Medin 2010 NE2571 180 MeV

Gagnebih 2010 Exradin T2 170 MeV

Sarfehnia 2010 Exradin T1 235 MeV

Medin 2006 NE2571 180 MeV

Vatnitsky 1996 Capintec PR06 250 MeV

Vatnitsky 1996 Capintec PR06 250 MeV

Vatnitsky 1996 PTW30001 155 MeV

0.96

Vatnitsky 1996 PTW30001 250 MeV

0.98

FIGURE 7.7 kQ values for various ionization chambers derived from water calorimetry (data points) compared with values from TRS-398 (black horizontal lines with gray boxes defining a 1.7% standard relative uncertainty interval). The three data points on the right-hand side are for scanned proton beams.

beams (12, 24, 66–68). Figure 7.7 compares those experimental values with the calculated values recommended in IAEA TRS-398. 7.2.2  Recommendations of IAEA TRS-398 and ICRU Report 78 It is not the aim here to give a comprehensive overview of the code of practice for proton dosimetry in IAEA TRS-398 (1), which has been integrally adopted in ICRU Report 78 (36). For all details the reader is referred to those reports. The main steps in the dose determination using ionization chambers calibrated in terms of absorbed dose-to-water will be briefly outlined and some import points to pay attention to concerning proton dosimetry will be discussed. The formalism for determination of absorbed dose-to-water, Dw,Q, in a proton beam with quality Q is

Dw,Q = MQ ⋅ N D,w,Q0 ⋅ k Q , Q0

(7.17)

where MQ is the ionization chamber reading corrected for influence quantities, N D , w ,Q0 , the absorbed dose-to-water calibration coefficient of the ionization chamber in a calibration beam of quality Q 0 and kQ ,Q 0 the beam quality correction factor accounting for the use of the calibration coefficient in a different beam quality Q.

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Because of the limited availability of experimental kQ ,Q 0 data, their values are in practice calculated from



kQ ,Q0 =

(Wair e )Q ⋅ ( sw,air )Q ⋅ pQ (Wair e )Q ⋅ ( sw,air )Q ⋅ pQ 0

0

(7.18) 0



in which all quantities have been defined before. The combination of Equations 7.17 and 7.18 leads to the factorization in Equations 7.8 and 7.9 as discussed above. kQ ,Q0 values are calculated with Equation 7.18 as a function of the beam quality index, Rres , defined as

Rres = Rp − z

(7.19)

where Rp is the practical range, defined as the depth distal to the Bragg peak at which the dose is reduced to 10% of its maximum value and z is the depth of measurement. Rres is related to the most probable energy of the highest proton energy peak in the spectrum. Concerning the correction for influence quantities of the ionization chamber reading, the corrections for atmospheric conditions (deviations from normal pressure, temperature, and relative humidity at which the calibration coefficient is valid) and electrometer calibration are the same as in all modern protocols for high-energy photon and electron beams and will not be discussed here. The correction for polarity effects and ion recombination are measured in the same way as well, but an important issue to be considered is if a proton beam should be regarded as pulsed or continuous with respect to ion recombination because this makes a difference in deriving the correction factor from the traditional two-voltage method. IAEA TRS-398 mentions that beams extracted from a synchrotron may have to be regarded as continuous. However, it has been demonstrated that proton beams from a cyclotron, which are inherently pulsed, should be regarded as continuous as well for this purpose given the short time interval between pulses compared with the ion collection time (69). In high dose rate beams like those used in ocular treatments, the error on the ion recombination factor could be up to 2% when applying the two-voltage method with the inappropriate assumption that the beam is pulsed. The calibration coefficient N D,w,Q0 is usually obtained in a 60Co calibration beam at a standards laboratory, and in that case IAEA TRS-398 omits the index Q 0 for both the calibration coefficient and the beam quality correction factor: ND,w and kQ. kQ values for all commonly used ionization chambers have been tabulated as a function of Rres in IAEA TRS-398 and are for a selection shown in Figure 7.8. It is clear that the variation with beam quality is rather limited. The differences between ionization chamber types is solely due to differences in the perturbation correction factors for 60Co.

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1.05

1.03

NE2571 (Farmer - graphite)

Capintec PR06C (Farmer - C552)

1.04

PTW 3001 (Farmer - PMMA)

IBA FC65P (Farmer - Delrin) PTW 30014 (PinPoint)

NE2581 (Farmer - A150)

kQ

1.02

Markus

1.01

FWT IC-18

1.00

Roos

0.99 0.98

NACP02

0.1

1

Rres / g cm–2

10

100

FIGURE 7.8 Calculated kQ data as a function of the proton beam quality R res for a selection of ionization chambers taken from IAEA TRS-398.

The ideal situation, however, would be that the ionization chamber is calibrated against a calorimeter in a proton beam that would then form the calibration quality Q 0. kQ ,Q 0 can then be obtained from the tabulated data as follows:



kQ , Q0 =

kQ kQ0

(7.20)

where both Q and Q 0 refer to a proton beam quality. A similar case is that in which a plane-parallel ionization chamber needs to be used, for example, in a spread-out Bragg peak in a low-energy beam with very limited extension. IAEA TRS-398 discourages the use of plane-parallel chambers with 60Co calibration coefficients because the perturbation correction factors in the 60Co calibration photon beams have a large uncertainty. It has therefore been suggested to cross-calibrate a plane-parallel ion chamber against a cylindrical chamber in a high-energy proton beam and subsequently use the chamber in other proton beams by using Equation 7.20 for kQ ,Q0 .

7.3  Microdosimetry Although radiotherapy prescription is based on the macroscopic quantity absorbed dose-to-water, multiplied with a quality factor, the effect of radiation on individual cells is governed by the local energy deposition within

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the cell or parts of the cell. Microdosimetry concerns the study of the spatial and temporal distribution of energy deposition accounting with the stochastic nature of energy losses and track structure and therefore provides the physical information that is more directly linked with the biological effects of radiation. 7.3.1  Microdosimetric Quantities Microdosimetry uses quantities that are the stochastic equivalents of absorbed dose and LET. The specific energy, z, in a miscroscopic volume, V, is defined as z = ε/ρV, where ε is the energy imparted in the volume and ρ the mass density of the medium. The energy imparted is defined as the sum of all kinetic energy carried by ionizing particles into the volume minus the sum of all kinetic energy carried by ionizing particles out of the volume plus the energetic value of any reduction of rest mass taking place within the volume. The lineal energy, y, is defined as y = ε1/ l , where ε1 is the energy imparted in the volume in a single event and l is the mean chord length of the volume. For any concave volume the mean chord length is given by l = 4V S, where S is the surface area. Radiation effects that are stochastic such as the biological response depend on the probability distributions of the microdosimetric quantities, f(z) and f(y), and can in principle be derived from those (71, 72). The distribution of lineal energy is usually represented graphically as y · f(y) plotted against log (y) or y2 · f(y) plotted against log (y). In the former representation, the area under the curve delimited by two values of y is proportional to the fraction of events between those two values of y, whereas in the latter representation the area under the curve delimited by two values of y is proportional to the fraction of dose delivered by events with lineal energy between those two values. Figure 7.9 gives an example of the second representation of a microdosimetric spectrum of a proton beam compared with that of a 60Co beam (73) together with a biological weighting function for the acute effects in the intestinal crypt cells of mice as an end point (74) as a function of lineal energy, indicating why the biological effect of protons is slightly enhanced compared with 60Co (see Chapter 19). 7.3.2  Experimental Microdosimetry A distinction has to be made between regional microdosimetry, the most common focus of experimental microdosimetry, which aims at measuring f(y) and f(z) for a particular site of interest, and structural microdosimetry, which aims at deriving microdosimetric quantities and actions from detailed 3D distributions of energy transfer points. The most commonly used detectors for regional microdosimetry are tissue equivalent proportional counters (TEPCs). In its most simple form a TEPC is a walled ionization chamber operated at high-voltage such that an avalanche

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Dosimetry

1.0

4

r(y)

0.6

3

0.4

2

0.2

1

r(y)

y 2f (y)

0.8

5 Co-60 p 200 MeV 17.6 cm

0.0 10–2

10–1

100 101 y / keV mm–1

102

0 103

FIGURE 7.9 Microdosimetric spectrum of a 200-MeV proton beam at a depth of 17.6 cm (squares), microdosimetric spectrum of a 60Co beam (triangles), and a biological weighting function (line). (Replotted from Coutrakon et al., Med Phys, 24(9), 1499, 1997. With permission.)

takes place. The number of ion pairs produced is assumed to be proportional to the energy transferred. By operating at low pressure, the energy deposition of a small site of tissue density is mimicked (e.g., a 2.5-cm sphere at pressure of 2.3 kPa is approximately equivalent to a 1-μm-diameter sphere of density 1 g cm−3). If the gas has the same atomic composition as the wall material, the fluence of secondary charged particles should be independent of density variations apart from the influence of the density effect on the stopping power. For proton beams, the energy deposition in a single event can be overestimated due to the following three effects (71, 75):





1. The delta-ray effect (a secondary electron that would normally not cross the same site as the primary proton does enter the volume because of the larger dimensions), 2. The V-effect (a secondary proton or heavier particle from a nuclear interaction that would normally not cross the same site as the primary proton does enter the volume because of the larger dimensions), and 3. The reentry effect (after leaving the collecting volume a secondary electron following a strongly curved path that would normally not reenter the measurement volume does reenter because of the larger dimensions).

For this reason, more sophisticated TEPCs are wall-less, either by using special electrodes to shape the field and that way define the measurement volume without the presence of a wall or by using a grid wall, thus minimizing

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the amount of wall material. Another problem with TEPCs is their size, which limits the achievable resolution, which is especially a problem in the Bragg peak, and makes them more vulnerable to pile-up effects in radiotherapy level dose rates due to the occurrence of simultaneous multiple events (76). Mini-TEPCs (77) and gas microstrip detectors (consisting of alternating anode and cathode metallic strips on a substrate and a drift electrode defining the gas volume) (78) have been developed to overcome these problems for proton microdosimetry. Calibration of a TEPC consists of establishing a relation between pulse height and energy deposition and is done using either a source of particles with known energy that are completely absorbed in the detector volume or by making use of the proton edge. The latter exploits the fact that near the end of the range the proton energy deposition is highest and the lineal energy distribution has a sharp edge (which is, however, blurred by energy and range straggling and by the contaminant presence of heavier recoils). The edge lineal energy for protons was determined as yedge = 136 keV μm−1 for a water sphere of 2 μm in diameter (79) (and should be scaled for the size and the operational gas density of the TEPC). Knowledge of the mean energy required to produce an ion pair in the gas, Wgas, is another source of uncertainty. Wgas is known to decrease with energy for a given particle mass and increases with particle mass for a given energy and is assumed to add about 5% uncertainty to the energy absorption measured with a proportional counter. Silicon-based devices for microdosimetry also measure ionization, via electron-hole pair creation in a depletion layer, but have as a main advantage compared with a TEPC that their size is much closer to the site of interest in water or tissue. For radiotherapy this results in both a higher spatial resolution and a reduction of the delta-ray effect, V-effect, reentry effect, and pileup effect. Disadvantages are that the collecting volume is poorly defined, that they are prone to radiation damage, and that they are not exactly tissue equivalent so that a conversion (with a scaling factor of about 0.63) is still needed (75). The mean energy required to produce an electron-hole pair, WSi, is about a factor 10 lower than Wgas in TEPCs. The same problem of the dependence of WSi on particle energy and particle type exists, but a value of WSi = 3.62 eV is often used. Application of an array of p-n junctions with a pixel area of 0.04 cm2 to two therapeutic proton beams revealed that in large beams even with a silicon diode, pile-up effects can occur (75), but silicon devices can be further miniaturized. Another interesting feature of silicon technology is that a construction integrating more than one detector with different functions is possible. For example, a ΔE-E silicon telescope has been described (80) consisting of two layers of silicon detectors sharing the same p+ electrode, the upper one being very thin (1 μm) and the lower one being 500 μm thick. When a particle passes through both layers, the signal from the upper layer provides the energy loss over 1 μm of silicon, whereas the sum of both signals provides

Dosimetry

215

the total energy of the particle (under the condition that it is stopped within the thick lower layer). This coincidence measurement allows resolving the particle type that hits the detector because different particle types will occupy different regions in a ΔE-E map and is thus of interest in mixed particle fields. Application of the detector to protons showed that contributions of other ion species in the radiation field are marginal. Besides the experimental methods for regional microdosimetry, some track structure measurement devices have been used in proton beams, which are mentioned here but of which a more extended overview can be found in Bradley (75). In cloud chamber microdosimetry, a low-pressure super-cooled gas is used in which the individual ionizations of the proton and its secondary particles create a 3D pattern of droplets that can be resolved by stereoscopic photography, providing extremely high-resolution detail on the location of individual ionizations within the gas. In an optical ionization chamber electrons in the particle track are made to oscillate rapidly by the application of an external, short duration, high-voltage electric field. The excited electrons produce additional ionization and electronic excitation of the gas molecules in their immediate vicinity, leading to fluorescent light emission from the gas that allows the location of the electrons to be determined with a resolution of 10 nm. In 3D optical random access memories the energy deposited along the proton track changes a bi-stable photochromic material from the stable nonfluorescent form to a quasi-stable fluorescent form. The location of the fluorescent sites can be read out by confocal laser microscopy.

References



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8 Quality Assurance and Commissioning Zuofeng Li, Roelf Slopsema, Stella Flampouri, and Daniel K. Yeung CONTENTS 8.1 Standards and Recommendations on External Beam Radiation Therapy QA and Commissioning............................................................222 8.2 Components of a Clinical Proton Therapy System................................223 8.2.1 Beam Production and Transport System..................................... 223 8.2.2 Beam Delivery Techniques/Nozzles............................................ 224 8.2.3 Mechanical Gantry or Fixed Beam Line...................................... 227 8.2.4 Patient-Positioning System............................................................ 227 8.2.5 Image-Guided Patient-Alignment System.................................. 227 8.2.6 Computed Tomography Scanners for Proton Therapy............. 228 8.2.7 Patient Immobilization Devices.................................................... 228 8.3 Design of Acceptance Testing and Commissioning Plan for a Proton Therapy System.............................................................................. 229 8.3.1 Acceptance Testing of Proton Therapy Systems........................ 229 8.3.1.1 Radiation, Mechanical, and Electrical Safety Issues................................................................ 229 8.3.1.2 Gantry, Snout, Patient-Positioning, and Patient-Alignment Systems............................................. 231 8.3.1.3 Proton Beam Characteristics.......................................... 233 8.3.1.4 Dose-Monitoring System................................................ 238 8.3.2 Commissioning of Proton Therapy Systems.............................. 239 8.3.2.1 CT HU-to-Stopping Power Calibration......................... 240 8.3.2.2 Treatment-Planning System Commissioning.............. 240 8.3.2.3 MU Calculations.............................................................. 242 8.3.2.4 Beam-Modifying Accessories......................................... 243 8.3.2.5 Patient Immobilization Devices..................................... 243 8.3.2.6 R&V System....................................................................... 245 8.4 Design of a Periodic QA Program for a Proton Therapy System........... 245 8.5 Dosimetry Instrumentation for Proton Therapy Commissioning and QA............................................................................ 251 8.6 Conclusions.................................................................................................. 259 References.............................................................................................................. 260

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Clinical proton therapy is delivered using proton beams produced by either synchrotron- or cyclotron-based accelerator systems, which differ significantly in operating details and beam controls (see Chapter 3). The mechanical and electronic components for formation of spread-out Bragg peaks (SOPBs) from pristine Bragg peaks may differ between different proton therapy systems as well (see Chapters 4–6). Such differences lead to significant difficulties in developing general, comprehensive recommendations for the commissioning and quality assurance (QA) programs of clinical proton therapy. It is therefore important that practitioners of proton therapy, especially the medical physicists, develop a machine-commissioning and QA process before initiation of patient treatment and continue to monitor system performance and improve the periodic QA program as more experience is gained over time with a particular proton therapy system.

8.1 Standards and Recommendations on External Beam Radiation Therapy QA and Commissioning Unlike the case of conventional photon-based external beam radiation therapy, standards of practice for proton therapy system commissioning and periodic QA programs have not been developed. The American Association of Physicists in Medicine (AAPM) has developed a number of recommendations for the commissioning and periodic QA of linear accelerator–based radiotherapy, as embodied in its task group reports (1–3). These reports outline detailed, specific, sometimes prescriptive recommendations of QA tests, together with acceptable performance tolerances, for the commissioning and periodic QA of linear accelerators. The AAPM TG45 report (1) provided stepby-step instructions on the acceptance testing and commissioning of linear accelerators. The commissioning of a linear accelerator follows successful acceptance testing of the unit and aims at the accurate collection and modeling of beam and nondosimetric machine data for treatment planning. AAPM TG40 and TG142 reports (2, 3) provide detailed guidelines on the periodic QA tests to be performed for radiotherapy equipment with test frequency and tolerance values. Although the overall structure of a proton therapy system acceptance testing, commissioning, and periodic QA program will be similar to those described in these reports, the specific recommendations of these standards of practice do not apply well to proton therapy systems in general. A proton therapy system, for example, will be capable of providing a continuously variable range of beam energies from a minimum value (e.g., 90 MeV) to a maximum energy of 230–250 MeV at the nozzle entrance. Depending on the system design, the system may subdivide this continuous span of beam energy into spans of beam energy or options. Proton therapy systems

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differ from conventional linear accelerator–based radiotherapy in additional details, including the production and delivery of treatment beams; the use of image guidance (currently provided by daily or field-by-field orthogonal x-ray imaging); the use of range compensators; and the use of 6 degrees of freedom (DOF) patient positioners, some with corrections for gantry sags. The acceptance testing, commissioning, and periodic QA tests will need to be carefully designed to customize to these differences. The International Commission on Radiation Units and Measurements (ICRU) has published a report (4), ICRU Report 78, on prescribing, recording, and reporting proton therapy. A chapter of this report is dedicated to QA of proton therapy systems, with discussions on the individual subsystems of proton delivery, patient positioning and immobilization, and treatment planning. The report provides two tables as examples for the periodic QA of passive-scattering beams and active scanning beams. These tables would serve well as the foundation in building a periodic QA program for a proton therapy institution; however, revisions and specifications of tolerances will be necessary to tailor to the requirements of individual proton therapy systems.

8.2  Components of a Clinical Proton Therapy System A modern clinical proton therapy system is designed to include multiple subsystems, such that they function collectively as an integrated unit to provide accurate patient treatment simulation, planning, and delivery. Many of these subsystems have the same functionalities as their counterparts in traditional radiation therapy and are different only in specific configurations when adapted for proton therapy applications. Guidelines for their commissioning and QA tests, whenever applicable, should follow the established standards. 8.2.1  Beam Production and Transport System An accelerator, either a cyclotron or a synchrotron, is used to produce the proton beam (see Chapter 3). Cyclotrons produce a nearly continuous beam of constant beam energy of up to 250 MeV, with adjustable beam current. The high-energy beam leaving a cyclotron is then reduced or “degraded” to a lower-energy beam as required for patient treatment, by use of an energy degrader of tissue equivalent materials of variable thicknesses. The insertion of an energy degrader, however, also degrades the beam quality by increasing beam emittance or angular spread, as well as the beam energy spread. An Energy Selection System (ESS) using collimators, slits, and magnets is then used to restore beam quality. Synchrotrons produce spills of a proton beam of variable energy, with each several-seconds-long spill consisting of a beam-on flat top and a beam-off bottom. No energy degrader and selection

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system is required for a synchrotron-based system because of the nearly continuous adjustability (in beam energy) of the accelerator. The proton beam, after exiting the ESS for a cyclotron-based system, or the accelerator in case of a synchrotron, then follows a beam transport system in vacuum to be directed to individual treatment rooms. Multiple magnets are used along the beam line for focusing and centering, so that beam quality is maintained at the highest level possible. Such beam quality parameters include average beam energy, energy spread, emittance (angular spread), spot size, and beam current intensity. These physical beam characteristics may have a significant impact on the quality of patient dosimetry. The constancy of these beam characteristics over the lifetime of the proton therapy system, therefore, needs to be considered carefully in the design of a proton therapy system commissioning and QA program. 8.2.2  Beam Delivery Techniques/Nozzles Proton delivery techniques, both passive scattering and active scanning, are ultimately implemented in the nozzle. The proton beam exiting the beam transport system is a narrow beam, with a nearly uniform energy spectrum. This beam produces a narrow pristine peak in water, whereas for clinical cancer therapy, the beam needs to create a dose distribution that conforms to the three-dimensional (3D) volume of a target. The nozzle receives the input of a narrow pencil beam, outputs a beam spread pattern suitable for delivery of a 3D dose distribution, through either the use of physical scatterers (Chapter 5) or active magnet-driven scanning of the pencil beam in the beam’s lateral direction (Chapter 6), and creates a depth–dose profile with a flat (SOBP) or customized shape in the beam axis direction. Figure 8.1 shows the components of a typical passive-scattering nozzle (5). The proton pencil beam enters the nozzle through IC1 (ion chamber 1), which monitors beam centering upon entrance into the nozzle. The first scatterer serves to expand the narrow pencil beam into a wide, Gaussian-shaped proton beam, and the second scatterer subsequently flattens the wide Gaussian beam into a flat proton beam to allow delivery of 3D conformal proton therapy treatments. Such use of two consecutive scatterers, similar to the use of scattering foils in conventional linear accelerators for electron beam production, is referred to as the double-scattering technique. The second scatterer may be removed, however, to achieve the single-scattering technique, which produces a beam with dome-shaped profile but avoids the scattering of protons in the second scatterer, thereby improving beam quality in lateral penumbra and distal falloff. Moveable collimators/jaws are used to eliminate scattered protons outside the intended treatment volume. Two ion chambers (IC2 and IC3) are used for dose and beam profile monitoring and control. The final field shape is defined by a treatment-field-specific aperture (block), mounted on a moveable snout so as to minimize the distance of the range compensator/bolus to patient skin and hence reduce in-air proton scattering.

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Range modulator wheels Magnet 2 IC1 Jaws (X and Y) (& range verifier) Snout retraction area Water phantom

Snout

First scatterers Magnet 1 Second scatterers IC2 and IC3

FIGURE 8.1 Schematics of a passive-scattering nozzle (IBA Universal Nozzle, Louvain-la-Neuve, Belgium). The beam enters from the right. (Adapted from Paganetti et  al., Med Phys, 2004, 31(7), 2107, 2004.)

The creation of SOBP is performed by use of modulation wheels in this nozzle. In the example of the nozzle by IBA (Ion Beam Applications, Louvainla-Neuve, Belgium) each of the three modulation wheels contains three circular tracks of step-wise increasing thicknesses, which allows step-by-step pullback of pristine peaks. The proton beam current is modulated based on precalibrated tables to maintain the flatness of the SOBP and is turned off to achieve a prescribed SOBP width (6, 7). Accuracy of beam current modulation directly impacts flatness of the delivered SOBP, as well as the absolute dose value in the middle of this SOBP (7) (see Chapter 5). The presence of scatterers and modulation wheels in the proton beam path should be of particular concern in the implementation of a periodic QA program, as they are the subject of significant mechanical wear and tear and over time may suffer radiation damage. The nozzle of Figure 8.1, in addition to providing single- and double-­ scattering techniques, also supports an active scanning technique, the “wobbling” or “uniform-scanning” technique (8). The first-scattered beam is scanned laterally using the two magnets in the nozzle to create a large lateral beam spread. One of the tracks in a modulation wheel is used for pristine peak pullbacks, with the wheel set in the indexing mode and the steps of the track serving as “range shifters.” The proton dose is therefore delivered in a layer-stacking fashion, with the modulation

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wheel indexed to a new position after completion of dose delivery to a given layer. Both scattering and wobbling techniques require the use of high-Z fielddefining apertures and range compensators, which are mounted on the snout. Apertures used in proton therapy are typically fabricated out of brass alloy or low-melting-temperature alloy such as Cerrobend™ (Cerro, Vineyard, UT). Range compensators may be similarly milled out of PMMA or high-impact wax. Accuracy of aperture milling affects treated field size. The range compensator material composition consistency, as well as its fabrication, directly affects dose distribution distal and proximal to the target. Figure 8.2 shows an active scanning nozzle (9). The insertion of an He chamber in the beam pathway, as well as removal of scatterers used in passive-scattering techniques, allows a minimal spot size of the pencil beam at the exit of the nozzle. Focusing magnets may, in addition, be installed in the nozzle to further reduce the beam spot size (10). The absence of modulation wheels and scatterers within a scanning nozzle eliminates concerns of their mechanical wear and tear and general degradation. The monitor chambers in scanning nozzles, however, must be able to measure the spot position and the cumulative doses quickly (10). For nozzles equipped with snouts that translate along the beam axis to allow minimal distance of apertures/range compensators to the patient’s skin, the accuracy of snout movement needs to be verified, because deviations from theoretic values would change the projected field size. The co-­linearity of snout travel to beam axis needs to be verified and tested at several gantry angles in a gantry treatment room. Window; Ti Profile monitor Scanning magnet (Y) He chamber Scanning magnet (X) 3.24 m

He chamber Scattering device X-ray tube Dose-monitor #2 Dose-monitor #1 Spot position monitor

0 – 0.38 m Iso - center

Energy filter Snout moving device Energy absorber Aperture

FIGURE 8.2 Schematics of a scanning beam nozzle. (Adapted from Gillin et al., Med Phys, 2010, 37(1), 154.)

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8.2.3  Mechanical Gantry or Fixed Beam Line The nozzle is mounted on a mechanical gantry or at the end of a fixed beam line. The mechanical isocenter accuracy of a proton gantry and the agreement of radiation and mechanical isocenters need to be calibrated and verified periodically in a manner similar to conventional linear accelerator gantry systems. Techniques including the pointer-tip-matching test and the starshot film test are suitable for this purpose. Moyers and Lesyna (11) described an extricate test of gantry mechanical isocentricity using theodolites and demonstrated that the isocenter movement of a proton gantry is similar to that of a linear accelerator of similar mechanical design. For a fixed beam line, either vertical or horizontal, an isocenter is defined as the intersection of beam axis to the patient treatment table rotation axis, and its verification simplifies to verification of that agreement. 8.2.4  Patient-Positioning System Although patient-positioning systems of proton therapy serve the same purpose of treatment tables of traditional radiotherapy units, they may provide additional capabilities compared with a conventional treatment couch of linear accelerators, including the following: • Ability of providing a limited range of patient pitch-and-roll corrections, in addition to the traditional three translational and one rotational DOF; • Absence of co-linear rotational axis. The table top and base may have different centers of rotation, such that a table rotation is achieved by a combination of table translations as well as separate rotations of the table top and base; • Ability to compensate for gantry sags using precalibrated lookup tables; • Capability of preprogrammed and stored automatic motion maneuvers, such as moving to predefined locations for the purposes of loading/unloading patients or for setting up QA devices such as a 3D scanning water tank. The QA tests of a proton therapy patient-positioning system need to be designed to explore and confirm the correct and accurate functioning of the device in these aspects. 8.2.5  Image-Guided Patient-Alignment System At the current time, all commercially available proton therapy systems are installed with orthogonal x-ray-based patient-alignment systems. The

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x-ray tubes may be installed at ±45o offsets from the beam axis or having a moveable x-ray tube inside the nozzle paired with a second tube at 90o from the beam axis. For the latter configuration, the x-ray tube in the nozzle is inserted into the beam path during imaging and is moved out of beam path during proton beam tuning and delivery. Software packages are generally used to align precalculated digitally reconstructed radiographs (DRRs) of setup and treatment fields to corresponding x-ray images of the patient. Geometric accuracy of such imaging systems relative to the proton beam isocenter and in various gantry rotation angles, as well as the accuracy and application of patient shifts calculated by the software package, need to be verified. Quality of images of these systems should be evaluated at the time of system commissioning and subsequently should be tested periodically for consistency. The radiation doses delivered by such imaging systems should be evaluated following the recommendations of the AAPM TG75 report (12). 8.2.6  Computed Tomography Scanners for Proton Therapy Proton therapy dose calculations rely on computed tomography (CT) images of the patient in the treatment position. The CT numbers (Hounsfield unit [HU]) of CT pixels are converted into relative stopping power values for proton range calculations. It has been demonstrated that, for photon dose calculations, dose calculation accuracy is relatively insensitive to uncertainties of HU-to-electron density conversions, with 2% to 5% HU value changes corresponding to 1% dose change, depending on beam energy and tissue type (13). Uncertainties in the CT HU-value-to-stopping-power conversion, however, are linearly transferred to uncertainties in proton range calculations. Accurate and careful calibration of the CT HU-to-stopping-power conversion is therefore an important and critical part of proton therapy system commissioning and QA processes. Other aspects of CT simulations, including geometric accuracy and image quality, require the same rigor in commissioning and periodic QA tests. The AAPM Task Group 66 report (14) provides detailed descriptions of these tests. 8.2.7  Patient Immobilization Devices Dosimetric effects of patient immobilization devices on proton dose distributions, both in range accuracy and in proton scattering, need to be carefully considered and investigated. Sharp variations of thicknesses in these devices increase dose distribution inhomogeneity, in addition to increasing uncertainties in the delivered beam ranges. The material composition of such devices should be homogeneous, because significant variations of their water equivalent thickness within treatment fields would compromise the delivered dose distributions if left uncompensated for.

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8.3 Design of Acceptance Testing and Commissioning Plan for a Proton Therapy System The acceptance testing and commissioning of clinical proton therapy systems, in principle, will include a similar flow of actions as those for linear accelerators detailed in the AAPM TG45 report (1). 8.3.1  Acceptance Testing of Proton Therapy Systems The acceptance testing of a proton therapy system includes demonstration of the system meeting specifications in the following aspects: • Radiation, mechanical, and electrical safety issues • Gantry, snout, and patient-positioning system mechanical, imaging, and therapy beam alignments • Proton beam characteristics • Dose-monitoring system Differences between a proton therapy system and linear accelerators, from facility construction and equipment installation, to the availability of a practically infinite number of beams, require that such a flow be modified. Acceptance testing procedures (ATPs) for linear accelerators, although vendor specific, have been long established and typically require only minor revisions specific to user requirements. Proton therapy system ATPs, however, are still evolving and would require detailed negotiations and discussions with system vendors as part of the purchasing agreement. 8.3.1.1  Radiation, Mechanical, and Electrical Safety Issues Radiation safety concerns in a proton therapy facility differ from traditional linear accelerator facilities primarily in the significant neutron exposure present around the proton accelerator, beam line, and treatment rooms, as well as the activation of system components. Ipe et al. (15) discussed in detail the mechanisms and methods of radiation production and interaction, shielding, and monitoring requirements, as well as personnel and patient safety considerations of charged particle therapy facilities (see Chapter 17). As soon as the accelerator is able to produce proton beams, radiation safety measures must be taken to ensure that the neutron exposure outside the accelerator and beam line vault is at a level meeting local regulatory requirements. Such a radiation survey must be performed at the highest beam energy and current to adequately reflect the maximum neutron exposure that the installation engineers, construction workers, and facility personnel may receive during the subsequent construction, installation, and acceptance phases. An x-ray exposure survey should be taken at the same time.

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The presence of activated materials, such as accelerator circulating cooling water, oil, and replacement parts must be carefully evaluated. Such materials need to be located in areas considered safe and adequate for radiation protection and must be posted as radioactive material storage areas as demanded by local safety requirements. Radiation safety concerns for a proton therapy facility also differ from a linear accelerator facility in that facility construction is often ongoing when beam testing starts. A particular scenario may be that vendor engineers work overnight to perform beam testing in a given treatment room, and then the room is turned over to construction workers to complete room furnishing and ancillary equipment installation. Construction workers are typically not radiation workers. A daily room survey will therefore need to be performed, to measure the ambient radiation exposure of the room due to activated materials. Potentially activated components, such as brass blocks, should be collected and removed from the room before it is turned over to construction workers. Completion of these radiation safety measures must be documented in a daily room radiation survey form posted at the entrance to the room. Training on these procedures needs to be provided to construction workers. Proton accelerator and beam line vault and treatment rooms are equipped with beam status indicator lights, crash buttons, door interlocks, and area radiation-monitoring devices. The accelerator and beam line vault, as well as treatment rooms, are also installed with search switches and alarms that disable beam production, transport, and delivery in these areas until manually cleared. As personnel evacuate these areas in preparation for beam-on operations, these switches are sequentially enabled, and alarms are sounded to warn any other persons of the pending start of irradiation sessions, such that no person is left behind and receives irradiation accidentally. Correct functioning of these devices must be validated. Moving subsystems in a proton therapy treatment, including the gantry, snout, treatment table, and imaging panels, may be equipped with proximity and collision sensors. The proximity sensors alert operators when a moving system, including gantry, snout, or treatment table, moves to within a predefined distance of another subsystem and may automatically slow the speed of a moving system. The collision sensors detect pressure above a predefined threshold on a given system and stop the moving system. The functioning status of such sensors should be verified during acceptance testing to operate according to specifications. In addition, recovery from a collision, using either electrical or manual power, should be tested and included in user training. Leakage radiation, as well as scattered radiation dose to patient outside treated volume, should be evaluated during the acceptance testing process. There should be no leakage of primary protons through the nozzle and snouts. Radiographic or radiochromic films may be wrapped around the nozzle and snout to identify the presence of any such leakage spots, and ion chambers used for quantitative measurement of absolute dose levels at any

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hot spots that are identified on the film. These measurements need to be performed for all snouts available. The scattered radiation exposure levels outside treatment field, both of photons and of neutrons, should be evaluated and documented (16–20). 8.3.1.2  Gantry, Snout, Patient-Positioning, and Patient-Alignment Systems The mechanical isocentricity of the gantry and treatment table should be verified during acceptance testing. A traditional method, such as “pointer matching” may be used. Moyers and Lesyna (11) described a method for measuring the axial as well as radial isocenter walks of a proton gantry using custom-fabricated gantry-mounted measuring blocks, theodolite, and a dial indicator (Figures 8.3 and 8.4). Note that, for systems equipped with removable snouts, such tests can only be performed after verification that the snouts are correctly aligned. Alignment of each available snout in the gantry radial and the axial directions, as a function of snout translation distance and of gantry angles, needs to be verified to within specifications. This can be tested by either mechanical means of measuring the position of a fixed point on the snout as it translates or by scanning the proton beam dose profiles in air and verifying their symmetry for different snout positions. Accuracy of snout translation distances should be measured and compared to its digital display values. The snout interlocks for detecting presence of apertures and range compensators should be tested to work as designed. The radiation isocenter of a proton gantry may be tested in the same manner as for a traditional linear accelerator using “star-shot” films. Such tests

FIGURE 8.3 Gantry isocentricity measurement using a theodolite. (Adapted from Moyers and Lesyna, Int J Radiat Oncol Biol Phys, 60(5), 1622, 2004.)

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FIGURE 8.4 Measurement of gantry walk in axial direction using a dial indicator. (From Moyers and Lesyna, Int J Radiat Oncol Biol Phys, 60(5), 1622, 2004. With permission.)

should be performed for all snouts to be used on the gantry. Custom apertures need to be fabricated for such tests. Acceptance testing of the patient-positioning system includes verification of the accuracy and reproducibility of table movements and their limits. Mechanical measurements using calibrated rulers and levels are sufficient for these tests. Barkhof et al. (21) described a scintillation screen–based system for such tests. Table rotation isocentricity may be tested using the starshot film technique as well. Treatment tables with roll and pitch correction capabilities should be tested with a small value of such corrections introduced during isocentricity tests. When the patient treatment table is used to compensate for gantry sags, the accuracy of such corrections must be validated for a wide range of gantry angles. The maximum values of such corrections should be identified and compared to measured gantry mechanical and radiation isocenter walks, as excessively large correction values during patient treatments may indicate malfunction of the system. Functioning of motion limit switches, of both software and hardware varieties, needs to be tested. Activation of these limits should stop movement of the relevant subsystem and should be readily recoverable. Acceptance testing of orthogonal x-ray patient-alignment systems used in proton therapy includes image quality evaluation in terms of low and high contrast and resolution, the accuracy of radiation exposure parameters of kVp (kilovolt potential) and mAs (milliampere seconds) x-ray tube leakage radiation, and radiation exposure measurements. Geometric accuracy of the patient-alignment system is critically important for accurate delivery of proton therapy and must be extensively tested. The central axis of the x-ray beam produced by the nozzle-mounted x-ray tube needs to agree with the treatment beam and also with the light field if so equipped. Such agreement needs to be tested for a number of gantry angles to assure that it is not affected by gantry sag. For systems using a hardware crosswire, this test is easily performed using ­double-exposure films and a commercial light- and ­radiation-field agreement testing device, illustrated in Figure 8.5. In systems with crosswires

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FIGURE 8.5 Daily QA. Laser/x-ray agreement test.

mounted on interchangeable snouts, all available snouts must be tested. The second x-ray tube may be similarly tested for agreement of its crosswire to the gantry isocenter through a number of gantry rotation angles. 8.3.1.3  Proton Beam Characteristics Proton beam dosimetric parameters to be validated during acceptance testing include beam range, distal falloff, SOBP or beam modulation width, SOBP flatness, and entrance doses in the depth direction. These measurements may be performed using a scanning water phantom and a parallel plate chamber as the field dosimeter. The lateral dose distribution profiles may be measured, again using scanning phantoms with a small diameter ionization chamber as field dosimeter, and the beam flatness, symmetry, and penumbra values at several depths are extracted. Figure 8.6 shows a definition of these depth–dose beam quality parameters as follows: Range: depth in water (g/cm2) from skin to distal 90% of depth dose SOBP width: distance in water from proximal 90% to distal 90% of depth dose Distal falloff: distance in water from distal 80% to distal 20% of depth dose Note that the definitions listed above use their historical values. The specific definitions of these parameters may be customized, as agreed upon with the system vendor and installation engineering team, to meet the clinical requirements of a given proton therapy facility. For example, Engelsman

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Proton spread-out-Bragg-peak Range SOBP width Proximal depth dose

%DD

110.0 100.0 90.0 80.0 70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0

Distal falloff 0

5

10

15 20 Depth (g/cm2)

25

30

35

FIGURE 8.6 Proton beam depth–dose parameters.

et al. (6) described an alternative definition of SOBP width to be from proximal 98% to distal 90% of the depth dose, due to the steeper gradient of the depth dose at proximal 98% than 90%, a better fit for the output factor predictive model used, and a closer correlation of SOBP width to target thickness when the target is covered by 100% (mid-SOBP) of the depth dose. Additional beam parameters to be measured include range and SOBP width resolution. These measurements may be performed for a single gantry angle using a scanning water phantom and a parallel plate chamber as the field dosimeter, for beams with varying beam ranges and SOBP widths, typically at resolutions of 0.1 g/cm2 for the former and 0.5–1 g/cm2 for the latter. The off-axis range uniformity and off-axis SOBP width and flatness of the beams need to be verified to be within design specifications as well by acquiring a set of depth–dose scans at a number of off-axis points. Lastly, the dependence of beam quality parameters on snout, dose rate, and gantry angle needs to be tested. The characterization of proton beams is one of the more difficult aspects of acceptance testing of a proton therapy system, because of the availability of beams with nearly continuous beam energy. Direct measurements of all available beams are intractable and in practice are unnecessary. A thorough understanding of the hardware and software controls that provide all the available proton beams is therefore a prerequisite in designing an acceptance testing procedure for a proton therapy system. The following discussions illustrate this process using the IBA Universal Nozzle (Ion Beam Applications) as an example. This nozzle, shown in Figure 8.1, is capable of delivering proton therapy treatment using two scattering techniques:

1. Single scattering: The pencil beam exiting the beam transport line is expanded through a first scatterer, such that the narrow Gaussian

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beam becomes a wider Gaussian beam. The outer parts of the beam at lower than 95% of the central axis value are blocked by the variable collimators, so that only the center part of the beam is used for treatment. SOBPs of specific widths are formed by use of step-wise thickening range modulator wheel tracks and are controlled by turning the beam off at the step corresponding to the prescribed SOBP width, or beam current modulation, created in tabulated files during system installation. There are a total of five single-scattering options, with all beams in each option sharing common first scatterers and modulation wheel tracks. Beam energy is selected by the energy selection system (ESS) comprised of an energy degrader at the accelerator exit followed by energy selection slits and magnets. 2. Double scattering: The single-scattered beam is flattened by a downstream second scatterer and then collimated by the variable collimators. The same beam modulation wheel tracks are used, together with beam current modulation files. A number of second scatterers are available that, working jointly with the first scatterers, form eight double-scattering options, again with each option sharing second scatterer and range modulation wheel tracks. The first scatterers are selected from a combination of up to eight Al or Pb foils, as calibrated at time of system installation.

In addition to the scattering beam options, the IBA Universal Nozzle is also capable of delivering active scanning beams in two forms: (1) a uniform scanning beam, which scans a first-scattered beam laterally to deliver the dose to a given layer with uniform intensity, before inserting a range shifter (implemented using a step of a range modulation wheel track) and changing beam intensity to scan a subsequent, shallower layer, and (2) a scanning pencil beam, which scans an unscattered, prefocused pencil beam with variable intensity in a given layer before pulling the range back to deliver an intensity-modulated scanning beam to subsequent layers (22). The subsequent discussions will be limited to the passive-scattering beam options in the IBA Universal Nozzle. Table 8.1 lists the clinical range and modulation limits of the double-scattering beams in this nozzle, together with their use of second scatterers and range modulation wheel tracks. Note that each option is further subdivided into three suboptions, and the beam current modulation files are custom-designed for each suboption. Acceptance testing of these options therefore should, at the minimum, verify that a representative beam within each suboption, corresponding to a distinct beam current modulation file, meets design specifications. The number of measurements required for acceptance testing is further estimated by an analysis of the dependence of clinical beam quality parameters, such as beam range and SOBP flatness, on how they are produced, including the scatterers and modulation wheel tracks used, as well as snouts and beam gantry angles. As an example, the beam range is considered to be dependent on the suboption used to generate

Range span, suboption 1 (g/cm2) Range span, suboption 2 (g/cm2) Range span, suboption 3 (g/cm2) Maximum modulation width (g/cm2) Maximum field radius (cm) Range modulation wheel Range modulation track Second scatterer ID

Option

4.60–4.99 4.99–5.41 5.41–5.87 9.05 12.00 3 1 8

B1 5.87–6.37 6.37–6.91 6.91–7.49 9.85 12.00 3 1 8

B2

Double-Scattering Options in an IBA Universal Nozzle

TABLE 8.1

7.49– 8.12 8.12– 8.81 8.81– 9.55 12.35 12.00 2 1 8

B3 9.55–10.20 10.20–10.90 10.90–11.65 15.25 12.00 2 2 8

B4 11.65–12.83 12.83–14.12 14.12–15.54 19.55 12.00 2 1 2

B5 15.54–16.86 16.86–18.28 18.28–19.83 19.70 12.00 2 2 2

B6

19.83–21.18 21.18–22.61 22.61–23.91 32.00 12.00 2 3 2

B7

22.80–24.79 24.79–26.95 26.95–28.40 32.00 7.00 3 2 3

B8

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the beam, but less likely on the gantry angle. Beam range dependence on the gantry angle can therefore be verified for two beams out of all available options: one with a large range and one with a small range. The lateral dose profile may have large dependence on beam gantry angle and should therefore be verified for each option, at prime gantry angles. Lastly, these measurements should be selected such that they may be used for subsequent treatment-planning system commissioning validations. The acceptance testing of active scanning beams is discussed by Farr et al. for the uniform scanning technique (8), and by Gillin et  al. for the pencil beam scanning technique (9). These delivery techniques use a significantly reduced number of nozzle hardware components, but rely on magnetic scanning of the beam to achieve a desired dose distribution in the lateral direction and use range shifters for pullback of the individual layers of pristine peaks. The uniform scanning technique aims to produce a cumulative dose distribution identical to that produced by a passive-scattering beam, with depthdose curve characterized by an SOBP, and lateral profiles described by beam flatness, symmetry, and lateral penumbra. Its acceptance testing is therefore in principle similar to that of scattering beams. The fact that a large-diameter beam spot is scanned laterally invariably introduces ripples in the lateral dose profiles; and the layer-by-layer delivery of dose in the depth direction, using a limited number of range shifters, also introduces ripples in the SOBP. Multiple repainting of the distal layer, up to 100 times (8), is used in typical uniform scanning schemes to minimize the effect of random beam intensity fluctuations. The reproducibility of delivered dose distribution of a representative field should be tested. The effect of beam spot size change as the dose layers are changed should be evaluated by acquiring the lateral dose profiles at several depths of a field. The depth–dose curve measurement for such scanning beams is complicated by the layer-by-layer delivery scheme, and special dosimetry equipment, such as a multilayer ionization chamber (MLIC) or a multipad ionization chamber (MPIC) (8), can be used to significantly improve the efficiency of data collection. Pencil beam scanning systems, or spot scanning, on the other hand, construct a desired dose distribution by summation of “spot doses,” each delivered by a narrow pencil beam with a narrow pristine peak (see Chapter 6). Each spot of such a composite dose distribution would correspond to a voxel of the patient’s anatomy, and the total dose delivered to each spot is calculated to achieve an intensity-modulated dose distribution. The acceptance testing of a pencil beam scanning system, therefore, will concentrate on the characteristics of the individual spots. Gillin et  al. described their experience in acceptance testing and commissioning of such a system (9). Each pencil beam is characterized by its depth–dose curve and lateral profiles. The widths of the pristine peaks, as a function of beam range, vary significantly, as reflected by the pullback values between neighboring layers. A large diameter ionization chamber (Bragg peak chamber, PTW-Freiburg,

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Freiburg, Germany) is used to perform point-by-point measurements of these pristine peaks. The lateral dose profiles of individual pencil beams in such a system are generally described by Gaussian distributions. However, the lateral lowdose tails extend to a large distance away from the beam central axis and need to be verified for accurate description by the treatment-planning system. Sawakuchi et al. (23, 24) performed Monte Carlo calculations and experimental measurements of the lateral low-dose envelopes of such pencil beams. Such lateral low-dose tails originate from particle interactions both with the nozzle components and in phantom, contribute significant doses to points as far as 10 cm away from the pencil beam, and can cause significant dose calculation deviations for fields up to 20 × 20 cm 2 if left unaccounted for. Pencil beam spot characteristics, including spot-positioning accuracy and reproducibility, spot shape, and spot diameters, as a function of beam energy and gantry angle, should be verified. Gillin et al. used radiochromic films and pinpoint ion chambers for such measurements (9). Spot shapes for a variety of beam energies were measured at two different gantry angles. For facilities with multiple treatment rooms, it would be desirable to have beams in identically equipped treatment rooms to be “matched,” or dosimetrically interchangeable, to facilitate future clinical operations when patients may be treated without being limited to a specific treatment room. Such requirements should be discussed in detail with the vendor’s installation engineers, and measured data from the matched treatment rooms should be reviewed for agreement. 8.3.1.4  Dose-Monitoring System Monitor chambers in proton therapy measure the absolute dose delivered, as well as providing measurement and feedback for beam symmetry control, using a primary and a secondary backup monitor chamber. Their tests during acceptance testing are similar to those for linear accelerator monitor chambers, including preliminary calibration, reproducibility, and adjustability. The linearity and end-effect tests of proton therapy monitor chambers may be complicated by the fractional doses delivered during beam tuning. For scattering beam techniques, several pulses of a beam are sent through the monitor chambers to provide final beam tuning and beam range measurements. Although these pulses are synchronized with the beam modulation technique and delivered to the treatment target during patient treatments, the total monitor units (MUs) delivered during beam tuning may vary randomly. The monitor chamber linearity and end-effect tests, being a characterization of monitor chamber response, should therefore be evaluated with these tuning MUs excluded. The delivered dose rate in proton therapy systems depends on the type of accelerators used: cyclotrons can typically produce a large beam current,

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allowing high dose rates for larger treatment fields, whereas synchrotrons are often more limited in their ability to deliver higher dose rates (25). Dose rate measurements to be performed during acceptance testing therefore should start with verification of the vendor-stated achievable dose rate, typically under conditions of a set of reference fields. Additional tests include determination of the average dose rates available, as a function of both field sizes and beam energy, for a set of representative beam ranges and modulation widths. Monitor chamber dependence on dose rates is determined through these measurements as well. Temperature and pressure correction for monitor chambers used in proton therapy may be achieved in two manners: automatic compensation based on chamber-integrated temperature and pressure-sensor measurements or manually entered temperature and pressure correction values. The temperature and pressure compensation of the former design can be evaluated by measuring the output of a reference field over days and establishing that the chamber response does not track temperature and pressure variations over these days. For the latter design, a range of temperature and pressure values may be entered into the system, and the beam output may be measured to demonstrate the correctness of system compensation calculations. Additional monitor chambers may be used in the pencil beam–scanning technique, as described by Gillin et  al. (9). These monitor chambers perform the functions of beam profile and spot position monitoring and trigger interlocks when the delivered beams deviate from prescribed values. The primary and secondary (or backup) monitor chambers also interlock on minimum and maximum MUs per spot. These interlocks need to be tested during acceptance testing, with support of the vendor’s installation engineers. 8.3.2  Commissioning of Proton Therapy Systems Commissioning of a proton therapy system includes calibration of the CT scanner to establish the CT HU number-to-proton stopping power conversion curves and acquisition of beam data for treatment-planning system beam modeling, as required by the selected proton therapy treatment-­ planning system. In addition, system commissioning will necessarily include evaluation of performance of integrated systems, from image acquisition to treatment delivery, using an electronic record and verify (R&V) system as appropriate. An end-to-end test should be performed at the end of system commissioning to ensure that the entire integrated system functions as expected. Disease site–specific operating procedures, especially in patient immobilization, imaging, treatment planning, and treatment delivery, should be developed as part of system commissioning. Training should be provided to radiation oncologists, physicists, dosimetrists, and radiation therapists on all procedures thus developed. Lastly, a periodic system QA program, based on the data acquired in the commissioning process, should be implemented, to ensure constant system performance over time.

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8.3.2.1  CT HU-to-Stopping Power Calibration The beam range required for patient treatment in proton therapy is calculated from CT images of the patient, with the CT HU numbers converted to proton stopping power values using a calibration curve determined at time of system commissioning. Errors and uncertainties in the HU-to-stopping power calibration curve translate directly into those of beam range calculations and need to be minimized. Schneider, Pedroni, and Lomax (26) proposed the stoichiometric method for obtaining this calibration curve. The HU values of a number of tissue equivalent materials are measured on the CT scanner, and their stopping power values are then calculated based on the known chemical compositions and may be confirmed by direct measurement in proton beams. These HU-to-stopping power correlations are then used to obtain fitting parameters of a HU calculation model describing the photoelectric, coherent-scattering, and Compton-scattering interactions of x-rays in the materials. Stopping power values of soft tissues, using chemical compositions of ICRU Report 49, are then calculated to obtain the complete HU-to-stopping power calibration curve. Schaffner and Pedroni (27) demonstrated the accuracy of this method for a number of tissue types. The tissue equivalent materials used for establishing the HU-stopping power calibration curve need to be verified to allow accurate stopping power calculations. Commercially available tissue equivalent materials, such as those used for photon CT-electron density calibrations, may not have chemical compositions of adequate accuracy and consistency for stopping power calculations. It is therefore important that the materials used in establishing the CT calibration curve for proton therapy are measured in proton beams to confirm the agreement of calculated and measured stopping power values. Additional uncertainties in HU-stopping power calibration include the beamhardening effect of CT scanning. High-density materials may produce significantly different HU values as a function of geometric locations at the center or peripheral regions of the phantom. The same materials placed in phantoms of different diameters will produce different HU values as well, further increasing the uncertainties of HU-to-stopping power conversions. The CT scanning technique used for imaging the phantom needs to include identical technical parameters, including kilovolts, collimator opening, and reconstruction algorithms. Variations of these parameters have the potential of significantly increasing the uncertainties in HU-to-stopping power conversion as well. Commissioning of a CT scanner for proton therapy should therefore include scanning of the phantom using various techniques, for phantoms of different diameters, and with the tissue equivalent materials in various locations within the phantom, so that estimates of these uncertainties may be documented. 8.3.2.2  Treatment-Planning System Commissioning Commissioning of a proton therapy treatment-planning system includes collecting the data required by the system for accurate in-phantom dose

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calculations. For systems using the pencil beam dose calculation model (28–30), these input parameters include the following: • Beam energy spread, which may be estimated from pristine peak measurements. A large enough number of pristine peaks should be measured for each available beam option as required by the planning system. • Source size, extracted from in-air measurements of half-beam dose profiles. • Virtual source-to-axis distance (SAD), describing beam divergence in air and extracted from in-air measurement of dose profiles at several different distances from the isocenter for a field of fixed diameter. • Effective SAD, describing variation of beam output as a function of source-to-calculation point distance, or the inverse square law. Additional parameters may be required for dose calculation using the pencil beam model, including the nozzle equivalent thickness (NET) of all nozzle components within the beam path and the description of range modulation wheel-step widths and thicknesses. In-phantom dose distributions, both depth doses and lateral profiles, are required for validation of the treatment-planning system as well. Many of these have been obtained during system acceptance testing. Additionally, the variation of depth doses, lateral profiles, and output factors as a function of the source-to-skin distance (SSD), snout position/air gap, snout size, and field size should be tested using measured beam data. Such data, although not part of typical vendor performance specifications and therefore not part of acceptance testing, are important considerations in clinical proton therapy treatment planning. Figure 8.7 illustrates the SOBP flatness changes as a function of SSD variations. The “tilt” of the SOBP part of depth–dose curve deteriorates as the measuring phantom is shifted toward or away from the

Tilt SOBP [% / cm]

0.2 0.15 0.1 0.05

B5 - data B5 - trend B7 - data B7 - trend

0

–0.05 –10

–8

–6

–4

–2 0 2 Shift in SSD [cm]

4

6

8

10

FIGURE 8.7 SOBP flatness, or tilt change as SSD changes. Solid line; B5 option (see Table 8.1). Dashed line: B7 option.

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Range = 15.1 cm, SOBP width = 10.4 cm (Option B5)

80%–20% Lateral penumbra [cm]

1.60

@ 0.5 cm depth

@ 9.9 cm depth

@ 14.1 cm depth

1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 0.0

5.0

10.0

15.0 20.0 Air gap [cm]

25.0

30.0

35.0

FIGURE 8.8 Beam lateral penumbra change as function of air gap for a B5 option field.

source. Beam penumbra variations as a function of air gap, or the effect of proton in-air scattering on beam penumbra, is shown in Figure 8.8. A 10-cm increase in air gap degrades beam penumbra by approximately 2 mm for the scenarios illustrated. The accuracy of planning system dose calculation in inhomogeneous media should be verified. A phantom consisting of various tissue equivalent materials, such as lung, soft tissue, and bone, may be constructed and imaged. Calculated dose distributions in the phantom may be compared to their measurement counterparts. The slit-scattering effect (31), or protons scattering off the walls of apertures, should be confirmed and documented. Such increases in skin doses are typically not modeled by pencil beam dose calculation algorithms, but are important in treatment planning and patient treatment considerations. Figure 8.9 shows the variations of slit-scattering effect as the air gap varies. 8.3.2.3  MU Calculations Although a common formalism for the MU calculations of proton therapy does not exist, system-specific algorithms have been developed and implemented (32–34). These algorithms are customized to the specific nozzle design and beam modulation techniques, and each has its own requirements of input parameters. Where applicable, the beam data required for the MU calculation schemes should be measured during the commissioning process, and calculated output factors should also be verified.

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Relative dose [-]

1 0.8 0.6 0.4 0.2 0

–10

–5

5 cm air gap 13 cm air gap 30 cm air gap 0 Radial position [cm]

5

10

FIGURE 8.9 Dose profile at 0.5-cm depth for three different air gaps. The slit-scattering effect, or the horns in the profiles, is maximum with a small air gap and reduces as the air gap increases.

8.3.2.4  Beam-Modifying Accessories Apertures and range compensators are typically used for scattering and uniform-scanning techniques, with the former to shape the treatment field portals and the latter to provide distal conformance to the target by pulling back the beam ranges locally. The geometric and dosimetric accuracies of these accessories, as modeled and calculated by the treatment-planning system, need to be validated by in-water measurements. The aperture thickness required to stop proton beams of a given range should be determined. Stopping power value of the material used for range compensator fabrication, typically acrylic, needs to be confirmed as well. A range compensator of relatively simply geometry may be fabricated, and the measured dose distribution through the compensator should be compared to the calculated one, such that dose calculation errors and inadequacies of the treatment-planning system may be identified. Figure 8.10 shows such a comparison, where differences between planned and measured dose distributions are the greatest near sharp edges of the compensator. A procedure for QA testing of patientspecific apertures and compensators should be developed based on these measurements. 8.3.2.5  Patient Immobilization Devices Patient immobilization devices used for proton therapy should be evaluated for their dosimetric properties. A CT scan of each device should be obtained and imported into treatment-planning system. The dose distribution for a

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Depth [cm.H2O]

100 60 40 20 0 Y [cm]

5

–10

10

Relative dose [%]

120 100 80 60 40 20 0 20 10 Depth 5 0–10 –5 0 [cm.H2O] Y [cm]

100 80 60 40 20 –5

0 Y [cm]

5

120 100 80 60 40 20 0 20 10 Depth 5 0–10 –5 0 [cm.H2O] Y [cm]

10

2 4 6 8 10 12 14 16 –10

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30 20 10 0 –10 –20

–5

0 Y [cm]

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10

40 Relative dose [%]

–5

Difference eclipse - measurement

120

Relative dose [%]

–10

80

Eclipse 2 4 6 8 10 12 14 16

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120

Depth [cm.H2O]

Measurement 2 4 6 8 10 12 14 16

20 0

–20 –40 20

10

10 Depth [cm.H2O]

0–10 –5

5 0 Y [cm]

10

FIGURE 8.10 (See color insert.) Comparison of calculated and measured dose distribution through a range compensator with sharp gradients.

beam through the device is calculated and compared to the measured dose distribution for agreement. In particular, the device is evaluated for the following: • Average range pullback: The range reduction, caused by the presence of the immobilization device, needs to be measured and compared to the value predicted by the treatment-planning system. Disagreements between the measured and calculated range pullbacks need to be investigated, and the device may be deemed unacceptable for proton therapy applications. • Range pullback uniformity: The device should in addition provide acceptable uniformity in its range pullback within the treatment field. Because of the multiple Coulomb scattering of protons in patients, such uniformity will vary as a function of measurement depth. The evaluation of range pullback uniformity will therefore need to be performed at several depths as appropriate, based on the expected beam ranges for the intended clinical disease sites. • Mechanical integrity: The device, if unsupported by the patient treatment table during clinical use, needs to be evaluated for sags. A weight approximating an expected clinical patient weight can be placed on the device, and the device sag values should be recorded. Uncertainties in the range pullback of a patient immobilization device that cannot be resolved may be considered as part of the overall beam range uncertainty. Such uncertainties should therefore be included in the calculation of

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beam range uncertainties for clinical treatment planning and be included in the facility’s site-specific treatment-planning procedures. 8.3.2.6  R&V System The use of an R&V system significantly improves the clinical flow of proton therapy and can help minimize occurrence of treatment delivery errors. These systems should be tested for data import accuracy, using treatment plans that use all parameters to be monitored by the R&V system. In addition to dosimetric parameters including range, SOBP width, and MUs, the recording and verification of geometric parameters (e.g., gantry angle, table rotation, pitch, roll, and translations) need to be thoroughly tested for a wide range of clinical scenarios. A set of initial patient setup parameters, determined by use of orthogonal x-ray imaging, and the table corrections thus deduced, need to be applied to all subsequent treatment fields accurately. Treatment plans used for commissioning of R&V systems should therefore include difficult treatment cases with table rotation and translation offsets away from the initial setup locations. The installation of a multiroom proton therapy system is in general a prolonged process lasting for months. It is likely that system acceptance installation, acceptance testing, and commissioning will occur concurrently among different treatment rooms and will compete for available accelerator beam time. The scheduling of such activities in a multiroom installation must therefore be carefully considered for maximum utilization of beam time and quickest facility startup.

8.4 Design of a Periodic QA Program for a Proton Therapy System A periodic QA program for proton therapy is designed to assure that the system continuously performs as it does at the time of acceptance testing and commissioning. The failure modes of a proton therapy system can be significantly different from those of a linear accelerator system. In addition, a proton therapy facility is often expected to provide a large number of daily patient treatments, with clinical operations extending up to 16 hours per day. Additional times must be allocated for periodic machine QA as well as patient-specific QA measurements. A periodic QA program for proton therapy, especially the tests to be performed, must therefore be designed with high efficiency. Measures to improve QA efficiency include design of specific tests that reflect performance of multiple system components, design of test tools that allow quick setup and removal from treatment rooms, and careful scheduling of tests such that the more extensive

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and comprehensive tests are performed on days without scheduled patient treatments, such as the weekends. A periodic QA program for proton therapy also needs to be designed to reflect the facility’s experience and confidence with the system. Although some reproducibility tests are performed during system acceptance testing, those do not represent the long-term stability of the system, especially mechanical wear-and-tear concerns that may take months or years to develop. The QA program will therefore necessarily be more complex and comprehensive in the initial stages of a facility’s clinical operations, while patient treatment volume is ramping up. QA test results need to be analyzed and reviewed frequently, and the QA program must be revised to reduce the frequency of some tests, while potentially increasing the frequency of tests on components that are identified to have higher than expected failure rates. Finally, selection of test frequencies in a proton therapy periodic QA program should be done with considerations of the criticality of system failures. Some tests, such as output measurement, reflect catastrophic failures of multiple system components and must be performed on a daily basis, whereas small variations in beam centering below those detected by the system’s built-in beam flatness and symmetry interlocks (as measured by dose profile measurements) would contribute to small errors in overall dose delivery accuracy and could be tested on a less frequent basis. The basic QA tests of a proton therapy system include periodic measurements of machine outputs at the middle of SOBP, beam ranges, SOBP widths and flatness, and dose profiles for reference fields. Depending on the system design and implementation, the variations of these parameters from baseline values may indicate potential failures and/or degradation of different system components. An understanding of the basic system design therefore is crucial in determining the frequency at which these measurements are performed. The following discussion illustrates this process using a cyclotronbased proton therapy system. Arjomandy et al. (35) described a QA program for a synchrotron-based proton therapy system, with test schedules and tolerances customized for that particular system. After extraction of the beam out of a cyclotron, an ion chamber is used to measure beam current. As beam current is modulated during delivery of a scattered beam treatment, deviations of the beam current away from expected values will lead to beam output, as well as SOBP flatness changes. Lu et al. (7) show that when the beam current offset is a large percentage of the prescribed beam current, the effect on SOBP flatness can be significant (Figure 8.11). Such changes are more significant for fields with large ranges, as the prescribed beam currents for such treatments are much smaller than for shorter ranges. It is therefore important that depth–dose measurements should be performed for fields with larger ranges in order to detect drifts of the ion chamber at cyclotron exit. The proton beam exiting from the cyclotron proceeds through the ESS. Subsequently, beam line magnets control the beam focusing and alignment

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110 108 106 104 102 100 98 96 94 92 90 88 86

(c)

(b) (a) 5

0

10

15 20 Depth [cm]

25

30

FIGURE 8.11 Effect of beam intensity offset away from requested values on shape of SOBP: trace a: with current modulation and an offset; trace b: with current modulation and no offset; and trace c: without beam modulation. (Adapted from Lu et al., Med Phys, 2007, 34(10), 3844, 2007.)

until the beam enters the treatment nozzle. Drifts in energy degrader and magnet settings cause range errors, as well as changes in beam energy spread, spot size, and angular spread. Paganetti et  al. (5) performed Monte Carlo calculations to evaluate the effects of beam energy spread, spot size, and angular spread changes on pristine peak distributions, shown in Figure 8.12. Beam misalignment within the nozzle, for scattering beams, causes pristine peak changes, as well as flatness and symmetry deviations. These effects were investigated by Paganetti et al. as well (5). Figure 8.13 shows the effect of a misaligned beam interacting with the frames of the first scatterers on pristine peak curve. The scattered protons off the first scatterer frame create a hump in the entrance dose region of the pristine peak. Effects of 100

Dose [%]

80 60 40

60 50 40 30 20

40

60

80

100

20 0

0

20

40

60 80 Depth [mm]

100

120

FIGURE 8.12 Effect of changes in energy spread, spot size, and angular energy spread on pristine peak. The dashed lines show the effects of 0.2% change in energy spread, the dotted lines of beam spot size change by up to 0.25 cm, and dashed-dotted lines of angular energy spread of 2 mm-mrad. (Adapted from Paganetti et al., Med Phys, 2004, 31(7), 2107, 2004.)

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Total dose

1.0

Relative dose

0.8 0.6 0.4

Total dose minus scraping Dose from scraping frames of the scatterers

0.2 0.0

0

2

4

8 6 Depth [cm]

10

12

FIGURE 8.13 Effect of beam scattering off the first scatterer frame due to beam misalignment in nozzle on pristine peak. (Adapted from Paganetti et al., Med Phys, 2004, 31(7), 2107, 2004.)

beam misalignment relative to the second scatterer are shown in Figure 8.14. Changes in SOBP flatness, distal falloff gradient, and proximal depth–dose shape, as well as lateral flatness and symmetry are easily identified. The first scatterers in this nozzle design contain a set of flat aluminum or lead foils and are moved in and out of the beam pneumatically. The

Second scatterer aligned

120 40 80 Depth [mm]

160

Second scatterer tilted by 5°

40 80 120 Depth [mm]

160

100 80 60 40 20 0 –80 –40 0 40 80 Lateral distance to isocenter [mm]

Dose [%]

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Dose [%]

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Dose [%]

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Dose [%]

Dose [%]

100 80 60 40 20 0

Second scatterer tilted by 10°

0

40 80 120 Depth [mm]

160

FIGURE 8.14 Sensitivity of depth–dose and lateral profiles on beam alignment on second scatterers. (Adapted from Paganetti et al., Med Phys, 2004, 31(7), 2107, 2004.)

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Dose [%]

100 80 60 40 20 0

0

20

40

60 80 100 120 140 160 Depth [mm]

FIGURE 8.15 Sensitivity of SOBP to range modulation wheel alignment. The solid line shows the result for a correct alignment and the dashed line for a 4% misalignment. (Adapted from Paganetti et al., Med Phys, 2004, 31(7), 2107, 2004.)

mechanical stress on the first scatterers, over time, may cause them to deform. Output variations up to 5%, as well as SOBP changes, have been observed to associate with such mechanical failures. Visual inspection of such devices periodically, as well as routine output and SOBP measurements, serve well to detect such failures. The formation of SOBPs, using rotating range modulation wheels, relies on the correct starting and stopping of the beam relative to wheel rotation angles. Paganetti et al. (5) showed that misalignment of range modulation wheels may cause significant changes in the SOBP delivered (Figure 8.15). Lu et al. (7) also investigated the effects of losing beam current modulation completely and/or timing errors in beam current modulation signals and demonstrated significant changes in SOBP flatness (Figure 8.16). These findings of potential system component failures and their effects on beam parameters are summarized in Table 8.2. Daily, weekly, and monthly beam QA tests may be selected out of the tests. In the beginning of 105 100 Dose [%]

95

90 6τ 4τ 85 2τ 80 τ –τ 75

–2τ

70 65

0

2

4

–4τ

–6τ

6 8 10 Depth [cm]

12

14

16

FIGURE 8.16 Effect of beam current modulation timing error on shape of SOBP. Dark line represents the desired SOBP with no timing errors. Others show SOBP with multiples of timing errors of 2 ms. (Adapted from Lu et al., Med Phys, 2007, 34(10), 3844, 2007.)

Beam misalignment on second scatterer within MU chamber limits Modulation wheel misalignment Beam current modulation timing changes Second scatterer radiation/ mechanical damage High High

Low Low Low, gradual change

Off-axis SOBP changes

Medium

High

Medium, gradual

Medium

High

Low

Medium

Medium

Medium

Low

Low, gradual

Beam alignment in nozzle change First scatterer failures

Low, gradual change

Range error

Criticality High

Beam energy spread, spot size, angular spread changes Beam scattering off nozzle components Beam flatness, symmetry, SOBP changes SOBP changes, profile changes, output changes SOBP changes SOBP changes

Low, gradual change

SOBP flatness change

Loss of beam current modulation (BCM) Beam current error due to cyclotron exit ion chamber drift Energy degrader and selection system drift Beam line magnet drifts

Likelihood Random, sudden

Beam Quality Change

SOBP flatness change

System Failure Mode

Proton Therapy System Component Failures and Their Dosimetric Consequences

TABLE 8.2 Tests for Detecting Failure

Off-axis SOBP measurements, visual inspection

SOBP scans Range verifier, SOBP scans

Output measurements, SOBP scans, profile scans

Range verifier readings, SOBP scans SOBP scans Output measurements, dose rate measurements, pristine peak curve scans, SOBP scans Output measurements, pristine peak curve scans, SOBP scans Output measurements, SOBP scans, profile scans, visual inspection

Real-time review of BCM using oscilloscope (7) SOBP scans

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operations, the SOBP scans were performed daily, until high confidence in the system’s beam delivery accuracy was established. Subsequently, these tests were moved to weekly measurements for two reference fields: one for the standard calibration field and an additional field with large (25 cm) range. Daily output measurements were performed using a custom-made Lucite output phantom mounted on the snout, to minimize setup errors and time (Figure  8.17). A light-/x-ray/proton beam agreement test was included, initially at weekly intervals, rotating through all available snouts (Figure 8.18). After accumulation of a large amount of data demonstrating excellent agreement (Figure 8.19), this test was moved to monthly intervals. Gantry, treatment table, and imaging system accuracy tests were included as well. Of particular interest were the treatment table accuracy tests, initially at monthly intervals, which were changed to weekly intervals after episodes of sudden table drive potentiometer failures. Tables 8.3–8.6 show the current daily, weekly, monthly, and annual QA tests at the University of Florida Proton Therapy Institute (UFPTI). The cumulative system performance data, illustrated in Figures 8.20–8.23, are periodically reviewed for identification of potential system performance drifts, as well as continued improvement of the QA program.

8.5 Dosimetry Instrumentation for Proton Therapy Commissioning and QA Many types of dosimeters have been used for proton therapy (Chapter 7), for both absolute and relative dose measurements (36). This section is limited

FIGURE 8.17 Daily QA. Output check using a custom-fabricated phantom.

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FIGURE 8.18 Double-exposure film test of x-ray and proton beam radiation field agreement. A commercial light-field and radiation-field agreement testing device (Iso-Align, Civco, Kalona, IA) may be used for such a test.

Percentage of measurements [%]

100%

crossline

inline

80%

60%

40%

20%

0%

≤0.25 mm ≤0.50 mm ≤0.75 mm ≤1.00 mm ≤1.25 mm ≤1.50 mm ≤1.75 mm ≤2.00 mm distance center proton field to x-ray crosshair [mm]

FIGURE 8.19 Results of light-/x-ray/proton beam field agreement tests.

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TABLE 8.3 Daily QA for Scattering and Uniform Scanning Beams Test

Tolerance/Comments

Review operator’s cyclotron and gantry startup checklists Safety interlocks, indicator lights, neutron detector, A/V systems Output constancy check for scattering and uniform scanning reference fields Dose rate measurement kV imaging and laser accuracy Range verifier measurements of scattering and uniform scanning fields Range modulation wheel control signal timing Scan field size length and width

Operator checks machine operating parameters daily.   2%. Output measurements in plastic phantom. 30% tolerance. 1 mm. Orthogonal x-ray crosshair and laser agreement. 1 mm. 0.2  ms. Review of system reported timing values compared to baseline data. 3 mm. Compare system reported values to expected values for uniform scanning reference field.

to discussions of common, commercially available dosimeters, including ionization chambers and diode detectors, including their multidetector configurations; as well as radiographic and radiochromic films and TLD (thermoluminescent dosimeter) detectors. Ionization chambers remain the single most important dosimeter for proton therapy. For absolute dose measurements, the ICRU and the International Atomic Energy Agency (IAEA) provide the KQ values of a large number of common ion chambers (4, 37). Their use for proton therapy absolute dose measurements is discussed in Chapter 7. This section therefore concentrates on discussion of dosimeters for relative dose measurements. TABLE 8.4 Weekly QA for Scattering and Uniform Scanning Beams Test Review daily QA results MLIC calibration Output constancy check for two scattering and two uniform scanning reference fields Range measurements of above fields SOBP width measurements of above fields SOBP uniformity measurements of above fields

Tolerance/Comments Review for system performance trends. MLIC calibration performed prior to use for PDD measurements. 2%. Output measurements using MLIC. Fields measured include intermediate and large range fields. 1.5  mm. Measurements performed using MLIC. 2 mm. Measurements performed using MLIC. 2%. Measurements performed using MLIC.

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TABLE 8.5 Monthly QA for Scattering and Uniform Scanning Beams Test Review daily/weekly QA results Output constancy check for two scattering and two uniform scanning reference fields plus random patient field Range measurements of above fields SOBP width measurements of above fields SOBP uniformity measurements of above fields Lateral dose profile measurements of two scattering and two uniform scanning reference fields Range verifier reading of pristine peak ranges with and without first scatterers in beam X-ray/light field/proton beam field agreement Patient-positioning system/gantry accuracy Digital imaging positioning system

Tolerance/Comments Review for system performance trends. 2%. Output measurements performed in water. Fields measured include intermediate and large range fields. Patient field measured to support MU calculation accuracy. 1.5  mm. Measurements performed using in-water scans. 2 mm. Measurements performed using in-water scans. 2%. Measurements performed using in-water scans. 3% flatness; 1.5% symmetry; 2-mm field size. Measurements performed using MatriXX ion chamber array. 1 mm. First scatterer integrity tested. 1 mm. Double-exposure film measurements. Rotating through snouts. 1 mm/1°. Tests include isocentric table rotation. 1 mm in calculated vs. set shifts. Tests performed for two gantry angles.

Parallel chambers are suitable for depth–dose measurements. The effective measurement point is taken to be the inside surface of the front electrode. However, attention should be paid to chamber design: parallel plate chambers with front windows made of foils may change geometry and thus may have uncertainties in effective point of measurements, as are chambers with inadequate guard ring-to-electrode spacing ratios (38). Although a small-diameter parallel plate chamber is adequate for scattering beam depth–dose scans, depth–dose profiles of pencil beams for pencil beam– scanning technique need to include all scattered particles away from the beam’s central axis. A large-diameter (8.2 cm) parallel plate chamber (Bragg peak chamber) has been used for such measurements, although there may remain a significant amount of scattered doses outside the diameter of this chamber (23, 24). Such missing doses, if not modeled in treatment-planning systems, may have a significant impact on the accuracy of MU calculations of pencil beam–scanning treatments. Additional measurements, using two-­ dimensional (2D) dosimeter instruments, including radiochromic films and/ or 2D ion chamber arrays, should be performed to evaluate the magnitude of scattered doses outside the diameter of such chambers. Depth–dose measurements of scanning beams, if performed using a singlechannel ionization chamber, can be very inefficient. A complete delivery of

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TABLE 8.6 Annual QA for Scattering and Uniform Scanning Beams Test Review daily/weekly/monthly QA results Dosimetry system intercomparisons

Output calibration

MU chamber linearity MU chamber dependence on dose rate Dose rate accuracy Output factors Output dependence on gantry angles Depth–dose scans

Lateral dose profile scans Lateral dose profile dependence on gantry angle Gantry accuracy and isocentricity Patient-positioning system translation, rotation accuracy, and isocentricity Snout position accuracy and alignment

Imaging system accuracy Safety interlocks and radiation monitors

Tolerance/Comments Review for system performance trends. All dosimetry systems used for daily, weekly, and monthly QA tests are compared to ADCL-calibrated dosimetry system and calibration factors determined. 1.5%. Scattering and uniform scanning reference field outputs calibrated using ADCL-calibrated dosimetry system. 0.5% 1% from 1 to 3 Gy/min 25% for scattering and uniform scanning reference fields. 2%. Performed for each option. 0.5%. Output of reference fields measured at prime gantry angles. 1 mm for range, 3 mm for SOBP width, 2% for SOBP uniformity. Measurements performed for each option. Off axis scans performed for 1 field. 2% for flatness and symmetry. Measurements performed for each option. 0.5% variations. 0.5° and -mm diameter. 0.5  mm, 0.2°, and 1-mm diameter. 5 mm in snout position accuracy; 0.5 mm in alignment in both in-plane and cross-plane directions. Within 1 mm for all snouts in both in-plane and cross-plane directions. A number of safety interlocks and in-room neutron monitors are tested.

the measured field needs to be performed for each point of measurement, because of the layer-by-layer nature of scanning beam delivery. A multichannel chamber system, such as the MLIC or MPIC (8), would significantly improve the efficiency of such measurements. A prototype system of a commercial version of this design (Figure 8.24) (Zebra, IBA, LLN, Belgium) has been in use at UFPTI for more than a year for the daily measurement of scanning beam depth–dose curves of reference fields, has proven to be reliable, and allows daily uniform scanning SOBP measurements without extending QA time. Multichannel ion chamber arrays in 2D planar configurations are especially useful for periodic QA measurements of dose profiles. Arjomandy

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5.0

Measured - Nominal Output [%]

4.0 3.0 2.0 1.0 0.0 –1.0 –2.0 –3.0 –4.0 –5.0 Jan-07

Jan-08

Jan-09 Date

Jan-10

Jan-11

FIGURE 8.20 Daily output measurement results.

et al. (39) reported use of such a system (MatriXX, IBA, LLN, Belgium). The beam’s lateral penumbra measured with such systems will depend on the distances between detectors and should be done with caution. However, for beam flatness and symmetry measurements, they found the system to agree with pin-point type ionization chambers to within 0.5%. 15.4

Measured Range [g/cm2]

15.3 15.2 15.1 15.0 14.9 14.8 14.7 Jan-07

Jan-08

FIGURE 8.21 Daily range verifier reading results.

Jan-09 Date

Jan-10

Jan-11

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Quality Assurance and Commissioning

15.30

Field 1 (R = 15.1, M = 1.4)

15.25

Range [cm]

15.20 15.15 15.10 15.05 15.00 14.95 14.90

08/1 10/1 12/1 02/1 04/1 06/1 08/1 10/1 12/1 02/1 04/1 06/1 08/1 10/1 12/1 02/1 04/1 06/1 08/1 10/1 12/1 4/06 4/06 4/06 3/07 5/07 5/07 5/07 5/07 5/07 4/08 5/08 5/08 5/08 5/08 5/08 4/09 6/09 6/09 6/09 6/09 6/09

Date

FIGURE 8.22 Weekly range measurement results from in-water depth–dose scans.

Field 1 (R = 15.1, M = 1.4) 11.40 11.20

Mod [cm]

11.00 10.80 10.60 10.40 10.20 10.00 9.80

08/1 10/1 12/1 02/1 04/1 06/1 08/1 10/1 12/1 02/1 04/1 06/1 08/1 10/1 12/1 02/1 04/1 06/1 08/1 10/1 12/1 4/06 4/06 4/06 3/07 5/07 5/07 5/07 5/07 5/07 4/08 5/08 5/08 5/08 5/08 5/08 4/09 6/09 6/09 6/09 6/09 6/09

Date

FIGURE 8.23 Weekly SOBP width measurement results.

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FIGURE 8.24 A prototypical MLIC system being used for uniform scanning beam depth–dose curve measurements.

Films, both the radiographic and radiochromic types, have been used for proton beam dosimetry measurements. Both types of films have significant beam energy dependence in proton fields, as has been demonstrated by various investigators (40–47). In particular, such energy dependence is demonstrated by significant underresponse in high-LET regions of proton depth doses or near the end of range, as demonstrated by Vatnitsky (41) (Figure 8.25). 4

MD-55 film, calibration at peak MD-55 film, calibration at SOBP Parallel plate ionization chamber

Relative dose

3

2

1

0

0

1 2 3 4 Water equivalent depth, cm

5

FIGURE 8.25 Comparison of pristine peak measurements using radiochromic film and parallel plate chamber. (Adapted from Vatnitsky, Appl Radiat Isot, 1997, 48, 643, 1997.)

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250

Diamond detector Si detector Markus ionisation chamber

150 100 50 0

Diamond detector Si detector Markus ionisation chamber

Relative dose in %

Relative dose in %

200

250 240 230 220 210 200 190 180 170

20 40 60 80 100 120 140 160 180 200 220

Depth [mm]

174 176 178 180 182 184 186 188 190 192

Depth [mm]

FIGURE 8.26 Comparison of high-p-doped diode detector and parallel plate chamber for proton depth–dose measurements. (Adapted from Mumot et al., Phys Med, 25(3),105, 2009.)

Their use for lateral dose profile measurements, however, have been common. Farr et al. used radiographic films to evaluate the field matching accuracy of a robotic patient-positioning system and found the results to agree with ion chamber measurements to within 2–5% (48). Diode detectors have been evaluated for use in proton therapy dosimetry. Of the various types of diode detectors, only the hi-p-type ones have been found to be suitable for proton dosimetry, including both depth–dose and lateral profile measurements (46, 49). Figure 8.26 shows a comparison of pristine peaks measured by a high-p-doped diode detector, diamond detector, and a parallel plate chamber. The agreement of the diode-measured curve to that of the parallel plate chamber is excellent. Diode detectors of small active volumes are especially suitable for the relative measurements of depth doses and lateral profiles, due to the minimal volume-averaging effect on measurement results. Their use for absolute dose measurements, even for output constancy checks, is plagued by response changes relative to the detectors’ radiation history. Diode detectors may suffer significantly higher radiation damage, causing the detector responses to decrease as the cumulative doses they receive increase.

8.6  Conclusions Because of the great variations of available beam options and the methods adopted to produce those among existing proton therapy systems, acceptance testing, commissioning, and periodic QA of proton therapy systems require detailed analysis and understanding of individual systems. Such analysis needs to include the sensitivity of beam quality parameters to system-operating conditions and performance changes, and in particular the different system failure modes and its consequent beam quality degradations. Monte Carlo methods (Chapter 9) have proven to be a powerful tool in supporting this analysis. Although the fundamental principles of designing

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such procedures and programs for proton therapy are no different from those of conventional linear accelerator–based radiotherapy programs, additional and/or alternative tests must be identified through such analysis and understanding. Continuous review and improvement of periodic QA programs are an integral part of the overall QA measures for proton therapy systems. The QA program may start with comprehensive measurement-based tests at high, for example, daily frequencies. Through such enhanced QA tests in the initial stages of a facility’s operations, additional knowledge, insights, and confidence in the performance of the system are acquired. The QA program should be revised on the basis of such experiences.

References



1. Nath R, Biggs PJ, Bova FJ, Ling CC, Purdy JA, van de Geijn J, et al. AAPM code of practice for radiotherapy accelerators: report of AAPM Radiation Therapy Task Group No. 45. Med Phys 1994, 21(7):1093–121. 2. Kutcher GJ, Coia L, Gillin M, Hanson WF, Leibel S, Morton RJ, et  al. Comprehensive QA for radiation oncology: report of AAPM Radiation Therapy Committee Task Group 40. Med Phys 1994, 21(4):581–618. 3. Klein EE, Hanley J, Bayouth J, Yin FF, Simon W, Dresser S, et al. Task Group 142 report: quality assurance of medical accelerators. Med Phys 2009, 36(9):4197–212. 4. ICRU. Prescribing, recording, and reporting proton-beam therapy. ICRU Report No 78. Bethesda, MD: International Commission on Radiation Units and Measurements. 2004. 5. Paganetti H, Jiang H, Lee SY, Kooy HM. Accurate Monte Carlo simulations for nozzle design, commissioning and quality assurance for a proton radiation therapy facility. Med Phys 2004, 31(7):2107–18. 6. Engelsman M, Lu HM, Herrup D, Bussiere M, Kooy HM. Commissioning a passive-scattering proton therapy nozzle for accurate SOBP delivery. Med Phys 2009, 36(6):2172–80. 7. Lu HM, Brett R, Engelsman M, Slopsema R, Kooy H, Flanz J. Sensitivities in the production of spread-out Bragg peak dose distributions by passive scattering with beam current modulation. Med Phys 2007, 34(10):3844–53. 8. Farr JB, Mascia AE, Hsi WC, Allgower CE, Jesseph F, Schreuder AN, et  al. Clinical characterization of a proton beam continuous uniform scanning system with dose layer stacking. Med Phys 2008, 35(11):4945–54. 9. Gillin MT, Sahoo N, Bues M, Ciangaru G, Sawakuchi G, Poenisch F, et  al. Commissioning of the discrete spot scanning proton beam delivery system at the University of Texas M.D. Anderson Cancer Center, Proton Therapy Center, Houston. Med Phys 2010, 37(1):154–63. 10. Lin S, Boehringer T, Coray A, Grossmann M, Pedroni E. More than 10 years experience of beam monitor with the Gantry 1 spot scanning proton therapy facility at PSI. Med Phys 2009, 36(11):5331–40.

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11. Moyers MF, Lesyna W. Isocenter characteristics of an external ring proton gantry. Int J Radiat Oncol Biol Phys 2004, 60(5):1622–30. 12. Murphy MJ, Balter J, Balter S, BenComo JA Jr, Das IJ, Jiang SB, et al. The management of imaging dose during image-guided radiotherapy: report of the AAPM Task Group 75. Med Phys 2007, 34(10):4041–63. 13. Thomas SJ. Relative electron density calibration of CT scanners for radiotherapy treatment planning. Br J Radiol 1999, 72(860):781–86. 14. Mutic S, Palta JR, Butker EK, Das IJ, Huq MS, Loo LN, et  al. Quality assurance for computed-tomography simulators and the computed-tomography-­ simulation process: report of the AAPM Radiation Therapy Committee Task Group No. 66. Med Phys. 2003, 30(10):2762–92. 15. Ipe NE, Fehrenbacher G, Gudowska I, Paganetti H, Schippers JM, Roesler S, et  al. Shielding design and radiation safety of charged particle therapy facilities, PTCOG Publications Sub-Committee Task Group on Shielding Design and Radiation Safety of Charged Particle Therapy Facilities. http://ptcog.web.psi .ch/Archive/Shielding_radiation_protection.pdf, accessed June 15, 2011. 16. Jiang H, Wang B, Xu XG, Suit HD, Paganetti H. Simulation of organ-specific patient effective dose due to secondary neutrons in proton radiation treatment. Phys Med Biol 2005, 50(18):4337–53. 17. Mesoloras G, Sandison G, Stewart R. Neutron scattered dose equivalent to a fetus from proton radiotherapy of the mother. Med Phys 2006, 33:2479–90. 18. Polf JC, Newhauser WD, Titt U. Patient neutron dose equivalent exposures outside of the proton therapy treatment field. Radiat Protect Dosim 2005, 115:154–58. 19. Shin D, Yoon M, Kwak J, Shin J, Lee SB, Park SY, et al. Secondary neutron doses for several beam configurations for proton therapy. Int J Radiat Oncol Biol Phys 2009, 74(1):260–65. 20. Yan X, Titt U, Koehler AM, Newhauser WD. Measurement of neutron dose equivalent to proton therapy patients outside of the proton radiation field. Nucl Inst Meth Phys Res A 2002, 476:429–34. 21. Barkhof J, Schut G, Flanz JB, Goitein M, Schippers JM. Verification of the alignment of a therapeutic radiation beam relative to its patient positioner. Med Phys 1999, 26(11):2429–37. 22. Kooy HM, Clasie BM, Lu HM, Madden TM, Bentefour H, Depauw N, et al. A case study in proton pencil-beam scanning delivery. Int J Radiat Oncol Biol Phys 2010, 76(2):624–30. 23. Sawakuchi GO, Titt U, Mirkovic D, Ciangaru G, Zhu XR, Sahoo N, et al. Monte Carlo investigation of the low-dose envelope from scanned proton pencil beams. Phys Med Biol 2010, 55(3):711–21. 24. Sawakuchi GO, Zhu XR, Poenisch F, Suzuki K, Ciangaru G, Titt U, et  al. Experimental characterization of the low-dose envelope of spot scanning proton beams. Phys Med Biol 2010, 55(12):3467–78. 25. Smith A, Gillin M, Bues M, Zhu XR, Suzuki K, Mohan R, et  al. The M.D. Anderson proton therapy system. Med Phys 2009, 36(9):4068–83. 26. Schneider U, Pedroni E, Lomax A. The calibration of CT Hounsfield units for radiotherapy treatment planning. Phys Med Biol 1996, 41(1):111–24. 27. Schaffner B, Pedroni E. The precision of proton range calculations in proton radiotherapy treatment planning: experimental verification of the relation between CT-HU and proton stopping power. Phys Med Biol 1998, 43(6):1579–92.

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28. Bortfeld T, Schlegel W, Rhein B. Decomposition of pencil beam kernels for fast dose calculations in three-dimensional treatment planning. Med Phys 1993 Mar-Apr;20(2 Pt 1):311–18. 29. Hong L, Goitein M, Bucciolini M, Comiskey R, Gottschalk B, Rosenthal S, et al. A pencil beam algorithm for proton dose calculations. Phys Med Biol 1996, 41(8):1305–30. 30. Schaffner B, Pedroni E, Lomax A. Dose calculation models for proton treatment planning using a dynamic beam delivery system: an attempt to include density heterogeneity effects in the analytical dose calculation. Phys Med Biol 1999, 44(1):27–41. 31. Titt U, Zheng Y, Vassiliev ON, Newhauser WD. Monte Carlo investigation of collimator scatter of proton-therapy beams produced using the passive scattering method. Phys Med Biol 2008, 53(2):487–504. 32. Kooy HM, Rosenthal SJ, Engelsman M, Mazal A, Slopsema RL, Paganetti H, et al. The prediction of output factors for spread-out proton Bragg peak fields in clinical practice. Phys Med Biol 2005, 50(24):5847–56. 33. Kooy HM, Schaefer M, Rosenthal S, Bortfeld T. Monitor unit calculations for range-modulated spread-out Bragg peak fields. Phys Med Biol 2003, 48(17):2797–808. 34. Sahoo N, Zhu XR, Arjomandy B, Ciangaru G, Lii M, Amos R, et al. A procedure for calculation of monitor units for passively scattered proton radiotherapy beams. Med Phys 2008, 35(11):5088–97. 35. Arjomandy B, Sahoo N, Zhu XR, Zullo JR, Wu RY, Zhu M, et al. An overview of the comprehensive proton therapy machine quality assurance procedures implemented at the University of Texas M.D. Anderson Cancer Center Proton Therapy Center-Houston. Med Phys 2009, 36(6): 2269–82. 36. Karger CP, Jäkel O, Palmans H, Kanai T. Dosimetry for ion beam radiotherapy. Phys Med Biol 2010, 55(21):R193–R234. 37. IAEA. Absorbed dose determination in external beam radiotherapy—an international code of practice for dosimetry based on standards of absorbed dose to water. Technical Report Series No 398. Vienna, Austria: International Atomic Energy Agency. 2000. 38. IAEA. The use of plane-parallel ionization chambers in high-energy electron and photon beams. An international code of practice for dosimetry. Technical Report Series No 381. Vienna, Austria: International Atomic Energy Agency. 1997. 39. Arjomandy B, Sahoo N, Ding X, Gillin M. Use of a two-dimensional ionization chamber array for proton therapy beam quality assurance. Med Phys 2008, 35(9):3889–94. 40. Kirby D, Green S, Palmans H, Hugtenburg R, Wojnecki C, Parker D. LET dependence of GafChromic films and an ion chamber in low-energy proton dosimetry. Phys Med Biol 2010, 55:417–33. 41. Vatnitsky SM. Radiochromic film dosimetry for clinical proton beams. Appl Radiat Isot 1997, 48:643–51. 42. Hartmann B, Martisikova M, Jäkel O. Homogeneity of Gafchromic EBT2 film. Med Phys 2010, 37:1753–56. 43. Spielberger B, Krämer M, Kraft G. Three-dimensional dose verification with x-ray films in conformal carbon ion therapy. Phys Med Biol 2003, 48:497–505. 44. Spielberger B, Scholz M, Krämer M, Kraft G. Experimental investigations of the response of films to heavy-ion irradiation. Phys Med Biol 2001, 46:2889–97.

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45. Spielberger B, Scholz M, Kramer M, Kraft G. Calculation of the x-ray film response to heavy-ion irradiation. Phys Med Biol 2002, 47:4107–20. 46. Mumot M, Mytsin GV, Molokanov AG, Malicki J. The comparison of doses measured by radiochromic films and semiconductor detector in a 175 MeV proton beam. Phys Med 2009, 25(3):105–10. 47. Arjomandy B, Tailor R, Anand A, Sahoo N, Gillin M, Prado K, et  al. Energy dependence and dose response of Gafchromic EBT2 film over a wide range of photon, electron, and proton beam energies. Med Phys 2010, 37(5):1942–47. 48. Farr JB, O’Ryan-Blair A, Jesseph F, Hsi WC, Allgower CE, Mascia AE, et  al. Validation of dosimetric field matching accuracy from proton therapy using a robotic patient positioning system. J Appl Clin Med Phys 2010, 11(2):23–32. 49. Grusell E, Medin J. General characteristics of the use of silicon diode detectors for clinical dosimetry in proton beams. Phys Med Biol 2000, 45(9):2573–82.

9 Monte Carlo Simulations Harald Paganetti CONTENTS 9.1 Introduction................................................................................................. 266 9.2 Monte Carlo Particle Transport Algorithms and Codes....................... 266 9.2.1 The Monte Carlo Method.............................................................. 266 9.2.2 Particle Tracking Using Monte Carlo........................................... 267 9.2.3 Handling of Secondary Particles.................................................. 268 9.2.4 Proton Physics Definition.............................................................. 270 9.2.5 User Input/Output in Monte Carlo Simulations........................ 271 9.2.6 Monte Carlo Codes......................................................................... 272 9.3 Monte Carlo Code Validation.................................................................... 273 9.3.1 Uncertainties Due to Physics Models.......................................... 273 9.3.2 Uncertainties Due to Material Constants.................................... 273 9.3.3 Validation Measurements for Proton Dose Calculations.......... 273 9.3.4 Validation Measurements for Proton Nuclear Interactions...... 274 9.4 The Use of Monte Carlo to Study Proton-Scattering Effects................ 276 9.5 The Use of Monte Carlo for Beam Line Design...................................... 277 9.6 The Use of Monte Carlo for Treatment Head Simulations or Treatment Head Design............................................................................. 277 9.6.1 Characterizing the Beam Entering the Treatment Head........... 277 9.6.2 Modeling of Beam-Monitoring Devices...................................... 279 9.6.3 Modeling of Beam-Shaping Devices in Passive Scattering...... 279 9.6.4 Modeling of Scanned Beam Delivery.......................................... 281 9.6.5 Time-Dependent Geometries........................................................ 283 9.6.6 Treatment Head Simulation Accuracy......................................... 283 9.6.7 Phase-Space Distributions............................................................. 285 9.6.8 Beam Models................................................................................... 286 9.7 The Use of Monte Carlo for Quality Assurance..................................... 287 9.8 Other Monte Carlo Applications.............................................................. 288 9.8.1 Organ Motion Studies.................................................................... 288 9.8.2 Modeling of Detector Systems...................................................... 288 9.8.3 Simulating Proton-Induced Photon Emission for Range Verification....................................................................................... 288 9.8.4 Simulating Secondary Neutron Doses........................................ 289 9.8.5 The Use of Computational Phantoms.......................................... 289 265

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9.8.6 Simulating LET Distributions for Radiobiological Considerations................................................................................. 291 9.8.7 Biology: Track Structure Simulations.......................................... 292 Acknowledgments............................................................................................... 293 References.............................................................................................................. 293

9.1  Introduction Computer simulations are used in many areas of research and development. Specifically, Monte Carlo simulations allow the precise simulation of experimental conditions. A properly benchmarked Monte Carlo system can thus save beam time for experiments or create potential scenarios that are difficult to create experimentally. Computer simulations are particularly important in a field such as radiation therapy because the patient can typically not be used as the subject of experiments. One of the main goals of computer simulations in radiation therapy is the prediction of the delivered dose distribution to the patient. This aspect is covered in Chapter 12 on dose calculation algorithms. This chapter aims at illustrating other applications of computer simulations in proton therapy. One might use such simulations to study the physics of proton beams (Section 9.4) or for beam line design (Section 9.5). Although proton therapy installations are commercially available, physicists working at a proton therapy facility are often involved in treatment head design, which will be covered in Section 9.6. Other sections cover Monte Carlo for quality assurance (Section 9.7) and other more specific applications of Monte Carlo in proton research (Section 9.8). First, however, Sections 9.2 and 9.3 will elaborate on the concept and the achievable accuracy of Monte Carlo simulations.

9.2  Monte Carlo Particle Transport Algorithms and Codes 9.2.1  The Monte Carlo Method Initially, Monte Carlo techniques were developed to solve differential equations, not necessarily to track particles through a medium. It turns out, however, that the stochastic process applied to solve differential equations can be used to simulate physics on a step-by-step basis. Particle transport is based on cross sections (i.e., interaction probabilities) per unit distance. Monte Carlo algorithms thus sample from stochastic distributions and the mathematical basis is governed by the central limit theorem (1).

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267

Random numbers are sampled from a probability density function. Random number generators have a period: that is, the number sequence repeats itself eventually. However, this period is typically long enough in modern random number generators not to affect simulations. In a transport simulation, at each step of the particle through the geometry, the probability density function is representing the probability of physics interactions and their outcome. Mathematically, this is equivalent to solving the Boltzmann transport equation for protons. 9.2.2  Particle Tracking Using Monte Carlo The Monte Carlo method is the most accurate method of simulating particle interactions within a medium. A particle history is defined as the knowledge of the trajectory of one particle including potential secondary particles. Many particles need to be simulated in order to achieve a given accuracy. The uncertainty of Monte Carlo results depends on the number of histories N with the error in the simulated quantity being proportional to 1/√(N). Simulation of particle histories begins by sampling a number of events from a starting source distribution. This can be a mathematical function or a parameter list resembling an initial particle source, such as the flux from an accelerator. One then simulates the passage of particles through a welldefined geometry, one particle at a time, one small step at a time, randomly sampling from one or more probability distributions at each step in order to choose how the particle might interact (be absorbed, be annihilated, change direction, or change energy) consistent with the laws of physics. This is known as tracking. The tracking geometry is a well-defined geometrical model, such as a treatment head or a patient geometry. Materials are characterized by their physical properties, such as elemental composition, electron density, mass density, or mean excitation energy. The outcome of Monte Carlo simulations depends on the chosen step size. The step size chosen should be small, so that the difference of the cross sections at the beginning and the end of the step is small. On the other hand, a large step size decreases the computing time. Monte Carlo codes often use various methods to ensure proper step sizes particularly near boundaries (changes in material) (2–4). Depending on the flexibility of the code, the user may be allowed to define the maximum permitted step size. For uncharged particles it is feasible to simulate all physics interactions. However, for charged particles, like protons, this would be computationally ineffective because they interact so frequently. For example, the simulation of each elastic Coulomb interaction would cause a huge number of small-angle scattering events. This observation lead to the development of so-called class  II condensed history algorithms (5). Energy losses and directional changes are condensed (or summed) into a single step. For proton scattering, the deflection angle of single-scattering events is very small. Multiple-scattering theories provide probability density functions that

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Creation of a second particle Scattering at an angle

FIGURE 9.1 Schematic illustration of a particle tracking using Monte Carlo. The particle is being scattered at certain angles for the first five steps, before a physics interaction causes a second particle to be created (dashed line). Consequently, afterwards two particles need to be tracked independently. Each step (straight line) might resemble several interactions in the condensed history method.

represent the net result of several single-scattering events (see Chapter 2). Therefore, one can sample these distributions to determine the scattering angle at the end of a simulation step. Furthermore, one might define a threshold for the production of δ-electrons. Above an energy threshold δ-electrons are produced explicitly, but below the threshold continuous energy loss of the primary particle is assumed. Typically, a maximum step size is defined, up to which continuous energy loss and a certain multiplescattering angle is assumed, unless a so-called catastrophic event occurs. The latter might include high-energy δ-electrons or nuclear interactions. The switch from continuous to discrete process considerations might be a user variable in some codes. Typically, Monte Carlo methods use a combination of continuous processes based on condensed history and discrete processes based on an explicit model of each interaction. In proton therapy, discrete processes are typically nuclear interactions, secondary particle production (including δ-electrons), and large angle Coulomb scattering. Figure 9.1 illustrates a particle being tracked through a medium. To save time specifically with small effects of low energy particles, particle transport is terminated based on a user-defined particle energy or particle range threshold. 9.2.3  Handling of Secondary Particles Secondary particles are typically saved on a memory stack and tracked after the primary particle is finished. Production cuts for secondary particles can influence energy loss and thus the simulation results (4). To improve computational efficiency, one might decide not to track all particles. Particles not being tracked should deposit their energy locally in order to ensure energy conservation. Figure 9.2 shows the primary and secondary proton fluence as a function of depth for a 160-MeV beam. For proton dose calculation, primary and

269

100 Dose [relative units]

Proton fluence [% initial fluence]

Monte Carlo Simulations

80 60 40 20 0

0

50 100 150 Depth in water [mm]

200

FIGURE 9.2 Monte Carlo–simulated proton fluence as a function of depth for a 160-MeV proton beam. The dose is shown as a dashed line, and the solid and dotted lines illustrate the primary proton and the total (primary and secondary) proton fluence, respectively.

secondary protons account for roughly 98% of the dose, depending on the beam energy (6). This includes the energy lost via secondary electrons created by ionizations. The δ-electron energy, Eδ, can be calculated assuming maximum energy transfer, which a point-charge particle can impart to a stationary unbound electron (masses of the proton and electron denoted as mp and me, respectively): −1



2   me   2 me β2 2 2   . E δ = 2 me c cos θ ⋅ 1 + + 2 m p    (1 − β 2 )  m ( ) 1 − β p  

(9.1)

For protons, the maximum energy of the δ-rays can be approximated as a function of the proton energy, Ep,



E δmax ≅ 4

me

mp

Ep ≅

Ep

. 500

(9.2)

This corresponds to a maximum range of the delta electrons of about 2.5 mm for a 250-MeV proton. The highest energy electrons are preferentially ejected in a forward direction. The energy of most electrons in a proton beam is much less than 300 keV, which corresponds to a range of 1 mm in water. Thus, explicit tracking of electrons is not necessarily required for dose calculations on a typical computed tomography (CT) grid. The tracking of secondary electrons is certainly required for microscopic simulations, for example, to study radiobiological properties, for microdosimetry, or for absolute dose simulations (7). The explicit tracking of secondary electrons should not be

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neglected for ion chamber simulations (7–9). For applications other than dose calculation, additional particles might need to be considered, such as neutrons (see Chapters 17 and 19). 9.2.4  Proton Physics Definition The reason for the increased accuracy of Monte Carlo simulations compared to analytical algorithms lies in the way the underlying physics is modeled. Monte Carlo simulations are able to take into account the physics of interactions on a particle-by-particle basis. This is done using theoretical models, parameterizations, and/or experimental cross section data for electromagnetic and nuclear interactions. Monte Carlo accuracy thus depends on the detailed knowledge of physics for a particular particle, energy region, and material. Typically, the energy loss of protons is calculated by the Bethe-Bloch equation down to 2 MeV. Below 2 MeV a parameterization based on stopping power formalism, for example, based on the International Commission on Radiation Units and Measurements (ICRU) (10), might be used. Multiple scattering is realized in condensed history class II implementations (11). The Moliere theory (see Chapter 2) predicts the scattering angle distribution but does not give information about the spatial displacement of the particle. The Lewis method (12) allows calculation of moments of lateral displacement, angular deflection, and correlations of these quantities. Multiple-scattering algorithms used in Monte Carlo codes may differ but are typically variations of Lewis’s theory. Typically, all possible interaction types need to be considered, such as ionization, excitation, multiple Coulomb scattering, and nuclear interactions. Although nuclear interactions are not responsible for the shape of the Bragg peak (the majority of dose is deposited via electromagnetic ionization and excitation), they do have a significant impact on the depth– dose distribution (see Chapter 2) because they cause a reduction in the proton fluence as a function of depth (about 1% of the primary protons undergo a nuclear interaction per centimeter range of the beam) (6). Multiple Coulomb scattering causes broadening of the beam, that is, a softening of the penumbra. An interaction between the projectile and the nucleus can be modeled as an intranuclear cascade with the probability of secondary particle emission. Once the energy of the particles in a cascade has reached a lower limit, a pre-equilibrium model can be applied. To accurately account for secondary particles from nuclear interactions, the nuclear interaction probability and the secondary particle emission characteristics must be known. Nuclear interactions are typically parameterized using cross sections, that is, interaction probabilities. Cross sections as a function of proton energy may not be available for all reaction channels. In these cases, models, parameterizations, or a combination of models, parameterizations,

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and experimental data must be used. The specific choice may depend not only on the particle or energy region, but also on the required accuracy (vs. efficiency) of a particular application. The cross section for a specific atomic or nuclear interaction caused by an incident particle is defined as the probability for the occurrence of the event for one target nucleus, P, divided by the particle fluence. With the fluence defined as the number of particles, N, incident on a sphere of cross-sectional area, A, a cross section is defined as



σ=

P . dN dA

(9.3)

Cross sections are divided into elastic cross sections (scattering of the incident particle of the nucleus with conservation of kinetic energy) and nonelastic cross sections (nuclear excitation with potential creation of secondary particles and no conservation of kinetic energy). Cross sections can be single differential or double differential. The latter would describe the probability for energy loss with the primary particle deflected under a specific angle. Cross sections for proton-nucleus interactions for applications in proton beam therapy are summarized by the ICRU  (13). Treatment head simulations require accurate cross sections in particular for steel (beam scatterers, collimator housing, magnet housing, detector housing), Lexan (beam scatterers, modulators, compensators), lead (beam scatterers, modulators), aluminum (beam scatterers, modulators, collimator housing, ion chambers), carbon (modulators), brass (collimators, apertures, magnets), nickel (collimators), copper (magnets), PVC (ion chambers), Mylar (ion chambers), and many others. The importance of accurate double-­differential cross sections may depend on whether these materials are used in either beam-shaping or beam-modifying devices and on what their typical position in the treatment head is. For pencil beam scanning, small uncertainties in the “nuclear halo” (secondary particles emitted in nuclear interactions surrounding the primary beam) or multiple Coulomb scattering can cause large uncertainties when adding multiple pencils (14). The dose distribution is small for each pencil but can be significant for a set of pencils delivering a dose to the target volume or in the sharp dose gradient at the distal falloff, as has been studied using Monte Carlo (15). 9.2.5  User Input/Output in Monte Carlo Simulations When designing a Monte Carlo simulation, one needs to define the following: the tracking geometry, the materials involved, the particles of interest, the generation of primary events, the tracking of particles through materials and electromagnetic fields, the physics processes governing particle interactions, the response of sensitive detector components, the generation of event

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data, the storage of events and tracks, the visualization of the detector and particle trajectories, and the analysis of simulation data at different levels of detail. Depending on the code, some of these tasks may be taken care of by default settings. If one uses an existing executable that is already tailored to a specific application, input parameters might be limited to defining, for example, the proton beam energy and the settings of a specific device in a bigger geometry assembly. The specific definition of these devices depends on the Monte Carlo code in use. Most Monte Carlo codes would expect a more or less complex definition of geometries in an input file, whereas others might expect a definition of geometry using a programming language. The results of Monte Carlo simulations are typically analyzed from one-, two-, or three-dimensional (1D, 2D, or 3D) histograms. Some Monte Carlo codes designate such histograms as tallies. These are filled during the simulation if certain conditions for a histogram bin are fulfilled (e.g., a particle has deposited a specific amount of energy in a specific area of the geometry). One can also store entire particle histories for retrospective analysis. Caution is warranted when dealing with dose scoring in a Monte Carlo system. A Monte Carlo system typically provides information about the status of a tracked particle either at the beginning or at the end of an individual step. Typically, Monte Carlo systems require a particle to stop at a geometrical boundary in order to adjust for the change in physics. It needs to be understood whether the Monte Carlo defines the post-step point as within the volume to be entered. Thus, one has to make sure that energy is deposited in the volume according to the path of the particle track to avoid dosimetric artifacts at boundary crossings. 9.2.6  Monte Carlo Codes There are various Monte Carlo codes for use in proton therapy, for example, FLUKA (16, 17), Geant4 (18, 19), MCNPX (20, 21), VMCpro (22), and ShieldHit (23). Typically, a Monte Carlo program is a software executable for which the user has to write an input file depending on the specific problem. There are also other approaches, such as Geant4, where the code provides only an assembly of object-oriented toolkit libraries with the functionality to simulate different processes organized in different functions within a C++ class structure. The ability to program is prerequisite for designing simulations using these types of codes. Monte Carlo codes also differ in the level of control over tracking parameters. The ability to control every parameter (e.g., physics settings, step sizes, and material constants) adds flexibility but may also make the code difficult to use and prone to inaccurate results due to user error. In addition to the codes mentioned above, there are also programs that serve as interfaces to Monte Carlo codes, for example, user platforms for specific tasks (24–26).

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9.3  Monte Carlo Code Validation 9.3.1  Uncertainties Due to Physics Models The accuracy of Monte Carlo simulations depends on tracking parameters, such as the step size (see above). Obviously, it also depends on the accuracy of the implemented physics. Some codes were originally developed for highenergy physics applications and therefore span a wide range of particles and energy domains. A Monte Carlo code might allow different physics settings from which the user can choose. There might even be different settings for different energy domains. Models might not be tailored for proton therapy simulations because they were originally designed for high-energy physics applications and therefore require adjustment (27–29). For example, there are different parameterizations for multiple-scattering models and although the physics might be reasonably well understood, different Monte Carlo implementations can result in discrepancies. The implementation of the multiple-scattering theory can differ slightly from Molière theory (30, 31), for example, for multiple scattering, the code Geant4 uses a condensed history algorithm that utilizes functions to calculate the angular and spatial distributions of the scattered particle implementations (32). The significance of uncertainties in nuclear interaction cross sections depends on the application. For example, for shielding calculations, accurate double-differential cross sections (in energy and emission angle) for ­proton-neutron interactions are important. According to the ICRU (13), angle-integrated emission spectra for neutron and proton interactions are known only to within 20–30% uncertainty. Total nonelastic and elastic cross sections have uncertainties of <10%. 9.3.2  Uncertainties Due to Material Constants Uncertainties in stopping power parameters also influence calculation uncertainties, specifically the proton beam range (see Chapter 13) (4, 33, 34). Values for the mean excitation energy might have uncertainties on the order of 5–15%. Such an uncertainty for beam-shaping materials can lead to more than 1-mm uncertainty in the predicted beam range in water (31). It is important to consider this uncertainty when simulating energy loss in thick targets (4, 35). Typically, mean excitation energies are adjusted to agree with measurement for elements where data exist and are interpolated, based on theory, where data do not exist. Note that the exact density for some materials (e.g., carbon) used in scattering system is often not known. 9.3.3  Validation Measurements for Proton Dose Calculations Monte Carlo code validation for the settings of different physics parameters (e.g., cross-section data, model parameterizations, cutoff values for particle

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production, and consideration of secondary particles) is typically done by code developers. If the code is used for applications not anticipated by the developers, benchmarking and validation have to be performed by the user. Direct experimental validation of cross sections is often not feasible in proton therapy institutions where the main users are located. Here, benchmarking is mostly based on Monte Carlo simulations of less fundamental quantities, such as dose. Benchmarking studies should not be too complicated in terms of the underlying geometry so that discrepancies can be attributed to differences in physics and not to shortcoming in simulating the geometry. Three of the most commonly used codes in proton therapy (Geant4, FLUKA, and MCNPX) were compared with each other and with measurements by Kimstrand et al (2). The physics settings within the codes were varied. The study aimed at the simulation of the scattering contribution at aperture edges where protons scatter at inner surfaces of apertures at very small angles (i.e., a situation where small uncertainties in scattering power would be measurable). The particle distribution was measured with a fluorescent screen and a CCD camera. Significant impact of user-defined parameters was found. Others have analyzed the multiple-scattering algorithm and beam profiles in water downstream of inhomogeneous targets and compensators for validation (28). For dose calculation, Monte Carlo benchmarking studies are typically done using heterogeneous geometries consisting of various materials (36, 37). Benchmarking studies comparing experimental depth–dose ­distributions and beam profiles have been conducted for complex treatment heads (34, 36, 37). Figures 9.3 and 9.4 show a comparison of Monte Carlo simulations using the Geant4 code with experimental data measured with an ionization chamber at the Francis H. Burr Proton Therapy Center at MGH. Studying heterogeneous half-beam blocks and measuring/simulating the dose downstream can be a valuable test of scattering models. 9.3.4  Validation Measurements for Proton Nuclear Interactions The correct modeling of nuclear interactions is important for dose calculation, especially if Monte Carlo is used for absolute or relative dosimetry (7). Although the comparison of dose distributions is a valuable benchmark for electromagnetic interactions, nuclear interaction components cannot be studied separately in an experiment solely measuring dose. An experimental tool particularly useful for testing proton nuclear interaction data is the multilayer Faraday cup (see Chapter 2) (40, 41). It is sensitive to electromagnetic and nuclear inelastic reactions and measures the longitudinal charge distribution of primary and secondary particles. Because it relies on charge rather than dose, it is capable of separating the nuclear interaction component from the electromagnetic component. This is because nuclear stopping of protons takes place predominantly in the plateau region of a Bragg peak, whereas electromagnetic stopping takes place around the Bragg peak.

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FIGURE 9.3 Measured data (open circles) and Monte Carlo generated data (solid lines) for two depthdose curves from the Francis H. Burr Proton Therapy Center at Massachusetts General Hospital. Top: a Bragg peak with a nominal beam energy at the treatment head entrance of ~190 MeV. The spread-out Bragg peak (bottom graph) is based on a clinical field with the prescription of 17.2-cm range and 6.8-cm modulation width. The Monte Carlo simulation included the entire treatment head geometry. (From Paganetti et al., Med Phys., 31, 2107, 2004. With permission.)

Various Monte Carlo physics models for the simulation of electromagnetic and nuclear interactions were validated against the measured charge distribution from a Faraday cup (42). The Faraday cup can only validate total cross sections. For treatment head simulations and beam characterization, total and differential cross sections for materials of beam-shaping devices are required to compensate for fluence loss due to nuclear interactions. For primary standards and reference dosimetry, these cross sections with high accuracy are needed for a limited set of detector materials. Another example is the simulation of nuclear activation of tissues relying on isotope production cross sections for human tissues (43–45). The International Atomic Energy Agency (IAEA) has recognized the need for standardizing the use and modeling of nuclear interactions in proton and heavy ion radiation therapy (46).

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120

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FIGURE 9.4 Measured (open circles) and simulated (solid lines) dose distribution. The left panel shows the experimental setup with the beam impinging on a half-block of bone equivalent material (black) into a water phantom (gray). The dashed lines indicate the directions of the scans shown in the middle and right panels. The beam profile (3) was measured in an SOBP plateau. (From Paganetti et al., Med Phys., 53(17), 4285, 2008. With permission.)

There are considerable uncertainties when it comes to simulating neutron production. A precise modeling of neutron yields is needed when simulating both scattered neutron doses to assess potential risks for patients (see Chapter 18) (47, 48) and neutron production for protection and shielding (see Chapter  17). These simulations require double-differential production cross sections for tissues, beam-shaping devices, and shielding materials. There are various nuclear interactions channels for neutron production, as neutron and secondary charged particle emissions from nuclear interactions can be the result of complex interactions. There are insufficient experimental data of inelastic nuclear cross sections in the energy region of interest in proton therapy. Parameterized models for Monte Carlo transport calculations based on theory in regions where experimental data do not exist can be difficult because of uncertainties in the physics of intranuclear cascade mechanisms. Proper validation of Monte Carlo codes to perform such simulations is required (38, 49). The agreement in neutron dose simulations is typically not as good as with photons, electrons, or protons. Agreements of Monte Carlo results and measured data have been reported to be only between 10% and 340% (38, 50–53).

9.4 The Use of Monte Carlo to Study Proton-Scattering Effects Analytical methods might have to estimate complex physics interactions. If proton beams pass through complex heterogeneous geometries, a phenomenon called range degradation occurs (54, 55), which can be simulated using

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Monte Carlo codes. Another effect that can be studied with Monte Carlo quite easily is scattering at sharp edges, for example, in apertures (56–58). One might consider Monte Carlo–calculated kernels that can be used within analytical methods, for example, simulated scatter kernels with Monte Carlo to incorporate aperture scatter in the treatment-planning algorithm (56). Multileaf collimators to replace patient-specific apertures have been studied with Monte Carlo as well, with the aim of improving the beam penumbra (59). Markers implanted in the patient for setup or motion tracking do have an impact on dose calculations. They are typically not modeled accurately in pencil beam algorithms because of their high-Z nature. Monte Carlo has been used to study the impact of such markers on the dose distribution (60).

9.5  The Use of Monte Carlo for Beam Line Design The basic beam line elements between the accelerator and the treatment room that might be simulated using Monte Carlo are bending magnets and energy degraders. Energy degraders are needed in cyclotron-based facilities because cyclotrons extract a single energy. Depending on the desired beam range, the energy has to be reduced using a degrader in the beam line outside of the treatment room or in the treatment head. The latter is typically avoided because of the scattering it produces, which broadens the beam and creates secondary radiation. Degraders are built as single or multiple wedges that can move in and out of the beam. Monte Carlo beam transport through carbon and beryllium degraders has been performed with the goal of improving beam characteristics (4). A large part of beam line simulations has to do with beam steering through magnetic fields. Although this can be done with many Monte Carlo codes, (e.g., Geant4), tracking through magnetic fields is usually quite slow because it is based on using Runge–Kutta algorithms and parameterized field maps. The curved particle in a specific field is broken up into linear chord segments. Beam optics calculations are therefore often done numerically (61), but there are specialized Monte Carlo codes that simulate magnetic beam steering (62).

9.6 The Use of Monte Carlo for Treatment Head Simulations or Treatment Head Design 9.6.1  Characterizing the Beam Entering the Treatment Head A parameterization of the phase space at treatment head entrance might in principle be defined from first principles, based on the knowledge of the magnetic beam steering system or by fitting measured data (37). For typical

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Monte Carlo applications in proton therapy, the beam line magnets that steer the beam into the treatment head would not be modeled, but the simulation would start at the treatment head entrance. A parameterization of the beam at the entrance of the treatment head can be done based on beam energy, energy spread, beam spot size, and beam angular distribution (36,  63). Measuring some of these parameters directly can be difficult, and a user might have to rely on the manufacturer’s information. The angular spread is not easily measurable and is typically on the order of 2–5 mm-mrad. It can also be parameterized using the emittance of the beam, defined as the product of the size and angular divergence of the beam in a plane perpendicular to the beam direction. The size of the proton beam spot is well known because a segmented transmission ionization chamber is typically located at the treatment head entrance for beam-monitoring purposes. For most facilities, the size of a proton beam is usually on the order of 2–8 mm (sigma). Using an incorrect spot size in the simulations can have a significant impact on the results, depending on the design of the treatment head. It has been shown that the exact knowledge of this parameter might not be significant for passive scattering simulations at least for certain modulator wheel designs (36, 64). The impact of the beam spot size depends on the width of each step used on the modulator wheel, that is, the number of absorber steps covered by the beam at a given time. For beam scanning, the exact beam spot size and its shape are, of course, vital, because it directly influences the spot size and shape at treatment head exit as prescribed by the planning system. The initial energy spread and spot size at nozzle entrance might influence the flatness of a spread-out Bragg peak (SOBP) because these parameters influence the peak-to-plateau ratio of the individual Bragg peaks that form an SOBP. Clinically, one of the most important parameters is certainly the beam energy, as fields are prescribed using the beam range in water. The energy and energy spread can be obtained either directly, using an elastic scattering technique (65), or indirectly, by measuring the range and shape of Bragg peaks in water (64). The energy spread of proton beams entering the treatment head from a cyclotron is typically <1% (ΔE/E), whereas a synchrotron may extract beams with an energy spread two orders of magnitude smaller. The parameters listed above are typically correlated. It has been demonstrated that this correlation is insignificant when modeling a passive scattering system, mainly because the amount of scattering material in the beam’s path uncouples the parameters at the treatment head exit (36). For beamscanning simulations such a correlation, for example, between the particle’s position within the extended beam spot and its angular momentum, needs to be taken into account, because it might affect the size of the pencil beam exiting the treatment head. Because of the energy spread of the beam, a deflection in a magnetic field will lead to a correlation of particle energy and position.

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9.6.2  Modeling of Beam-Monitoring Devices Beam-monitoring devices are typically transmission ionization chambers. To simulate a realistic dose distribution, simulating these chambers in detail might not be necessary because they cause only a little scattering and energy loss of the beam. Simulating plain or segmented ionization chambers is done for the purpose of designing ionization chambers or studying beam steering, as well as calculating the absolute dose in machine monitor units. For a patient’s treatment the prescribed dose is converted into machine monitor units. A monitor unit typically corresponds to a fixed amount of charge, collected in a transmission ionization chamber incorporated in the treatment head. This reading is related to a dose at a reference point in water (66, 67). Absolute dose can thus be simulated if a detailed model of the treatment head, including the ionization chamber geometry and readout, is available  (7). In a segmented ionization chamber the volume used for absolute dosimetry can be quite small (e.g., 1–2 cm in diameter). This causes low statistics when simulating the chamber response (from energy deposition events) and thus requires a large number of histories to be simulated. Figure 9.5 shows the Monte Carlo model of an ionization chamber. As an approximate approach, one might simulate the energy deposited in the ionization chamber without predicting the actual output charge (68), that is, simulate a relative number that has to be normalized against a reference charge (27, 69). 9.6.3  Modeling of Beam-Shaping Devices in Passive Scattering Monte Carlo simulations are extremely valuable in treatment head design studies, as they can reduce the required number of experiments considerably. Small design changes can be tested computationally before building or modifying hardware components. Furthermore, for research studies requiring accurate characterization of the radiation field, treatment heads are modeled to characterize the beam at treatment head exit. Such simulations can also be useful when commissioning planning systems (70–72). There are various reports on Monte Carlo treatment head simulations (27, 28, 36, 39, 51, 68, 69, 72–74).

FIGURE 9.5 Monte Carlo model of an ionization chamber at the Francis H. Burr Proton Therapy Center at the Massachusetts General Hospital. Shown is a vertical cut through the device. The simulation was done with the TOPAS Monte Carlo system.

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Most Monte Carlo models attempt to model machine-specific components in the treatment head using manufacture blueprints (36, 37, 39). Creating a Monte Carlo model of a treatment head could also be based on a computer-aided design (CAD) interface to the Monte Carlo code (75). If Monte Carlo codes only allow the definition of geometrical objects out of a library of standard objects, a complex geometry can be represented as a combination of regular geometrical objects. Some devices can be modeled easily by using boxes or tubes, whereas others require complex solutions due to their irregular shapes. The most important beam-shaping devices to be modeled are the passive scattering system, as well as apertures and compensators. Treatment heads in passive scattering proton therapy can be rather complex, and the position or state of certain devices can change depending on the specified field. For example, scattering foils might be inserted or different modulator wheels evoked for a certain combination of range and modulation width. The Monte Carlo model of a treatment head has to accommodate all possible variations of geometrical settings. One might generate a generic treatment head in the Monte Carlo code that is initialized when the code is set up (or compiled) and then modify the generic geometry using parameters provided via an input file. To simulate a specific field, one has to define specific treatment head parameters or the range and modulation width, which can subsequently be converted into the treatment head parameters. The parameters are provided either by a treatment-planning system (if it prescribes the treatment head settings for a patient field) or by the treatmentcontrol system (if the treatment head settings are defined by an interface to the planning system or manually by an operator), or they can simply be defined arbitrarily by the user. The targeted accuracy when modeling the treatment head in a Monte Carlo system depends on the purpose of the simulation. For calculating phase-space distributions for dose calculation in the patient, it is probably sufficient to have only beam-shaping devices included in the simulation. Passive scattering simulations require the double- or single-scattering system, the modulator wheel, aperture, and compensator. For other applications such as ionization chambers for detector studies for absolute dosimetry or housing of devices to study scattering or shielding effects, one might need a more realistic description of other treatment head components. The following paragraphs describe the modeling of the most important devices in a treatment head. A contoured scatterer typically consists of two components: one made of a high-Z material and one made of a low-Z material. The thickness of the high-Z material decreases radially with distance to the field center, whereas the thickness of the low-Z material increases as a function of radial distance. The bi-material design ensures that the scattering power is independent of the beam energy. Such a complex geometry might be modeled by combining regular objects, for example, by combining cones (36).

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A modulator wheel can be simulated by using segments out of a circular structure. Each of these segments is characterized by thickness, material, and minimum and maximum radius, as well as the angle covered. Note that because beam spots often overlap with several wheel steps, it is not sufficient to use one simulation per absorber step and combine simulations. Figure 9.6 depicts Monte Carlo models of a contoured scatterer and a modulator wheel. The geometries of patient field-specific apertures and compensators are typically provided by the planning system. There can also be hard-coded versions in the Monte Carlo if standard regular shapes are being used for commissioning or testing purposes. Apertures are often studied because of both the secondary radiation they produce (47) and the effects of edge scattering. An aperture opening might be characterized by a set of points following the inner shape of the drilled opening. If the Monte Carlo code can translate this information into a 3D object representing the aperture, the information can be used directly. Otherwise, different parameterizations need to be applied (36). For a compensator, the geometry can be described by a set of points in space defining the position and depth of drill bits for use in a milling machine. A Monte Carlo code might use these milling machine files directly. Using standard regular shapes (such as tubes), the geometry can then be modeled (36). 9.6.4  Modeling of Scanned Beam Delivery Treatment heads for beam scanning are, geometrically, less complicated to model because there are fewer objects in the beam path. Essential to model might only be the scanning magnets and, perhaps an aperture. Treatment head simulations for scanned beams have shown good agreement (73).

(A)

(B)

(C)

FIGURE 9.6 Monte Carlo model of a contoured scatterer used in a double-scattering system (left: mesh type image) and a modulator wheel based (middle: transparent steps of the wheel; right: actual simulated proton tracks) at the Francis H. Burr Proton Therapy Center at the Massachusetts General Hospital. The simulation was done with the TOPAS Monte Carlo system (26).

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Depending on the scanning system, accurate description of the field lines compared with binary fields, and accurate beam emittance is important when simulating dose distributions using Monte Carlo. To fully model a scanned beam treatment head, the Monte Carlo code has to be able to simulate magnetic beam steering. Depending on the beam steering, a scanned proton beam can be convergent or divergent. Magnetic fields are typically not modeled physically but rather geometrically by defining an area within the geometry in which particle tracking is affected by a magnetic force of certain strength (36). Particle tracking is then performed according to field equations. As an approximation, instead of implementing the field lines, one might approximate a magnetic field with a certain strength as simply on or off as a function of positioning in the geometry (i.e., assume perfect dipoles). Attention needs to be given to the maximum step size while tracking protons through the magnetic field because large steps lead to considerable uncertainties when simulating the curved path of particles through the field. Figure 9.7 shows an example of protons steered through a magnetic field. If the scanning pattern for a prescribed treatment for pencil beam scanning is simulated, the magnetic field settings are prescribed by either the planning system or by a treatment control system, based on information by the planning system (76). These field characterizations are typically beam spot positions at a plane upstream of the patient that are parameterized as x and y coordinates and spot energy. If the spots are being modeled using Monte Carlo tracking through the nozzle, this information needs to be translated into magnetic strengths in Tesla. The relationship is typically known from results of commissioning measurements.

FIGURE 9.7 Proton tracks steered though a magnet with a specific field strength as modeled within Geant4. The simulation was done with the TOPAS Monte Carlo system (26).

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9.6.5  Time-Dependent Geometries For passive scattering (modulator wheel rotation) as well as beam scanning (changing magnetic field), the treatment head geometry involves devices with a time-dependent setting. Considering time-dependent settings by adding numerous individual runs can be cumbersome because separate executables or input files might be needed for each potential setting. The rotation of the modulator wheel can be simulated by adding individual runs of pristine Bragg peaks that are subsequently added based on weighting factors obtained from the wheel geometry (27, 72). One can also use a slab of a fixed thickness and then change the start position of the beam inside the slab to modulate different thicknesses (68). An alternative is to change the geometry dynamically by applying a four-dimensional (4D) Monte Carlo technique (77). Although still discrete, the technique is basically continuous, as it allows geometry changes after each particle history. In a simulation of passive scattered delivery, the wheel position was changed in steps of 0.7°. The resolution of the simulation had little influence on the speed of the calculation, because motion was handled by simply changing pointers within the computer memory (36). To simulate a beam-scanning pattern, 4D Monte Carlo techniques can be used to constantly update the magnetic field strength (76, 77). This allows studying beam-scanning delivery parameters (73, 76, 78). Another time-dependent feature in beam delivery might be the modulation of the beam current in passive scattering systems (see Chapter 6) (79). Because each patient field is unique in terms of range and modulation width, there needs to be a unique wheel design for each field (each range and modulation width). Because this is impractical, one uses a finite set of modulator wheels, each resembling a unique step design to create full modulation to the patient’s skin. To deliver a certain modulation width, as well as meet specifications for SOBP flatness, the beam current might be regulated at the accelerator (beam source) level to fine-tune the shape of the SOBP depthdose distribution (see Chapter 6) (79). Thus, the beam current is continuously modulated as a function of rotation angle. This can be incorporated into the Monte Carlo code by using a finite set of look-up tables correlated to the rotating wheel in 4D Monte Carlo. 9.6.6  Treatment Head Simulation Accuracy Figure 9.8 shows the simulated geometry of a proton therapy treatment head. The accuracy has to be validated experimentally, for example, by comparing the flatness of the SOBP and the shape of the lateral beam profile (see Figures 9.3 and 9.4). For beam scanning one might validate the simulation by analyzing the beam spot size and Bragg peak width. For a passive scattering treatment head having many beam­-shaping devices, the accuracy of the simulation depends on the available information

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FIGURE 9.8 Monte Carlo model of one of the treatment heads at the Francis H. Burr Proton Therapy Center at Massachusetts General Hospital. The simulation was done with the TOPAS Monte Carlo system (26).

regarding the geometry of treatment head elements, for example, whether drawings of geometries are provided by the vendor (36). In addition, it might depend on our knowledge of exact material compositions and material properties (64). Thus, the desired accuracy might not be reachable based on first principles, depending on the complexity of the treatment head or beam settings or the geometry information. Certain parameters describing material compositions may not be known to sufficient precision. The SOBP range might be very sensitive (up to 1–2-mm range variations) to changes in the density of materials in the modulator wheel or scatterers (64). Materials commonly used for these devices are polyethylene (Lexan), lead, and carbon. Specifically, in the case of carbon, the nominal density as specified by the manufacturer can vary substantially from the actual density because carbon is available in various specifications. The knowledge of material constants affects not only the range but also the modulation width. The question arises: how precisely can one simulate beam delivery with a Monte Carlo treatment head model if one has to rely on specifications given in the manufacturer’s blueprints? Good agreement might be found based on first principles (36, 64), but in certain cases the results of a Monte Carlo–based passive scattering proton beam system might show discrepancies when compared with experiments. If the simulations differ from experimental data, adjusting parameters might be difficult because

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of the complexity of proton therapy treatment heads. For example, adjusting nozzle geometries to improve a slight tilt in an SOBP will correspondingly affect the modulation width (64). Additional experimental information might be needed to adjust settings of material characteristics within the Monte Carlo. An alternative solution is the simulation of the treatment head based on the available geometrical and initial beam information and then fine-tuning if the outcome in terms of range and modulation width does not exactly match the experimental data. Beam current modulation (beam weight as a function of modulator wheel angle) can be used to correct the Monte Carlo simulations if the desired SOBP flatness can not be reached based on first principles (64). Any “tuning” should be done with caution and only for small corrections, because it might affect the beam characteristics or might even point to a problem in the Monte Carlo settings. 9.6.7  Phase-Space Distributions The results of particle tracking through a treatment head are typically stored in a phase-space distribution to be used for further simulations. A phasespace distribution is a file containing the parameters for a large set (typically tens or hundreds of millions) of particles. It is generated when protons are tracked through the treatment head and the kinetic parameters are recorded for each particle. Thus, a phase space is a file where each particle is represented as a point in space with some of its characteristics. It can be defined at a particular surface of any given shape recording all particles that cross this surface (e.g., particles that enter a particular device). For dose calculations the phase space is normally defined at a plane perpendicular to the beam axis between the treatment head and the patient or phantom. The aim is to minimize calculation time due to reusing the phase space if multiple scenarios with the same field characteristics are to be studied. Phase-space files may only contain the most relevant parameters, such as the energy, directional cosine, and particle type. However, for specific studies one is often interested in the history of particles (e.g., if the particle is a secondary or primary particle or if the particle was scattered at a specific device). In this case the phase space may contain additional parameters or binary flags to allow partial reconstruction of a particle’s history. The IAEA has suggested a standardized phase-space format. In photon therapy, phase-space distributions play a big role in dose calculation. For dose calculations in passive scattered proton therapy, phase spaces are less useful because each field typically has a unique setting of the treatment head and beam energy, thus making it unlikely that the phase space can be reused. This is true in particular if the patient-specific aperture and compensator are included in the treatment head simulation. For beam scanning one might be able to find a beam parameterization as will be discussed in the next section.

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Typically, protons, neutrons, electrons, and photons are included in phasespace distributions. For beam scanning, the contribution of secondary particles in the phase space can often be entirely neglected. However, even for passive scattered proton beams, the contribution of secondary protons from the treatment head reaching the patient is quite small. Secondary protons generated upstream of the final collimator are typically emitted at an angle that prevents them from passing through the patient-specific collimator. In addition, those generated within the collimator will most likely be stopped in it. For a very small aperture (diameter of the opening just 3 cm), the treatment head efficiency (protons exiting versus protons entering the treatment head) at the Francis H. Burr Proton Therapy Center was simulated to be just 0.7%, whereas for a bigger aperture opening (15-cm diameter) it increased to 17.7%. The yield of secondary protons per primary proton in the phase-space files was just 0.5% and 0.6%, respectively (i.e., almost independent of the field size). However, nuclear interactions do play a role in the yield of the primaries, as they cause a loss of primary protons along the beam path through the treatment head. Figure 9.9 shows energy distributions of protons and neutrons at the exit of a treatment head. 9.6.8  Beam Models Beam models are a mathematical parameterization of a radiation field exiting the treatment head. They are a standard feature in Monte Carlo simulations for conventional photon or electron beams (80). As we have described above, proton therapy treatment head settings are highly field dependent, and thus beam models are more difficult to define.

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FIGURE 9.9 Energy distribution at the exit of the treatment head for a field with a range of 20 cm in water and a modulation width of 6 cm at the Francis H. Burr Proton Therapy Center at Massachusetts Genera Hospital (left: primary protons; right: secondary protons from nuclear interactions [dashed] and neutrons from nuclear interactions [dotted]).

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It is possible to deconvolve an SOBP into its pristine peak contributions for optimizing beam current modulation (79). This method, in combination with assumptions about the angular spread of the field, could also serve to construct a beam model depending on the complexity of the double-scattering system. Whether such a beam model is realistic depends on the purpose of the study. It might be fine for dose calculation purposes but not for studies where the underlying energy distribution of the beam needs to be known exactly. Note that similar dose distributions can be delivered with different underlying proton energy distributions (but different fluences). The creation of a given SOBP might not be unique in terms of the underlying pristine Bragg peaks. The situation is different for beam scanning. Here, beam models are feasible because a field can be characterized by a fluence map of pencil beams (x, y, beam energy, weight, divergence, and angular spread). The parameters can be obtained by Monte Carlo simulations of the entire treatment head including the magnetic fields (34) or by experiments, for example, fluence distributions of pencil beams in air and depth–dose distribution measured in water (81). For some scanned beam deliveries one might want to use an aperture to reduce the beam penumbra. In this case, it is essential to consider aperture scattering in the beam model. The fact that realistic beam models can be constructed for pencil beam scanning has important implications when using Monte Carlo for clinical dose calculation. For passive scattering simulations, the majority of calculation time is spent tracking particles through the treatment head due to the low efficiency of proton therapy treatment heads for passive scattering (typically between 2% and 40%, depending on the field). The use of beam models allows the use of fast Monte Carlo routinely in the clinic for beam scanning (37).

9.7  The Use of Monte Carlo for Quality Assurance Monte Carlo simulations are very helpful for designing a new facility, for quality assurance (QA), and for supporting everyday operation (e.g., calculating tolerances on the appropriate beam delivery parameters; see Chapter  8). QA is based on routine measurements. Monte Carlo simulations can assist clinical QA procedures. By simulating dose distributions and varying beam input parameters, tolerance levels for beam parameters can be defined (36). Monte Carlo simulations are particularly valuable for studying scenarios that cannot be created easily in reality, (e.g., slight uncertainties or misalignments in the treatment head geometry that might occur over time).

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9.8  Other Monte Carlo Applications 9.8.1  Organ Motion Studies Monte Carlo simulations in radiation therapy are mainly used for dose calculation (as will be described in Chapter 12). Given its accuracy, especially for low-density materials and in the presence of heterogeneities, Monte Carlo dose calculation is attractive for studying motion effects in lung dosimetry (82, 83). For studying dosimetric effects in time-dependent geometries, the results of individual 3D calculations are usually combined. This method can potentially become cumbersome, in particular when assessing double-dynamic systems, for example, investigating the influence of time-dependent beam delivery (i.e., magnetically moving beam spots in proton beam scanning) on the dose deposition in a moving target. In 4D Monte Carlo simulations, the time parameter is translated into the number of histories per updated geometry. The use of this technique when modeling time-dependent structures in the treatment head has been described above. It has also been used to model respiratory patient motion (77, 83) and to study interplay effects between respiratory motion and beam-scanning (76). If the dose is to be calculated based on a time-dependent patient geometry, it cannot be accumulated based on a fixed voxel grid. It was therefore suggested to track points in the geometry based on voxel displacement maps generated via deformable image registration (83). The local dose is calculated as a function of well-defined, moving subvolumes and not as a function of position in a fixed coordinate system. It has also been shown that deformed voxels might be used within Monte Carlo dose calculation (84). 9.8.2  Modeling of Detector Systems One of the first applications of Monte Carlo methods in radiation therapy was the simulation of detector systems. For example, Monte Carlo simulations have been performed to design a prompt gamma detector for QA (85). Another example is the use of Monte Carlo simulations to optimize image reconstruction for proton CT (86, 87). 9.8.3 Simulating Proton-Induced Photon Emission for Range Verification Protons undergo nuclear interactions in the patient, which can lead to the formation of positron emitters. Because the patient is “active” after being irradiated for therapy, one can use a positron emission tomography (PET) image for in vivo verification of treatment delivery and, in particular, beam range (see Chapter 16). Monte Carlo simulations play a vital role for this purpose and are used to generate a theoretical PET image based on the prescribed radiation

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field, which can then be compared to the measured PET distribution for treatment verification (44, 45). The problem when simulating these images is the low statistics due to the relatively low cross section for generating a positron emitter. Fluence-to-yield conversion methods are therefore being used where positron emitter distributions are calculated by internally combining the proton fluence at a given voxel with experimental and evaluated cross sections for yielding 11C, 15O, and other positron emitters (43). Lack of detailed cross sections data is currently limiting the accuracy of in vivo range verification (88). Similarly, the emission of gamma rays from excited nuclear states, so-called prompt gammas, can be simulated using Monte Carlo (89). 9.8.4  Simulating Secondary Neutron Doses Monte Carlo simulations have been used for shielding design studies (see Chapter 17) (90–92). Secondary neutrons reaching the patient are of concern because of potential side effects (see Chapter 18). The neutron-generated dose can not be calculated using an analytical dose calculation method implemented in a treatment-planning system because the dose calculation is not commissioned for low doses. Neutron doses are very low (typically <0.1% of the target dose) and are thus negligible for treatment planning. Furthermore, secondary neutron doses are difficult to measure because neutrons are indirectly ionizing and interact sparsely. Monte Carlo simulations are very valuable for assessing neutron dose in patients (47, 93, 96) or studying the influence of treatment head devices and their design on neutron production (97, 98). The MCNPX code was used to assess neutron and photon doses in proton beams (51–53, 72, 93, 104). Further, FLUKA (50, 103) and Geant4 (47, 94, 96) were applied to assess secondary doses in proton beams. Neutron production in proton beams was also studied using the Shield-Hit (105, 106) and PHITS codes (107). For uncharged particles, like neutrons, interacting less frequently, Monte Carlo simulations might be time consuming because more histories are required to achieve a reasonable statistical accuracy. One approach to overcoming this problem is the use of tabulated energy-dependent fluenceto-equivalent dose conversion coefficients (108–115) in combination with calculating particle fluences at the surface of a region of interest (organ) (51, 102, 116). This approach avoids the time-consuming simulation of each energy deposition event. Radiation weighting factors (see Chapter 18) can be applied on an average basis or during the simulation at each energy deposition event (47, 48). Different dose-scoring methods when simulating neutron equivalent doses have been compared (48). 9.8.5  The Use of Computational Phantoms Organs not directly considered in the treatment-planning process are typically not imaged. Consequently, whole-body computational phantoms can

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play an important role when combined with Monte Carlo dose calculations to simulate scattered or secondary doses (e.g., neutron doses) to organs far away from the target region (117). Initially, the radiation protection community had defined stylized phantoms that are based on simple geometrical shapes (e.g., an elliptical cylinder representing the arm, torso, and hips, a truncated elliptical cone representing the legs and feet, and an elliptical cylinder representing the head and neck). Human anatomy is too complex to be realistically modeled with simple geometrical shapes. A more realistic representation of the human body can be achieved using voxel phantoms, where each voxel is identified in terms of tissue type (soft tissue, hard bone, etc.) and organ identification (lungs, skin, etc.) (118). In a Monte Carlo environment each phantom voxel is usually tagged with a specific material composition and density. Voxel phantoms are largely based on CT images and manually segmented organ contours. For each organ and model and age- and genderdependent densities, as well as age-dependent material compositions, can be adopted based on ICRU (119) and organ-specific material composition as a function of age can be based on individuals at the International Commission on Radiological Protection (ICRP) reference ages (120, 121). Dosimetric differences between the use of stylized phantoms and the use of voxel phantoms can be up to 150% (110, 122–126). In addition to standard adult male or female models, models of pregnant patients (127, 128) and the pediatric population have been designed (129–137). To match a particular patient as closely as possible using a voxel phantom in a Monte Carlo simulation, one might have to interpolate between two different phantoms doing uniform scaling. There is also the problem of differences in the distribution of subcutaneous fat when trying to create an individual from a reference phantom. The latest developments in whole-body computational phantoms for Monte Carlo simulations are hybrid phantoms (138, 139). These phantoms are typically based on combinations of polygon mesh and nonuniform rational B-spline (NURBS) surfaces. They provide the flexibility to model thin tissue layers and allow for free-form phantom deformations for selected body regions and internal organs. Each organ can be adjusted to the desired shape and volume using patient-specific images and deformable image registration ­(140–144). Patient body weight can be accommodated through adjustments in adipose tissue distribution (145–147). A series of reference (i.e., 50th height/ weight percentile) pediatric hybrid models has been developed (136). Figure 9.10 shows a hybrid phantom and how it can be shaped to resemble a specific patient. Details regarding source images, developmental procedure, modeling issues, and resulting hybrid phantoms can be found elsewhere (138). Phantoms have been implemented in many Monte Carlo codes to assess neutron doses in proton therapy (47, 94–96, 101, 103). For example, work has been done on neutron dose contamination in proton therapy in pediatric patient anatomies (47) based on computational phantoms (134, 137).

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FIGURE 9.10 Frontal views of patient-dependent pediatric female phantoms at a specific targeted standing height and at their 10th, 25th, 50th, 75th, and 90th percentile body masses. Also shown are lateral views for different targeted standing heights. (From Johnson et al., Proc IEEE, 97(12), 2060, 2009. With permission.)

9.8.6  Simulating LET Distributions for Radiobiological Considerations Prescription doses to cancerous tissue as well as dose constraints to organs at risk are based on clinical experience with photon beams. Proton doses are related to photon doses using the relative biological effectiveness (see Chapter 19). Biophysical modeling is far from being able to simulate all radiation effects in subcellular structures. The physics, however, can be simulated reasonably well. To interpret biological experiments one needs to know the characteristics of the radiation beam. The absorbed dose can be described as the integral of the particle fluence times the total mass stopping power over the particle energy distributions (148, 149). One parameter that is being used to interpret biological effectiveness of proton beams is the linear energy transfer (LET). One might simulate dose-averaged LET distributions in a patient geometry to identify potential hot spots of biological effectiveness (see Chapter 19) (150). When calculating the dose-average LET during a Monte Carlo run, one needs to record each energy loss, dE, of a particle and the length of the particle step that leads to the energy deposition event, dx. In a CT geometry, all values can be scored voxel by voxel (v):

∑ dE ⋅ ( dE dx ) ⋅ ρ . ∑ dE 1

LETd ( v) =

events

(9.4)

events

Note that when simulating LETd using Monte Carlo simulations, the cutoff defined to stop further tracking of the proton can have a significant influence (151).

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9.8.7  Biology: Track Structure Simulations To understand the biological effect of radiation, Monte Carlo simulations can be used to study the interactions of particles with biological structures, like the DNA (152–170). More accurately than by using the LET, one might analyze proton track structure to gain insight into biological effects (see Chapter 19) (165). The particle track structure describes the pattern of energy deposition events of proton tracks, including the secondary electrons, on nanometer scale. At a given LET, smaller tracks are most likely to produce more significant DNA damage. Simulations are based on energy depositions and/or simulation of ionization frequencies. Considering energy depositions is more accurate because excitations play a role in radiation damage as well. In Monte Carlo codes DNA damage can be associated with a specific energy amount imparted per track length or per assumed subcellular volume (171). Simulations have been used to predict the passage of proton tracks through DNA and to correlate the energy deposition events to different types of strand breaks (164). The production of very small DNA fragments is the result of energy depositions within the nanometer scale and is due to correlated events from the same track (156). Simulations may assume a certain proportionality between ionization frequency and lesion type in the DNA, which might be further refined by modeling subvolumes of the DNA that can have different geometrical shapes (172). Predictions can be made on the likelihood of DNA damage and damage clustering, which in turn can be used to make assumptions about repair probability for certain DNA damages. Analyzing the distance of two energy deposition events on a nanometer scale can give insight into lesion complexity (173). Track structure can be simulated with the same codes that are used for macroscopic dose simulations. However, many specific codes have been developed, particularly to deal with low-energy particle tracks and with the δ-electrons produced by proton tracks (174, 175). For example, the code PARTRAC includes an accurate representation of the chromatin and of the physical and physiochemical processes associated with the energy deposition by radiation (157, 158, 161). The code is based on an extension of MOCA14 (176, 177). Another example is the MCDS code (169, 170), a code applicable to a variety of different particles. Accurate single and double-differential cross sections for inelastic and elastic interactions, including ionization, leading to δ-electron emission are needed (173, 174, 178, 179). Specific Monte Carlo models based on clustered DNA damage, taking into account the stochastic aspects of δ-electron emission, have been developed (171, 180–182). Currently, Monte Carlo simulations are not able to fully simulate radiation action and radiation effects on living cells. Although Monte Carlo codes have been used successfully for predicting DNA damages (183), the link to cellular response, including repair mechanisms, has not yet been fully established. To model cellular radiation effects, it is necessary to predict the relationship

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between the lesion distribution and the kinetics of damage processing. There are approaches combining the Monte Carlo simulation of microdosimetric quantities with biological models. For example, the Monte Carlo code PHITS has been modified to allow the simulation of radiolysis (184) to be combined with the MKM model (see Chapter 19) in order to predict biological effects (107).

Acknowledgments The author thanks Dr. Bryan Bednarz and Jocelyn Woods for proofreading and Dr. Jan Schuemann and Clemens Grassberger for their help with some of the figures.

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10 Physics of Treatment Planning for Single-Field Uniform Dose Martijn Engelsman CONTENTS 10.1 Introduction................................................................................................. 305 10.2 Prerequisites for Treatment Planning...................................................... 307 10.2.1 Clinical Information....................................................................... 307 10.2.2 Treatment-Planning System.......................................................... 308 10.3 The Tools of Treatment Planning............................................................. 309 10.3.1 Beam-Specific Choices....................................................................309 10.3.1.1 Lateral Safety Margins....................................................309 10.3.1.2 Distal and Proximal Safety Margins............................. 312 10.3.1.3 Beam Direction................................................................. 317 10.3.1.4 Patching............................................................................. 318 10.4.1 Treatment-Plan-Specific Choices.................................................. 320 10.5 SFUD with Pencil Beam Scanning........................................................... 321 10.6 Specialized Treatments.............................................................................. 322 10.6.1 Eye Treatments................................................................................ 323 10.6.2 Proton-SRS....................................................................................... 324 10.6.3 Proton-SBRT..................................................................................... 326 10.7 Patient Treatment-Planning Examples.................................................... 326 10.7.1 C-Spine Tumor................................................................................. 326 10.7.2 Lung.................................................................................................. 329 10.8 Future Perspectives of SFUD.................................................................... 332 References.............................................................................................................. 332

10.1  Introduction Radiation therapy is a multidisciplinary science. It requires continuous and accurate communication between physicians, clinical physicists, treatment planners, therapists, and nurses. Arguably the most important step in the radiation treatment of a cancer patient is the act of treatment planning. Treatment planning combines the available clinical information about the 305

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patient with the physics aspects of proton therapy and the proton therapy equipment (Figure 10.1). For optimal treatment plan design it is important that both physicians and clinical physicists have at least a rudimentary understanding of each other’s specialization. The goal of treatment planning is to design the best possible treatment given the limitations of the radiation therapy equipment available (1–3). A good treatment plan ensures the delivery of the desired dose to the tumor while delivering the lowest possible dose to surrounding normal tissues. This requires elaborate tweaking of many beam properties, such as beam direction, field shape, and beam weight. Treatment planning allows those responsible for the radiation treatment of a patient (i.e., the radiation oncologist and clinical physicist) to determine the three-dimensional (3D) dose distribution that will be delivered to the patient. With the dosimetric consequences of each tweaking visualized before actual treatment delivery, it

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is possible to design the treatment that best satisfies the wishes of the radiation oncologist, that is deliverable with the equipment available, and that is robust under typical radiotherapy uncertainties. This chapter will discuss treatment planning of proton radiotherapy for ­single-field uniform dose (SFUD), in which each proton radiotherapy beam delivers a homogeneous dose to the tumor. SFUD proton therapy can be delivered with passively scattered proton therapy (PSPT) as well as by means of pencil beam scanning. Most of this chapter will be focused on PSPT. The notable differences between SFUD using pencil beam scanning and SFUD using PSPT will be discussed in the section “SFUD with Pencil Beam Scanning.” Though discussed in detail in Chapters 13 and 14, touching on aspects of the uncertainties in a proton treatment plan cannot be avoided completely because the physicist and the radiation oncologist have to be intimately aware of these uncertainties at the time of treatment plan design.

10.2  Prerequisites for Treatment Planning The prerequisites for proton treatment planning are clinical information and a treatment-planning system (TPS). 10.2.1  Clinical Information Clinical information consists of imaging data and the radiation oncologist’s intent (i.e., a dose prescription for the target and dose limits for surrounding healthy tissues [OAR, organs at risk]). Even in routine proton therapy treatment planning an abundance of imaging data, over multiple imaging modalities, is used by the physician to determine the exact location(s) of cancer within the patient. Without going into detail, the minimum amount of imaging information is the treatment-planning CT (computed tomography) scan. On this CT scan, the target and OAR are delineated. Outlining the target in proton therapy follows the guidelines of the International Commission on Radiation Units and Measurements (ICRU) (4–6). Briefly, the physician delineates the visible tumor (visible on any imaging modality), which is denoted the gross tumor volume (GTV). On the basis of clinical experience, the physician can expand the GTV into a clinical target volume (CTV) to account for suspected invisible spread of the cancer. The physician also provides a prescription, in dose to be delivered to the target and dose constraints for the OAR. In prescribing the dose to the target it is common for the GTV to have a higher prescription dose than the CTV. A prescription for the target consists of a fraction dose and the total number of treatment fractions. For the target the goal of treatment planning is to satisfy the prescription as accurately as possible. Overdosing and underdosing

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(parts of) the target is undesired. Prescriptions for the OAR are an upper limit and can be expressed in many different ways: for example, a maximum dose to any point, a maximum volume that cannot receive more than a certain dose, and the mean dose. For the OAR, the goal is not to exactly meet the constraint but to, if possible, further minimize the dose while still satisfying the dose prescription of the target. Prescriptions for the target and one or more OAR are, however, frequently mutually exclusive. Treatment planning is therefore a balancing act between maximizing the probability of curing the patient (TCP, tumor control probability) and minimizing the probability of serious adverse side effects (NTCP, normal tissue complication probability). The last clinical, and clinical physics, input into the design of the treatment plan is an estimate of target motion and the expected setup accuracy of the patient in the treatment room. This information is used to expand the CTV with a safety margin into a planning target volume (PTV), or it can otherwise be taken into account in the design of the treatment plan. For a more detailed discussion on the use of the PTV in proton therapy, see Chapter 11. Chapter 15 discusses a more advanced method of taking uncertainties into account in the treatment-planning process. From here on in this chapter, when we refer to the “target,” we will be referring to any delineation of the tumor; i.e., the GTV or the CTV. Also, in this chapter uncertainties in the target location are directly taken into account in the beam-specific parameters rather than using a PTV as an intermediary step. 10.2.2  Treatment-Planning System The clinical information serves as input for the TPS. Within the TPS the planning CT scan is a virtual representation of the patient at the moment of treatment delivery. For uncertainties related to the treatment-planning CT scan, see Chapter 13. The TPS also, as much as possible, provides a representation of the capabilities of the treatment delivery system (e.g., gantry angles, aperture shapes, available proton energies, and beam penumbra) (Figure 10.1). The treatment planner uses the TPS to define all treatment beam-specific information such that the treatment prescription is satisfied to the maximum possible extent. At completion of the treatment plan the output of the TPS consists of all data to be used for actual treatment delivery. This not only includes dosimetric data such as the prescribed range and modulation width of each treatment field, but also imaging information to be used for accurate patient alignment at the time of treatment, such as digitally reconstructed radiographs. It is of great importance for the clinical physicist and the physician to understand the limitations of the TPS. Especially the dose calculation algorithm, which is at the heart of the TPS, is an approximation, albeit one that has acceptable accuracy for the vast majority of treatment scenarios. For details on dose calculation algorithms, see Chapter 12.

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10.3  The Tools of Treatment Planning Table 10.1 shows the many attributes under control of the treatment planner during proton radiotherapy treatment planning. For ease of discussion they have been subdivided into beam-specific and treatment plan–specific parameters. Also indicated is what safety margin is affected by which beamspecific parameter. The order of discussion of each of these parameters may at times appear somewhat arbitrary. For example, in clinical practice the treatment planner will first choose the beam direction before deciding on the more detailed aspects such as aperture shape and beam range. The choice of beam angle is, however, easier to understand with details regarding the choice of range and modulation already explained. 10.3.1  Beam-Specific Choices 10.3.1.1  Lateral Safety Margins For each beam direction the aim during treatment planning is to conform the dose closely to the target, both laterally and in the depth direction. In the lateral direction this conformality is achieved by using a custom-milled aperture or a multileaf collimator (MLC) (Chapter 5). For simplicity this chapter will use the word “aperture” to denote either. A target can have a very complex 3D shape and the optimal shape of the aperture can therefore TABLE 10.1 The Many Attributes under Control of the Treatment Planner in Designing a Passively Scattered Proton Therapy Treatment Plan Parameters Beam specific   Range (R)   Modulation (M)   Aperture shape (AP)   Range compensator shape (RC)   Smearing   Air gap/snout extension   Isocenter location   Beam direction (gantry angle, couch rotation)   Patching Treatment plan specific   Number of beams   Relative beam weights   Beam combinations per treatment fraction (“fraction groups”)   Use of photon beams

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best be determined in the beam’s eye view (BEV). The two aspects affecting the lateral safety margin are the penumbra of the proton beam at the depth of the target (dosimetric margin) and the expected uncertainty in the target position due to setup errors and intrafractional tumor motion (setup margin) (see Figure 10.2a). The penumbra depends on the proton beam-line specifics a)

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Left optic nerve

FIGURE 10.2 (a) The lateral margin between aperture edge (50% isodose level) and target edge consists of a dosimetric margin and a setup margin. The central white area indicates the target, which, in this example, needed to be covered with the 95% isodose level assuming a 5-mm setup margin. (b) Beam’s eye view of a single field for the treatment of an intracranial tumor. The dashed white circle indicates the maximum available aperture size. The dark structure indicates the target, whereas the thick solid white line indicates the aperture shape that was used. A uniform margin of 7 mm was needed to ensure target coverage. To remain within the dose tolerance of the brainstem, a reduced margin was needed. An even smaller margin toward the optical nerves and chiasm was needed to sufficiently spare these OAR.

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and varies with range and depth in the patient (Chapter 4). The dosimetric margin is the distance between the 50% isodose level (the field edge) and the desired isodose coverage (typically the 95% isodose level). Expected setup errors are part of the clinical input by the physician and clinical physicist. The setup margin can vary from 1–2 mm for intracranial radiosurgery treatments to about 10 mm for prostate treatments. To first order, the shape of the aperture will be a simple geometric expansion of the shape of the target in the BEV (Figure 10.2b). Just as in photon radiotherapy, the magnitude of the lateral safety margin can be based on clinical experience, but also on a margin recipe; for example, van Herk et al. (7). Frequently, the treatment planner has to locally alter the shape of an aperture. Because of multiple Coulomb scattering within the range compensator (RC) and within the patient, a uniform margin between target and aperture edge will typically not result in a uniform margin between the prescription isodose level and the target. This requires local expansion and shrinking of the aperture. Furthermore, dose limits to adjacent OAR may also require the treatment planner to manually alter the aperture shape. In Figure 10.2b, the lateral margin between aperture and target has been reduced in the direction of the brainstem and is even more reduced toward the optic nerves. The achievable shape of an aperture furthermore depends on the limitations of the milling machine (e.g., diameter of the drill) that creates the physical aperture, and the TPS has to mimic these limitations accurately. If an MLC is used, the aperture shape is limited by the width of the MLC leafs. Dose calculation within the TPS provides feedback to the treatment planner as to the adequacy of the shape of the aperture. Typically, passively scattered proton therapy beam lines allow motion of the aperture and RC combination along the beam axis by means of snout translation. This allows the treatment planner a choice of air gap (Figure  10.3), defined as the distance between the downstream side of the RC and the patient skin. The TPS has to be able to model the choice of air gap and the consequences for the shape of the aperture. An increase in air gap increases the penumbra in the patient, and this should be modeled by the dose calculation algorithm (Chapter 12). More important, an aperture projection discrepancy may occur in the treatment room if the aperture has been created for a specific air gap that cannot be reproduced at the moment of actual treatment. The patient’s shoulder may, for example, not be part of the CT scan and limit snout translation. The increased air gap results in more dose to normal tissues because it leads to an increase in field size and to a softening of the lateral penumbra. Especially when an aperture edge is used to exactly control the dose to an OAR, every millimeter can be important. At the time of treatment planning an air gap of a few centimeters is typically chosen to allow for some wiggle room at the time of treatment. For patient treatments that require abutting fields, an intentional increase in the air gap and related increase in penumbra can be beneficial as it reduces underdosage and overdosage at the match line.

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Sn Tran out slati on

AirGap

FIGURE 10.3 The snout can be translated along the beam direction to bring the field-specific hardware (aperture and RC) as closely as possible to the patient. Minimizing the air gap reduces the lateral penumbra of the dose distribution.

10.3.1.2  Distal and Proximal Safety Margins The largest benefit of protons for sparing OAR is the finite range of protons. The many uncertainties in the calculated range in the patient of protons at the time of treatment planning and in the required proton range at the time of treatment delivery, necessitate the use of safety margins both distally and proximally to the target. Proximal safety margins can be larger than distal safety margins because of smearing of the RC (see below). The distal safety margin is, however, certainly more important. Keeping the spread-out Bragg peak (SOBP) depthdose distribution in mind, an error in the range of a proton field can be the difference between 0% and 100% of the beam dose to the target (and to an OAR), whereas an error in the modulation width has more moderate consequences. The prescribed range is chosen to ensure distal target coverage with the prescribed dose for that beam direction. Typically, the range of a SOBP is defined by the water equivalent depth of the distal 90% isodose level. The required range to cover the target is determined by ray-tracing the water equivalent depth (more precisely; the proton stopping power) over the extent of the target in BEV. The rays emanate from the virtual source position, and accumulation of water equivalent depth will take place from the location where the ray enters the patient geometry to the distal edge of the target. The uncertainty applied to this required range is 3.5% of the range plus an additional millimeter (see Chapter 13), but this may differ slightly between institutions. The prescribed range R, in cm, therefore, is

R = 1.035 ⋅ max(Ri ) + 0.1 ,

with Ri the range for each ray i.

(10.1)

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If a RC has a minimum thickness (e.g., 1–2 mm, for milling purposes), then this minimum thickness is taken into account for each ray as well. Defining the range by the distal 90% isodose level means that a small part of the target will receive a dose down to 90% rather than 100% of the prescribed dose for that beam direction if these range uncertainties are actual (see Chapter 13). The volume of the target receiving a too low dose will be limited as distal conformality in a typical patient scenario is never submillimeter tight. Also, the typical use of multiple beam directions mitigates the magnitude of the possible underdosage. The prescribed modulation width is chosen to ensure proximal coverage of the target with the prescribed dose. The required modulation width of a beam is also determined by means of ray-tracing, but with range uncertainties (3.5% plus 1 mm) applied both at the distal end and the proximal end:

M = max(1.035 ⋅ Ri − 0.965 ⋅ Pi ) + 0.2 ,

(10.2)

where Pi is the water equivalent depth of the proximal edge of the target along each ray. This modulation width may need to be altered as a function of the amount of smearing applied to the RC (see below). For a treatment plan that consists of multiple beams, one could in principle achieve adequate target coverage even when not all beams individually ensure proximal and distal target coverage. However, in clinical practice such detailed tweaking of a treatment plan is very labor intensive and is not performed. The RC ensures tight distal target coverage. It allows increased sparing of OAR and normal tissues distal to the target by locally pulling back the SOBP as much as possible without affecting target coverage. The TPS provides a method to determine the 3D shape of the RC and can model the presence of the RC and its effect on the beam-specific dose distribution in the patient. As mentioned, the minimum thickness of an RC has to be taken into account in the prescribed range. A typical method to determine the RC thickness as a function of the BEV position is ray tracing to the distal edge of the target. Along each ray, the thickness of the RC is then determined by

RC i = max( Ri ) − Ri .

(10.3)

This method of RC design, however, ignores the effect of multiple Coulomb scattering in the patient that is taken into account when performing the dose calculation based on this RC. The result may be that distal dose conformality is inadequate, with location-specific overshoot and undershoot depending on the patient geometry. The worst-case scenario is that an additional “RC volume” has to be manually drawn in the CT scan to which the RC will be designed, thus “faking” the TPS into designing an adequate RC. This is extremely labor intensive, but better methodologies are currently not yet

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available in commercial TPSs. An improvement would be, for example, to allow the treatment planner to virtually “pull” isodose lines, thereby locally affecting the RC thickness. Best is to have an algorithm that automatically optimizes the RC based on the actual dose calculation algorithm (i.e., a dosimetric rather than a radiologic/geometric determination). The thickness of the RC lateral to the target, but within the aperture circumference, is undefined and typically is set to the nearest still-defined thickness. An important aspect affecting distal conformality is RC smearing (e.g., [6, 8]). Smearing is best explained by assuming that the only uncertainties are setup errors (e.g., no range uncertainties or patient density changes). In this case, the RC could be designed to tightly conform the distal falloff of the SOBP to the target (Figure 10.4a). This is accurate as long as point p in the patient is aligned with point r in the RC. At the time of delivery of a treatment fraction, however, the patient may be slightly misplaced with respect to the beam-specific hardware. A typical setup error could be up to a few millimeters, and such a setup error is mimicked in Figure 10.4b. Point p is underdosed because protons traveling to this point have to pass through too thick

skin RC

Target

r

Beam

Target

p

r

p

a)

r

c)

p Target

p Target

r

b)

d)

FIGURE 10.4 Schematic diagrams explaining smearing in a 2D geometry. In reality, smearing is applied to a 3D range compensator (RC). The dark circle indicates a high-density structure. (a) No smearing applied, patient and RC aligned. (b) No smearing applied, patient misaligned. (c) Smearing applied, patient and RC aligned. Also indicated is the shape of the RC prior to smearing. (d) Smearing applied, patient misaligned.

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a part of the RC (points p and r are no longer aligned). The process of smearing is effectively a “hollowing out” of the 3D RC. The thickness at a specific location of the RC after smearing is the minimum thickness of the unsmeared RC as found within a certain distance (i.e., the “smearing radius”) from this point. Figure 10.4c shows the dose distribution in the patient for the smeared RC as observed in the treatment-planning geometry (i.e., without any patient alignment error). Smearing the RC results in regional overshoot of the proton beam. This overshoot is necessary to ensure target coverage in case of a patient alignment error (Figure 10.4d). Smearing does not affect the prescribed range, but it may affect the prescribed modulation; see the numerical example below. In fact, the large modulation chosen in Figure 10.4 is necessary to ensure proximal target coverage under setup errors and smearing. Please note that no material is taken away at any point on the RC that already has the minimum thickness prior to smearing. Proper patient alignment minimizes the necessary smearing and the undesired overshoot, and undershoot of protons into healthy tissue. Although the smearing process does not take into account secondary effects such as altered multiple Coulomb scattering inside the RC and patient, the smearing process is a good method to ensure target coverage for setup errors (shifts of the entire patient) with a magnitude up to the smearing radius. Smearing is not a fail-safe method to deal with relative changes in the patient density distribution, such as an upstream high-density structure moving to a different relative location with respect to the target, but it may have some merit even in those cases. Smearing has also been suggested as a non-fail-safe method of handling breathing motion for lung cancer (see section “Patient examples”). Because smearing and its application in the TPS are not intuitive, a numerical example follows using a two-dimensional (2D) geometry. Figure 10.5 shows a hypothetical tumor in a, mainly, unit-density phantom. Each voxel is 1 cm × 1 cm, and the dark area in the bottom right corner has a density of twice unit-density. The proton beam enters from below, lateral target coverage is not taken into consideration, and a 1-cm smearing radius is assumed. Table 10.2 shows the steps in the design of the beam focusing on the rays aimed at positions A–E in Figure 10.5. The required range to cover the distal edge of the tumor in the case of no uncertainties (Dr) is largest for ray E (i.e., 12 cm). Taking into account range uncertainties of 3.5% + 1 mm (Du), the prescribed range (R) is 12.52 cm. A RC has to be designed to pull back the distal falloff where necessary (column RCr). The RC thickness after smearing is shown in column RCsm, leading to a depth of the distal falloff along each ray as according to column Du,sm. Especially for rays B and D smearing increases the proton beam penetration inside the patient. The required modulation along each ray, to ensure proximal target coverage, requires calculation of the water equivalent depth of the proximal tumor edge (Pr) corrected for the same range uncertainties of 3.5 % + 1 mm (Pu). The difference between Du,sm and Pu provides the required local modulation width (Msm), the maximum of

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A

B

C

D

E

BEAM

FIGURE 10.5 Stylized unit-density 10 × 12-cm2 phantom irradiated with a proton beam incident from below. The thick black line indicates the target. The dark gray area indicates a high-density structure.

TABLE 10.2 Steps in Determining, for a Passively Scattered Proton Therapy Field, the Beam-Specific Range, Modulation Width, and Range Compensator Thickness Distal, Range

A B C D E

Proximal, Modulation

Dr

Du

RCr

RCsm

Du, sm

Pr

Pu

Msm

8.00 8.00 11.00 11.00 12.00

8.38 8.38 11.49 11.49 12.52

4.14 4.14 1.03 1.03 0.00

4.14 1.03 1.03 0.00 0.00

8.38 11.49 11.49 12.52 12.52

5.00 5.00 7.00 7.00 8.00

4.73 4.73 6.66 6.66 7.62

3.65 6.76 4.83 5.86 4.90

The values represented take into account range uncertainties and setup errors, for the situation depicted in Figure 10.5. The underlined numbers designate the prescribed range (R) and modulation width (M).

which is the prescribed modulation width (M). For this phantom, the largest water equivalent tumor thickness was 4 cm, but the prescribed modulation taking into account range uncertainties and smearing (setup errors) is almost 7 cm. Counterintuitively, in this example this modulation is needed to cover the target at its thinnest water equivalent thickness (ray B).

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10.3.1.3  Beam Direction Now that we have a detailed understanding of how certain beam-specific parameters are chosen and, more importantly, how they affect target coverage and dose to normal tissues, we can discuss the choice of beam directions. Gantries and robotic treatment couches allow the choice of almost any incident beam direction over a 4π solid angle. For isocentric gantries the beam is always aimed at isocenter, which is, simply put, the point at which the central beam axes for any gantry angle coincide. The choice of isocenter location inside the patient is an important aspect of treatment planning. Typically it will be near the center of the target; however, it is always chosen to be at a location that can be accurately reproduced at the time of patient treatment, based on imaging information provided by the TPS and as acquired by means of imaging on any treatment day. It is important to realize that the isocenter location is “fixed” in the treatment room, and one aligns the patient such that the anatomical location of the isocenter as chosen during treatment planning corresponds with the location of the room isocenter. Once the patient is aligned with the room isocenter, the treatment couch allows rotation of the patient around the room isocenter while maintaining alignment between the anatomical and room isocenter. Many of the considerations in choosing beam directions also play a role in conformal photon radiotherapy, but they are much more important in proton therapy because of the finite range of protons. An obvious consideration is to geometrically avoid OAR. One tries to prevent multiple beams to overlap on the patient skin because the skin is a very sensitive OAR and proton therapy beams do not have the skin-sparing effect of photon beams. The lack of a build-up effect at the patient skin for proton beams on the other hand allows a choice of beam directions through the immobilization devices used without significantly increasing the skin dose. Bulky immobilization devices may, however, require an increase in snout extension, thus increasing the lateral penumbra and the dose to normal tissues. Furthermore, immobilization devices may lead to abrupt variations in water equivalent path length, not only at the edge of the immobilization device but also within the device itself, increasing dose to normal tissues due to smearing. In general, beam directions should avoid “skimming” steep density gradients, for example by preferring angles of beam incidence that are nearperpendicular to the patient skin, and by not aiming a beam parallel to the mediastinum-lung interface or diaphragm-lung interface. Beam directions parallel to the auditory canal and the base of the skull should also be avoided because these may challenge the accuracy of the dose calculation algorithm. High-density material in the patient, such as titanium rods used for stabilizing the spinal column after tumor resection, are avoided as much as possible due to range uncertainties and dose shadowing effects. If it is unavoidable to treat through these high-density materials, one aims to use multiple beam directions to mitigate the possible dosimetric consequences.

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To prevent aperture projection errors (see section “Lateral Safety Margins”) the treatment planner needs to be aware of the exact geometry of treatment nozzle and treatment couch, choosing a safe beam direction if necessary. In general, treating obliquely through the treatment couch (less than 45° angles) is avoided. Such a beam direction would increase the penumbra because of the increased snout extension and because of the increase in prescribed range for that beam angle. A final point of consideration is range variations that occur if the treatmentplanning CT is an incorrect representation of the patient geometry at the time of treatment delivery. These interfractional variations in the 3D density distribution of the patient make, for example, the following beam directions unfavorable: skimming a patient breast fold, treating through the diaphragm, and treating through an air-filled rectum. 10.3.1.4  Patching In principle, the choice to do patching is also beam direction related, but it is such a specialized issue in proton therapy that it will be treated independently. Patching is used if no single field direction can be chosen that would allow delivery of the required dose to the entire target without running the risk of severely overdosing an OAR very close to this target. Patching is typically considered if the target wraps closely around an OAR, with the tolerance dose of the OAR smaller than the prescribed target dose. To deliver the (remaining) dose to such a target with a single field, one would have to, partially or fully, irradiate through the OAR, thereby overdosing it, or one has to aim the beam directly at the OAR while trying to spare it by means of proton range. Because of range uncertainties, this latter solution is not favored unless there is a sufficient gap (e.g., >2-cm water equivalent path length) between the distal target edge and the OAR. Rather, the choice is to stay-off the OAR by means of the much more certain lateral aperture edge. A typical example case for patching is shown in Figure 10.6. The “through”field treats a part of the target volume from the proximal to distal edge. The aperture is designed to cover as much of the target as possible while staying off the OAR. The OAR in this example are the spinal cord and the brainstem. Figure 10.6, d and e, show the beam’s eye view for the through field with the target volume and patch volume, respectively. The patch volume is that part of the target volume that is not captured within the aperture outline of the through field. The aperture of the “patch” field is subsequently designed to this patch volume. The proton range for the patch field is chosen such that the distal dose falloff matches on the lateral penumbra of the through field along the patch line. Figure 10.6, f and g, show the beam’s eye view for the patch field. Both the through field and patch field stay off the OAR by means of aperture edge. The combined dose distribution, as calculated by the TPS, is shown in Figure 10.6c. Unless special measures are taken (9), the distal and lateral SOBP dose gradient are dissimilar enough

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Physics of Treatment Planning for Single-Field Uniform Dose

Through

Target Volume Through beam

105 % 95 % 50 % 20 %

d)

Patch

105 % 95 % 50 % 20 %

Through beam

Patch Volume a)

e)

b)

Patch beam

Target Volume

105 % 95 % 50 % 20 %

f)

Patch beam

Patch Volume

c)

g)

FIGURE 10.6 (See color insert.) Example of a patch combination in proton therapy. (a and b) The beam direction and relative dose distribution of the through field and patch field, respectively. The red area indicates the target, and the blue area indicates the spinal cord. (c) The relative dose distribution for the patch combination. (d–g) The beam’s eye view of the patch fields with either the entire target volume (in red) or only the patch volume (in purple).

that dose homogeneity along the patch line is in the order of ±10% even in the absence of any range uncertainties. Furthermore, any subsequent millimeter of overshoot or undershoot of the patch field varies the local dose variation by about another 10%. Some proton therapy institutes will apply

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smearing to the RC of the patch field; others do not. In either case, tissues near the patch line can get a considerable overdosage or underdosage on a per treatment fraction basis depending on the setup error and the uncertainty in the range calculation. For this reason, the total dose delivered by any single patch combination is limited. For targets that need to receive a large (remaining) dose by means of patching, the treatment planner will try to find multiple patch combinations, limiting the use of each patch combination to 3–5 fractions. This substantially averages out the uncertainty in absolute dose along the patch lines. The aim is to have patch lines not cross, but sometimes this is unavoidable. 10.4.1  Treatment-Plan-Specific Choices As a single proton field can deliver a homogeneous dose to the target, it is possible to deliver the entire prescribed dose with only a single field. For some tumors such as lacrimal gland tumors this is indeed clinical practice. More frequently, however, multiple beams are used to spread out the dose to normal tissues, just as in photon radiotherapy. A very complex head-andneck treatment, with for example a large CTV requiring the use of abutting fields and multiple boost regions, can consist of 10–15 unique treatment fields. The fact that each proton field (or patch combination) delivers a homogeneous dose to the target allows the treatment planner great flexibility in choosing individual beam weights. This can help spare certain OAR. Homogenous dose delivery per field also allows treatment of only a limited number of fields for each treatment delivery fraction, instead of treating all fields every day. Many proton therapy centers pursue this strategy of treating fraction groups at some cost in biologically corrected dose to the healthy tissues (10). For this strategy to be safely and effectively applied, one needs to confirm at the time of treatment planning that target coverage is not only achieved by delivery of all fields over the entire treatment course, but for each fraction group. Once the total dose delivered by a field and the number of fractions this field will use are known, the output of the field (dose per monitor unit, MU) can be determined. As there are only a very limited number of proton therapy centers and as the proton therapy beam-line layouts are still in the process of “normalizing,” current commercially available TPSs are typically not able to calculate the expected number of MUs for a treatment field. This important characteristic, MU, is therefore at the moment often determined by an in-house-developed output prediction model or by individual field measurements (Chapters 8 and 12). It is possible that photon fields are intermixed into what is mainly a proton therapy treatment plan. The reason would be one of the following: (1) to decrease skin dose, (2) to allow a patient treatment to start even though no proton treatment slots are yet available, and (3) to allow patient treatments to continue in case of unexpected unavailability (downtime) of the proton treatment machine.

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10.5  SFUD with Pencil Beam Scanning In many respects SFUD treatment planning with pencil beam scanning is the same as intensity-modulated proton therapy (IMPT) treatment planning. The main difference is that automatic optimization of the spot weights in SFUD is performed on a per-beam basis, ensuring that a homogeneous dose is delivered to the target by every field individually. In IMPT, spot weight optimization is performed over all fields in parallel. Each individual field can deliver a highly inhomogeneous dose distribution to the target, with all fields combined ensuring the desired (homogeneous) target dose coverage. For details as to the implementation of pencil beam scanning into the TPS and the use in everyday clinical practice (e.g., choice of spot locations and representation of range shifters), we refer the reader to Chapter 11. This section is limited to comparing SFUD using pencil beam scanning and PSPT. SFUD treatment planning with pencil beam scanning has the same goal as PSPT: each treatment field ensures a homogeneous dose to the target volume under setup errors and range uncertainties. There are a few notable differences, however, most of which are benefits. The main dosimetric benefit of pencil beam scanning is that it allows both distal and proximal conformality for a single beam (Figure 10.7). Although not an accurate description of how spot weights are chosen in pencil beam scanning, one way of looking at it is that it allows the range and modulation width to be set on a per-proton-ray-beam (source to distal target edge) basis. Range uncertainties and setup uncertainties (smearing) and their effect on the Photons

Skin

PSPT

PBS

Skin

FIGURE 10.7 Schematic diagram showing the lateral conformality of a photon beam (left), the lateral and distal conformality of a passively scattered proton beam (middle), and the lateral, distal, and proximal conformality of SFUD using pencil beam scanning (right). (Courtesy of Benjamin Clasie.)

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location-specific required range and modulation width will be taken into account for each individual ray beam, thereby sparing normal tissues proximal and distal to the target. The exact choice of range and modulation along any ray beam is, however, limited by the step size between rangeenergy layers. In other words, without the use of a RC, distal conformality will probably be slightly worse compared to PSPT. Proximal conformality will also not be perfect, even without range uncertainties, but both effects are expected to be clinically insignificant, especially in a multiple-field treatment plan. Another advantage of pencil beam scanning may be the possibility to allow for improved dose homogeneity along patch lines under range uncertainties by intentionally softening both the lateral penumbra of the through field and the distal penumbra of the patch field. Just as a wedged field combination in photon therapy is not considered intensity-modulated radiotherapy (IMRT), use of this patch-line smoothing should be considered SFUD instead of IMPT. At the time of this writing it is unsure if commercially available TPSs have the capability to automatically design such smoothed patch combinations. The main practical benefit of pencil beam scanning is that design and fabrication of field-specific RCs and apertures is no longer necessary or at least substantially reduced. This improves the workflow considerably and reduces the time between treatment plan completion and the first treatment. For example, rather than a laborious manual tweaking of a RC, the dose distribution for a field can be automatically optimized (Chapter 15). Adaptive treatment planning in proton therapy using apertures and RCs (i.e., PSPT), is very resource intensive both in manpower and materials. The improved workflow of pencil beam scanning allows faster treatment adaptation to a changing patient geometry over the course of radiotherapy treatment. Treatment adaptation in proton therapy is not as widely applied as in photon therapy, but the increased availability of pencil beam scanning may close this gap. Two possible downsides of pencil beam scanning over PSPT are interplay effects (discussed in Chapter 14) and the achievable lateral penumbra, especially for shallow ranges (see Chapter 4).

10.6  Specialized Treatments This section discusses three proton therapy treatments that are a bit less mainstream: eye treatments, proton stereotactic radiosurgery (proton-SRS), and proton stereotactic body radiotherapy (proton-SBRT). In this chapter, SRS denotes a high-precision single-fraction (or occasionally double-fraction) treatment of a target within the patient’s skull. SBRT is used to describe a

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high-precision treatment of a target lesion within the patient’s body over at most a handful of treatment fractions. 10.6.1  Eye Treatments With a local control rate of well over 95% after 5 years of follow-up (e.g., [11]), treatment of ocular tumors is one of the success stories of proton radiotherapy. Depending on the tumor type, a typical prescription is five fractions of either 10 or 14 Gy each, delivered in five consecutive treatment days. The main OAR are the lens, the macula, and the optic nerve. Treatment planning is typically based on a recreated geometry rather than on CT-imaging information (Figure 10.8). Briefly, a model of the eye and tumor is created in the TPS based on ultrasound measurements and orthogonal x-rays. The ultrasound provides information regarding the axial length of the eye, lens thickness, and the thickness (“height”) of the tumor. The base of the tumor is reconstructed based on the location of four or more tantalum clips, visible on x-rays, that are sutured near the edge of the tumor during a surgical procedure. These clips also help guide patient setup at the moment of treatment. For a detailed description of the target-localization procedure for treatment planning and treatment delivery, see Delaney and Kooy or Albert et al. (2, 12). The model in the TPS accurately reproduces the location of the OAR for the gaze direction that is preferred for treatment. Apertures are used to tightly Disp. Width: +29.7 mm Center: (+3.1, +9.1)

Disp. Width: +36.8 mm Center: (-2.2, +6.7)

Dose % 100 90 70 50 30 10

2 2

3 1 mm

a)

1

1 mm

Scale: 5.389 : 1

3

14

Scale: 4.345 : 1

b)

FIGURE 10.8 (See color insert.) Model of the eye as created within EYEPLAN (version 3.05, Martin Sheen, Clatterbridge Centre for Oncology, Bebington, UK). (a) Beam’s eye view. The thick magenta line indicates the aperture outline. Also indicated are the optic nerve (yellow cone), the lens (green and blue circles), the optic axis (blue line), the macula (magenta cross), and some of the clips (thin magenta ellipses, labeled 1–4). (b) Dose distribution in the vertical beam plane in a slice through the center of the tumor.

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conform the dose distribution to the tumor in the lateral direction. If patient setup is based on orthogonal x-rays of the tantalum clips, the aperture margin is typically 3 mm. Half of this distance (1.5 mm) is to account for the lateral dose gradient between field edge and 90% isodose level. The other 1.5 mm is to take into account target delineation and setup uncertainties. If patient setup is based on the beam-line light field rather than orthogonal x-rays, the aperture margin is increased by 0.5 to 1.0 mm because of the additional setup uncertainty. The aperture outline can be locally adjusted to spare OAR. With few exceptions, a typical aperture has an area of less than a few square centimeters. The use of RCs in ocular proton therapy is uncommon. Range and modulation width are chosen to ensure target coverage in the depth direction. Range uncertainties vary between 2.5 and 4.0 mm for anterior to posterior tumors, respectively. An extra millimeter of range may be added if the location of the tumor brings the proton beam in close proximity to the eyelid. The proximal margin is 3.0 mm unless the target extends all the way toward the surface of the eye. Every millimeter of functioning retina can mean an improvement in the quality of life of the patient. Ocular proton beam lines therefore are optimized to have a very sharp lateral falloff to allow maximum sparing of the OAR. The beam-line layout of the worldwide available ocular treatment beam lines varies greatly. Depending on the dosimetric characteristics of the beam line, there may be a large effect of aperture shape and size on the output (in cGy/MU) (13). However, in general the ocular TPS is not able to predict this output, and fields need to be individually calibrated to determine the required MUs to deliver the prescribed dose. 10.6.2  Proton-SRS In proton-SRS a very high dose, typically 10–20 Gy, is delivered in only a single fraction (sporadically: two fractions) to a small tumor. The healthy tissues tolerate the high-fraction dose because of the small irradiated volume. Compared to photon therapy, the characteristic depth–dose distribution of protons can certainly benefit the sparing of healthy tissues (14). The main difficulty with proton-SRS treatments is that there is no mitigation of setup and range uncertainties by averaging out of the dosimetric consequences over multiple fractions. All dose is delivered in a single fraction, which means that any setup error and range uncertainties have a maximum negative impact. To ensure target coverage, one would like to apply wide safety margins. The necessity to limit the dose to, and the volume of, irradiated healthy tissues, however, implies a strong need for applying small distal, proximal, and lateral safety margins. SFUD treatment planning for proton-SRS to a large extent is the same as for normally fractionated treatments, except that there is even more emphasis on high-accuracy treatment delivery. Extra measures are taken in patient immobilization (bite-block or invasive stereotactic frame), target and OAR

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delineation by means of additional imaging (e.g., high-resolution MRI or CT angiography), and patient position verification (use of fiducial markers) (2, 6). Typically the dose is prescribed to the 90% isodose level relative to the dose in the center of the target. This ensures a steep dose falloff (lateral, distal, and proximal) at the cost of increased target dose inhomogeneity. It also makes the minimum dose within the target insensitive to the few-percent dose variations that can be present in the depth direction of the SOBP. The altered prescription isodose level only slightly affects the choice of range, modulation width, and target-to-aperture margin, when compared to standard fractionation in which the aim typically is to ensure coverage of the target with the 95% or even 98% isodose level. For same-day treatments (CT scanning, treatment planning, and treatment) one may have insufficient time to create patient-specific hardware, and therefore one may have to choose to use standard aperture shapes and no RC. The increased convenience for the patient then has to be balanced against the increased dose to healthy tissues and risk of complications. Compared to normal fractionation schedules, it is even more important to choose beam directions that minimize density variations (e.g., avoiding sinuses), especially if the CT scan and patient treatment are not on the same day. It is also important to minimize the dose delivered by beam directions that are challenging for accurate dose calculation (e.g., bony anatomy mixed with air-filled cavities such as the auditory canal). Even in the absence of much tissue inhomogeneity, the dose algorithm has to accurately represent the dose distribution for a single beam, which is challenging for very small fields (see Chapter 13). Standardized beam arrangements can be used for standard indications such as the treatment of pituitary tumors. The number of treatment fields for a lesion can vary between 2 and 6, with more beams allowing more spreading out of the dose to the healthy tissues and also providing some dose-­averaging effect in case one beam inadvertently underdoses the target. The small target sizes make patching (see section “The Tools of Treatment Planning”) an unnecessary technique. If it were beneficial in a rare case to spare an OAR, dose uncertainty on the patch line in combination with the very high fraction dose contraindicates its use. Designing a treatment plan for a patient with multiple spatially separated intracranial lesions is an especially complicated process, as any overlap between treatment fields for different targets will double the dose to local healthy tissue. The fact that proton beams have no exit dose helps in preventing such beam overlap. It is possible to perform proton-SRS treatments with (SFUD using) pencil beam scanning as long as the achievable lateral penumbra is sharp enough to provide sufficient sparing of healthy tissues lateral to each field. Especially for small targets the distance between spot positions also has to be small enough to allow tight lateral, proximal, and distal coverage. For more information on proton-SRS, see Delaney and Kooy or Chin and Regine (2, 15).

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10.6.3  Proton-SBRT Typical treatment sites for proton-SBRT are pancreas, liver, and lung. Just as with proton-SRS treatments, proton-SBRT treatments are characterized by a high dose per fraction. The number of treatment fractions, however, is increased and can vary between three fractions of about 20 Gy and 15 fractions of about 5 Gy. Compared with a single-fraction radiosurgery treatment, the use of multiple fractions will result in some averaging out of the dosimetric consequences of setup errors and range uncertainties. There are, however, a number of additional uncertainties that indicate a need for increased safety margins (also Chapters 13 and 14). Setup accuracy in general is compromised, which indicates a need for increased safety margins. It is harder to align the target laterally with respect to the beam because the target itself may not be visible by means of in-room imaging modalities, and it may move with respect to the more clearly visible bony anatomy. The movability of surrounding organs and the target due to, for example, breathing, heartbeat, and filling of the gastrointestinal tract, can result in large intra- and interfractional range variations. This aside from the “automatic” increase in range uncertainty due to the increased ranges that will be needed to treat these deep-seated targets. Because the number of treatment fractions is still quite limited, it is important for the data used for treatment planning (CT scan) to closely represent the patient density distribution at the time of treatment. For this, one should minimize the time between planning CT scan acquisition and the first day of treatment, as well as to minimize the time of the overall treatment course. One can also acquire more than one CT scan on different days before treatment to ensure overall reproducibility of the patient geometry, for example, the level of the patient’s breathing.

10.7  Patient Treatment-Planning Examples Proton radiotherapy nowadays is applied to treat almost any tumor site. This section will, however, be limited to two examples for passively scattered proton therapy only. The section “SFUD with Pencil Beam Scanning” provides details as to how these plans would be different if pencil beam scanning were applied. The C-spine tumor example highlights treatment planning in a geometry without (much) density variation but which requires patching. The lung cancer example highlights the difficulties of proton therapy planning in a time-varying density geometry. 10.7.1  C-Spine Tumor The patient shown in Figure 10.9a has a tumor within the neck region, wrapped around the spinal cord and the inferior aspect of the brainstem. The

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Dose (cGy * RBE) FIGURE 10.9 (See color insert.) Treatment planning of a C-spine tumor for a prescribed dose of of 50 Gy (5000 cGy). (a) Single slice indicating the target (red) and spinal cord (blue). (b) Multiple patch lines (yellow) for multiple patch combinations. (c) Absolute dose delivered by a left- and a rightlateral field. Beam directions are indicated by white arrows. (d) Dose distribution of the first patch combination. (e) Dose distribution of the second patch combination. (f) Dose distribution of the third patch combination, when using the right-lateral through field. (g) Cumulative dose distribution taking into account all treatment fields. (h) Dose-volume histogram of the CTV, spinal cord, and brainstem. The vertical dashed lines indicate 95% and 107% of the prescription dose. The solid red areas indicate underdosing and overdosing of the CTV.

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challenge for this particular patient and radiotherapy treatment course was to deliver the prescribed dose of 50 Gy to the target in 25 fractions of 2 Gy, while limiting the maximum dose in the spinal cord and brainstem to 30 Gy. This example highlights two other aspects that are especially of concern for proton therapy and that are related to range uncertainties (Chapter 13). Dental fillings resulted in artifacts in the CT. The density around the filling was, however, not overridden because the preferred beam directions for this treatment are lateral to posterior. The large density variations in the mouth (high-density teeth, air cavities, and tongue repositioning accuracy) as well as the sensitivity of the oral mucosa to radiation contraindicate use of anterior beam directions. Titanium screws and other hardware are present near the posterior border of the target. Care was taken to ensure that the observed electron density of this hardware was converted into the correct relative proton stopping power. Beam directions for this patient were chosen to minimize the extent of titanium hardware within the BEV, while allowing a proper choice of beam angles for the multiple patch combinations. The choice of which beam angles to use for what part of the treatment is driven by the need for multiple patch combinations. Limiting the use of each patch combination to 3–5 fractions, at least two patch combinations are needed to deliver the final 20 Gy on top of 30 Gy with conformal fields. Use of only two patch combinations would, however, allow no more dose to be delivered to the spinal cord with any of the patch fields. This then requires each of these fields to have a substantial margin between the aperture edge and the spinal cord, thereby compromising target coverage near the spinal cord. Rather, the choice is to have the conformal fields deliver a reduced dose of, in this case, only 22 Gy, permitting the patch fields to have tighter margins to the spinal cord. This allows treatment of almost the entire target to the prescribed dose, at the cost of finding a third patch combination. The three patch lines are indicated in Figure 10.9b, and the treatment planner has this in mind when designing the conformal fields and subsequent patch combinations. In other words, the entire treatment is mapped out before the first beam is designed within the TPS. Treatment planning was started with a right lateral field and a left lateral field delivering a homogeneous target dose of 22 Gy(RBE) (relative biological effectiveness). As indicated in Figure 10.9c, these fields did not attempt to spare the spinal cord, and this OAR gets 100% of the dose delivered with these fields. As the subsequent patch fields have intended right-posterior and left-posterior beam directions, the conformal fields were chosen to be right- and left-lateral in order to spread out the dose to the healthy tissues. Figure 10.8, d and e, show the first two patch combinations, each delivering 10 Gy(RBE) to the target and using lateral-oblique fields. The isodose lines show some underdosage and overdosage along the patch lines. The third patch combination uses two patch fields and alternating right-lateral and leftlateral through fields to deliver 8 Gy(RBE) to the target. Figure 10.9f shows the patch combination using the right-lateral through field. The cumulative dose

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distribution for the entire treatment plan is shown in Figure 10.9g. The corresponding dose-volume histograms of the target, spinal cord, and brainstem are shown in Figure 10.9h. The vertical dotted lines indicate 95% and 107% of the prescribed dose, which are the ICRU tolerance levels for dose inhomogeneity (4, 5). Underdosage occurs in the region of the target closest to the OAR and is unavoidable because this OAR has to be spared. Overdosage occurs on the patch lines. Overdosage and underdosage is very limited, as indicated by the red-filled areas in Figure 10.9h, this despite the close proximity of the OAR to the target and a low dose-constraint for these OAR. 10.7.2  Lung Proton radiotherapy of a near unit-density tumor that is moving within low-density lung tissue is a major challenge. Variation in the density geometry can occur within the fraction, between fractions and over the whole course of the treatment. Details regarding these uncertainties are provided in Chapters 13 and 14; this section will be limited to describe a “forward” planning approach. “Forward” in this context means a treatment planning approach that mimics classical conformal photon treatment planning as much as possible (i.e., use of a single CT scan and manual individual beam design). A number of such approaches for forward planning have been discussed in the literature (16–19). Moyers et al. already pointed out the difference from classical treatment planning in which the aim is to ensure dose coverage of the CTV by conforming the prescribed dose to the PTV (16). In their approach, the PTV is only used for determining lateral (aperture) margins, whereas range, modulation, and RC smearing are chosen on a per-field basis to ensure target coverage under range uncertainties. Engelsman and Kooy use a two-step approach first choosing parameters of each individual beam to ensure tight dosimetric coverage of the CTV on the mid exhale representative CT scan (17). This is followed by the application of lateral, distal, and proximal margins on a per-field basis to ensure target coverage under setup errors and range uncertainties. Their simulations show that the magnitude of both the lateral aperture margin and distal smearing margin can be less than the sum of the expected maximal setup error and breathing amplitude. This approach works for the stylized phantom used in their study because the required range to cover the most distal target edge does not vary over the breathing cycle. For at least some patients underdosage of the target can occur if motion of the tumor relative to other densities in the patient requires an increase of range, something that the simple approach of smearing the RC can not provide. An improved approach is described by Engelsman, Rietzel, and Kooy (18), in which field-specific apertures and RCs are an aggregate of the required aperture and the RC for all phases (or at least the most important phases) of the four-dimensional (4D) CT scan. This approach is, however, labor

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intensive and requires automation before it can be routinely applied. Even then it would guarantee tumor coverage over all phases of the planning 4D CT scan, but not necessarily under variations in patient geometry with respect to this planning 4D CT scan. Kang et al. (19) describe an internal target volume (ITV) approach (5) with density override of the iGTV (internal GTV) to ensure target coverage in every phase of the breathing cycle. As they define the iGTV to be the envelope of all GTVs over the breathing cycle, target delineation requires a 4D CT scan. Treatment planning uses only a single CT scan: the density-averaged CT scan. Individual beams can, but do not have to, be designed using the previously mentioned two-step approach. The density override simulates the tumor to be at all possible locations at once and more than ensures target coverage over all phases of the 4D CT scan. It also provides a “buffer” for density variations over the course of the treatment, such as tumor growth or a moderate change in breathing motion. During any treatment delivery, however, the tumor will be only in one location at a time and the “loss” of density will result in an increased dose to normal tissues distal to the target compared to what is displayed at the time of treatment planning. In general, and especially for lung tumors, the price of ensuring target coverage, for example, under density variations, range uncertainties, and setup errors, is an increased dose to surrounding normal tissues. Even the most conservative of the lung tumor treatment-planning approaches described (19) does not guarantee target coverage for all patients and all possible density variations with respect to the treatment-planning CT. The aim is therefore to use more than two beam directions such that target regions that may be underdosed by a single beam receive full dose from at least two other beam directions, thus mitigating the possible negative clinical consequences. Figure 10.10 shows an example of a lung tumor treatment plan, according to the treatment planning protocol as described in Engelsman and Kooy (17). The fractionation is 70 Gy in 35 fractions of 2 Gy each. Treatment planning is performed on the mid-exhale CT scan, and beams are designed in two steps. In step 1 the high-dose region of each beam separately is conformed tightly to the target. Step 2 takes range uncertainties, setup uncertainties, and breathing motion into account by increasing the range, modulation, and smearing distance and by expanding the apertures. The treatment plan avoids beam directions that are parallel to density gradients. This serves two purposes. First, it minimizes overshoot due to smearing (see section “Distal and Proximal Safety Margins”), and second, it reduces the probability of target underdosage should the breathing motion vary from treatment planning CT to fractions of treatment delivery. Figure 10.10, a–c, shows the dose distribution for each of three individual beam directions after step 1. The overshoot of a few millimeters is deemed acceptable on a multifield treatment plan, and tweaking this is very time consuming because our TPS does not allow automatic dosimetric optimization of the RC. The overshoot is also a consequence of the need to cover the target in more superior or inferior

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CT slices. The modulation width appears too large for the same reason. The undershoot is only about 5 mm water equivalent but appears especially large because it is in low-density lung tissue. Figure 10.10d shows the cumulative dose distributions for all beams combined, with each field having an equal weight. Figure 10.10, e–h, shows similar dose distributions, but after step 2. It is obvious that for any single beam the high-dose region (95% isodose level) does not conform to a geometric expansion of the target. This means that, for proton therapy planning in nonuniform geometries, a PTV-based approach has limited merit. The cumulative dose distribution for step 2 is shown in Figure 10.10h. A similar cumulative dose distribution could have been designed using a PTV-based planning approach. It is, however, very important to keep in mind that such an approach would not result in the beam-specific dose distributions (Figure 10.10, e–g) that are necessary to guarantee target coverage under range uncertainties, setup errors, and target motion.

10.8  Future Perspectives of SFUD For most tumor sites SFUD treatment plan design is straightforward. SFUD proton therapy is a very powerful tool. It allows conformality of the prescribed isodose to the target nearing what is achievable with IMRT, while reducing the (integral) dose to surrounding normal tissues by up to a factor of three. It is, however, of vital importance that the detrimental effects of range uncertainties and patient density variations are adequately taken into account in the treatment planning process. The treatment planner, physician, and medical physicist have to be continuously aware that the finite range of protons is not only a blessing but also a risk. For many patients IMPT may be able to make only modest improvements to the treatment plans as the application of SFUD proton therapy already allows high conformality of the high-dose region to the target. SFUD proton therapy is likely to continue to be applied for many patients, or at least for a substantial fraction of the prescribed dose to many patients. Full-scale clinical use of IMPT (Chapter 11) may have to wait until the proton therapy community has minimized range uncertainties or is able to take the remaining uncertainties effectively into account by means of, for example, robust optimization.

References

1. Meyer JL. IMRT, IGRT, SBRT: advances in the treatment planning and delivery of radiotherapy. Basel, Switzerland: S. Karger AG; 2007. 2. Delaney TF, Kooy HM. Proton and charged particle radiotherapy. Philadelphia (PA): Lippincott, Williams & Wilkins; 2008.

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3. Goitein M. Radiation oncology: a physicist’s-eye view. New York (NY): Springer; 2008. 4. ICRU Report 50: Prescribing, recording and reporting photon beam therapy. International Commission on Radiation Units and Measurements, 1993. 5. ICRU Report 62: Prescribing, recording and reporting photon beam therapy. International Commission on Radiation Units and Measurements, 1999. 6. ICRU Report 78: Prescribing, recording, and reporting proton beam therapy. International Commission on Radiation Units and Measurements, 2007. 7. van Herk M, Remeijer P, Rasch C, Lebesque JV. The probability of correct target dosage: dose-population histograms for deriving treatment margins in radiotherapy. Int J Radiat Oncol Biol Phys. 2000 Jul 1;47(4):1121–35. 8. Urie M, Goitein M, Wagner M. Compensating for heterogeneities in proton radiation therapy. Phys Med Biol. 1984 May;29(5):553–66. 9. Li Y, Zhang X, Dong L, Mohan R. A novel patch-field design using an optimized grid filter for passively scattered proton beams. Phys Med Biol. 2007;52(12):N265–75. 10. Engelsman M, Delaney TF, Hong TS. Proton radiotherapy: the biological effect of treating alternating subsets of fields for different treatment fractions. Int J Radiat Oncol Biol Phys. 2011 Feb 1;79(2)616–22. 11. Egger E, Schalenbourg A, Zografos L, Bercher L, Boehringer T, Chamot L, et al. Maximizing local tumor control and survival after proton beam radiotherapy of uveal melanoma. Int J Radiat Oncol Biol Phys. 2001 Sep 1;51(1):138–47. 12. Albert D, Miller J, Azar D, Blodi B. Albert & Jakobiec’s principles & practice of ophthalmology. 3rd ed. Orlando (FL): Saunders Elsevier; 2008. 13. Daartz J, Engelsman M, Paganetti H, Bussière MR. Field size dependence of the output factor in passively scattered proton therapy: influence of range, modulation, air gap, and machine settings. Med Phys. 2009 Jul;36(7):3205–10. 14. Bolsi A, Fogliata A, Cozzi L. Radiotherapy of small intracranial tumours with different advanced techniques using photon and proton beams: a treatment planning study. Radiother Oncol. 2003 Jul;68(1):1–14. 15. Chin LS, Regine WF. Principles and practice of stereotactic radiosurgery. New York (NY): Springer Science+Business Media; 2008. 16. Moyers MF, Miller DW, Bush DA, Slater JD. Methodologies and tools for proton beam design for lung tumors. Int J Radiat Oncol Biol Phys. 2001 Apr 1;49(5):1429–38. 17. Engelsman M, Kooy HM. Target volume dose considerations in proton beam treatment planning for lung tumors. Med Phys. 2005 Dec;32(12):3549–57. 18. Engelsman M, Rietzel E, Kooy HM. Four-dimensional proton treatment planning for lung tumors. Int J Radiat Oncol Biol Phys. 2006 Apr 1;64(5):1589–95. 19. Kang Y, Zhang X, Chang JY, Wang H, Wei X, Liao Z, et al. 4D proton treatment planning strategy for mobile lung tumors. Int J Radiat Oncol Biol Phys. 2007 Mar 1;67(3):906–14.

11 Physics of Treatment Planning Using Scanned Beams Antony Lomax CONTENTS 11.1 Introduction................................................................................................. 336 11.2 Basic Principles............................................................................................ 336 11.2.1 The Power of Modulation.............................................................. 336 11.2.2 There Is No Spread-Out Bragg Peak............................................ 337 11.2.3 There Are No Collimators and Compensators........................... 339 11.2.4 Field Design and the Need for Optimization............................. 339 11.2.5 Dose Calculations for Scanning and IMPT................................342 11.2.6 The Impact of Secondary Particles...............................................344 11.2.7 The Problem of Superficial Bragg Peaks...................................... 347 11.3 SFUD or IMPT............................................................................................. 349 11.3.1 SFUD Planning............................................................................... 349 11.3.2 Intensity Modulated Proton Therapy (IMPT) Planning........... 351 11.3.3 Normalizing IMPT Plans.............................................................. 352 11.4 Optimization Strategies for IMPT............................................................ 353 11.4.1 Degeneracy in IMPT Optimization.............................................. 353 11.4.2 When Less Is More: Field Numbers in IMPT Planning............ 355 11.4.3 Bragg Peak Numbers, Beam Sizes, and Bragg Peak Placement......................................................................................... 356 11.4.4 The Importance of Starting Conditions in IMPT Optimization................................................................................... 360 11.5 Dealing with Uncertainties.......................................................................364 11.5.1 Magritte’s Apple.............................................................................. 364 11.5.2 Sources of Delivery Uncertainties................................................ 364 11.5.3 To PTV or Not to PTV? That Is the Question.............................. 365 11.5.4 Robust Optimization...................................................................... 368 11.5.5 Tools for Evaluating Plan Robustness.......................................... 369 11.6 Case Studies................................................................................................. 372 11.6.1 Case 1: Nasopharynx Carcinoma................................................. 372 11.6.2 Case 2: Sacral Chordoma............................................................... 373 11.7 Summary...................................................................................................... 375 References.............................................................................................................. 376 335

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11.1  Introduction It is becoming increasingly clear that the most flexible method of delivering proton therapy (or particle therapy generally) is by the use of active scanning. In this approach, narrow pencil beams of the selected particles are scanned across the target volume in three dimensions, using deflector magnets in the directions orthogonal to the beam direction, and some form of energy modulation for positioning of the Bragg peak in depth. In its most flexible form, such delivery systems are capable of complete control of the dose delivered by each such pencil beam, resulting in a true fluence modulation in three dimensions from each individual incident field direction; see for example, Webb and Lomax (1). This is truly the particle therapy equivalent of intensity-modulated radiotherapy (IMRT) with photons, and brings similar (if somewhat more) advantages and potential disadvantages. In this chapter, we will look into both the physics and methods of treatment planning for scanned particle beams, starting with the similarities to conventional IMRT and the main dissimilarities to passive scattering proton therapy. In addition, we will look at different modes of optimizing scanned proton therapy treatments and look into how possible delivery uncertainties can be dealt with. Finally, case studies will be presented to indicate the potential power of these techniques.

11.2  Basic Principles 11.2.1  The Power of Modulation The introduction of intensity-modulated methods into conventional radiotherapy with photons can truly be described as a revolution. Although the more advanced (and computer aided) three-dimensional (3D) planning techniques developed in the 1980s were capable of producing extremely complex and conformal treatments, it was the introduction of optimization algorithms, together with the development of hardware for the delivery of more or less arbitrary fluence profiles, that really opened up the world of highly conformal radiotherapy to clinics large and small. The secret of IMRT’s success lies in its ability to fully exploit a degree of freedom that had hitherto only been manipulated in a rather limited way. This degree of freedom is the manipulation of the cross-field fluence profile of the delivered field. Cross-field fluence had, of course, been modulated for many years in conventional planning, through the use of collimators (essentially a binary fluence modulation of the delivered field) and by the use of wedges, either fixed or dynamic. Indeed, somewhat more sophisticated fluence modulation could (and was) achieved using compensators to compensate for missing tissues.

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However, all these methods were limited in their extent. Nevertheless, they indicated the power of fluence modulation, and it was only a matter of time before a number of breakthroughs were made that could provide both the calculational techniques necessary for fully exploiting this approach and the hardware necessary to deliver it, which were the implementation of optimization techniques to radiotherapy (sometimes called inverse planning) and the development of computer-controlled, dynamic multileaf collimators, respectively. Although it is somewhat overstated to say that this combination turned radiotherapy from a predominantly palliative discipline to a predominantly curative therapy, there is no doubting that the introduction of IMRT helped transform radiotherapy into the precise and accurate therapy that we know today. Consequently, intensity modulation has been shown to be an extremely powerful tool for conforming radiation to the target volume. Imagine what could be achieved if not just the cross-field fluence could be modulated, but also the depth–dose curve of the radiation as well? This is what essentially can be achieved with active scanned proton (particle) therapy. 11.2.2  There Is No Spread-Out Bragg Peak Conventional (passive scattering) proton therapy is based very much on the concept of the spread-out Bragg peak (SOBP) (see Chapter 10). This is the basic deliverable depth–dose element, produced by either a continuously rotating range modulator wheel or a ridge filter (see, e.g., Koehler et al. [2]). As described in more detail in Chapter 5, the SOBP is constructed generally before the beam has been spread laterally and before the laterally scattered beam is subsequently shaped using collimators and compensators. This is an important limitation of this technique. As the SOBP is constructed on the narrow, unbroadened beam, the width of the SOBP along the beam direction is invariable across the field. Put another way, although the length of the SOBP (and in principle its shape) can be varied from field to field, within a single field, the SOBP depth–dose curve is constant across the field. The consequence of this is shown in Figure 11.1, which shows a single slice of a large Ewing’s sarcoma and the calculated dose distribution from a single, passively scattered proton field incident from the posterior aspect. Although this field direction may not be optimal for this particular case, it has been chosen deliberately in order to show the limitations of the SOBP technique. Indicated in the figure is the “length” of the SOBP that must be produced in order to fully cover the target volume. For this case, the SOBP must be about the same length as the thickest portion of the target volume along the beam direction, as indicated by the solid white line in the figure, in this case about 10 cm. However, the target thickness varies extensively across the target and in this slice is considerably narrower in the portion directly posterior to the femoral head. Thus, the same SOBP delivered here will be far too wide (as shown by the broken line), with the consequence that the whole

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Dose % 104 90 80 70 60 50 40 30 0 FIGURE 11.1 (See color insert.) The dose distribution for a single, passively scattered proton beam (indicated by the green arrow) incident from the anterior aspect of a large and complex Ewing’s carcinoma. The white double-headed arrows show the minimum SOBP length necessary to cover the whole target, and how, due to the irregularity of the distal edge of the target, such fixed SOBPs can extend well into the normal tissue areas even when the target is quite deep seated.

femoral head, although proximal to the target volume, will receive the full dose. In addition, at the lateral border of the target, as the distal edge comes closer to the surface and the thickness of the target narrows, the SOBP dose can extend well beyond the proximal border of the target to the surface of the patient. Once again, it should be pointed out that this is an extremely poor field direction for treating such a target, but it nicely illustrates the problem of passive scattering delivery and the use of a field-invariant SOBP depthdose curve. Indeed, due to this limitation, passive scattering can be directly compared to the delivery of open fields with photons. The depth–dose curve is invariant (a fixed extent SOBP in the proton case), and the fluence of particles across the field is also uniform. Therefore, proton therapy using passive scattering is essentially the direct equivalent of open-field therapy with photons. However, this chapter is about beam scanning, so why all the discussion about passive scattering and SOBPs? Because one of the most important differences between beam scanning and passive scattering, particularly when we get to intensity-modulated proton therapy (IMPT), is that the effective depth–dose curve for the proton field can vary across the field. During the delivery, the treatment planning (and the delivery machine) has complete control over the fluence delivered by each Bragg peak delivered to the patient, with the consequence that, in the most general case, Bragg peaks can be distributed in three dimensions throughout the target volume (see Section 11.2.4). Thus, the effective depth–dose curve (that resulting from the superposition of all energy/range-shifted Bragg peaks along one pencil

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beam direction) can also be varied. In other words, and as we will see in more detail later, there is no SOBP in pencil beam scanning. 11.2.3  There Are No Collimators and Compensators Now let’s look at differences between scanning and passive scattering when conforming the dose to the target volume. Again, there are two major differences: how the dose is conformed to the distal edge of the target and how lateral dose conformation is achieved. As described elsewhere, for passive scattering, such conformation is achieved through the use of field-specific compensators (for distal edge conformation) and field-specific collimators/ apertures (for lateral dose conformation). With pencil beam scanning, these devices are no longer necessary. Because the Bragg peaks lateral to the beam direction can be freely chosen (and delivered) at the treatment-planning stage, then it is a feature of the planning process to identify those Bragg peaks that intersect with the target volume and to deliver only these. As we will see below, this preselection process as part of the treatment planning effectively acts as a 3D aperture, simultaneously cutting out Bragg peaks that are outside the volume laterally as well as distally and, crucially, proximally as well. Thus, for pencil beam scanning, there is no need for collimators and compensators. However, in order not to propagate a misunderstanding around this point, this is not the same as saying that collimators and compensators cannot be used. Of course, as long as the delivery nozzle supports the mounting of such devices, there is actually no reason why collimators/compensators cannot be used as well with scanning, and particularly for the treatment of superficial tumors these devices can provide a valuable method for sharpening the lateral penumbra over and above that resulting from the pencil beam size itself. I will return to this issue in Section 11.2.7. 11.2.4  Field Design and the Need for Optimization So let’s now look in a little more detail into field design for pencil beam–­ scanning treatments. I do not mean here the selection of field angles. In this context, by field design I want to describe in more detail exactly the steps that are required for designing a single, scanned proton beam field, assuming that the field direction has already been defined. The description given here is mainly based on the process used for planning at the Paul Scherrer Institute (PSI), but the general principles will be the same for any scanning field. The main steps of the field-design process for scanned proton fields are shown in Figure 11.2. Once a field direction has been defined, the first step is to determine the possible set of all deliverable Bragg peaks within the patient. This set of Bragg peaks will clearly be dependent on the physical characteristics of the delivery machine. For instance, the resolution of the energy selection (i.e., is it continuous or discretized?), the maximum deliverable energy, the minimum deliverable energy, and the maximum extent

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FIGURE 11.2 (See color insert.) The main steps in the field-design process for a single SFUD (Single Field, Uniform Dose) field irradiating a meningioma (a). (b) All possible Bragg peaks that can be delivered from the selected field direction and with the field geometry parameters as described in the text. (c) The subset of Bragg peaks automatically selected for subsequent optimization based on their position in relation to the surface of the selected target volume. (d) The initial dose distribution resulting from the preselection process and initial set of Bragg peak fluences (starting conditions) shown by the colors in (c). (e) Bragg peak fluences after the optimization process, displayed using the same color scale as in (c). (f) The dose distribution resulting from the set of optimized Bragg peak fluences shown in (e).

of the field size, which will generally be defined by the scanning range of the deflector magnets used for scanning. For the case shown in Figure 11.2, these parameters are as follows. A maximum proton energy of 138 MeV was selected for the field, minimum energy is close to zero due to the fact that the energy is modulated at our facility by the insertion of range shifter plates into the beam directly before the patient (see, e.g., Pedroni et  al. [3]), and for an energy of 138 MeV, our delivery system has enough such plates to

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bring the Bragg peaks right to the surface of the patient. In addition, spacing between the Bragg peaks in depth is defined by the thickness of these plates, which are 4.6 mm water equivalent. Finally, orthogonal to the beam direction, each pencil beam can be deflected ±10 cm from the central axis and with a user-defined pencil beam separation. For the case shown in Figure 11.2, pencil beam spacing orthogonal to the beam direction was defined as 5 mm. Figure 11.2b therefore shows, for one slice of this patient, all the possible Bragg peaks that could be delivered using the parameters defined above. Each red cross is a possible Bragg peak position, now converted from water equivalent range to depth in the patient, which is obviously different due to the varying density of tissues within the patient. This transformation (from a uniform spacing of Bragg peaks in water equivalent space to an irregular spacing of Bragg peaks within the patient) can clearly be seen from the spacing of the Bragg peak in the air of the nasal cavities, as well the irregular shape of the maximum Bragg peak penetration distal to the target volume. To reiterate, the Bragg peaks range out on this side simply because the maximum energy selected for this field (138 MeV) has a maximum range in water of about 13 cm, and the irregular end-of-range line in the patient is therefore essentially the 138-MeV isodepth line. That this is irregular in shape is simply due to the different tissue densities within the patient. Step two in the field-design process should be relatively obvious. Clearly, we do not need to understand too much about physics or Bragg peaks to realize that if we want to only irradiate the outlined target, we do not need to deliver Bragg peaks (and therefore dose) in tissues a long way outside of the target, so we can easily preselect the Bragg peaks that we will need for delivery based on this distribution. Simply put, all Bragg peaks outside of the target can be removed (switched off), whereas all Bragg peaks within the target volume are retained. In fact, it is not quite that simple. As can be seen in Figure 11.2c, which shows the subset of selected Bragg peak positions that will be used subsequently in the field-design process, Bragg peaks a little distance outside the target have also been preserved. This is necessary because of the discrete spacing of the Bragg peaks. If only peaks within the target are selected and because the pencil beams are defined on a 5-mm grid, in the worst case, the most superficial Bragg peaks could be up to 5 mm inside the target volume, leading to potential problems of target coverage at the edge of the target. To avoid this, for the example shown in the figure, all Bragg peaks up to 5 mm outside have also been selected for the subsequent steps of the calculation. The reader will have noticed that in Figure 11.2c, the subset of selected Bragg peaks are now also color coded to represent the relative fluence of each Bragg peak. That is, we have assigned an initial set of relative weights to all Bragg peaks that will be used for input into the subsequent optimization process. The importance of this step will be considered in more detail in Section 11.4.4. Suffice it to say that these are what we call the initial starting conditions for the optimization. Figure 11.2d shows the dose distribution resulting from the set of weighted Bragg peaks shown in Figure 11.2c after the application of an

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analytical dose calculation (outlined below). What is immediately clear is that, based on the initial guess for the starting beam weights, the dose in the target is anything but homogenous. In the middle of the target there is generally too much dose, whereas at the edges, there is too little. This is mostly an effect of the irregular shape of the target, as well as the large size and substantial overlapping of neighboring pencil beams. That is, where there is overlapping of many different pencil beams (in the center of the target), there is sufficient (even too much) dose, whereas at the edges, where inevitably there are fewer overlapping pencil beams, the dose is too low. To improve dose homogeneity across the target then, an optimization procedure needs to be applied in order to find a set of Bragg peak beam weights that satisfies this condition. The result of this optimization process is shown finally in Figure 11.2e, with the resultant dose distribution in Figure 11.2f. What is interesting in Figure 11.2e is the quite different distribution of Bragg peak weights after optimization compared with the initial weights. Although the Bragg peaks at the distal end generally have higher weights, the internal Bragg peaks (those within the target volume) have very low weights (<5% of the maximum weight in the field indicated by the white crosses in the figure). Figure 11.2f, however, shows that the optimization was necessary and successful. The final dose distribution conforms quite well to the target contour at the 95% dose level (red area) and also provides a relatively homogenous dose across the whole target. It is also important to note that this is the result of the field design, as well as the optimization, for a single field only. Before moving on, some remarks need to be made about the Bragg peak preselection process. In principle, if the optimization algorithm is good enough, the preselection of Bragg peaks is not absolutely necessary. In this case, the optimization would automatically switch off the Bragg peaks outside the target volume, at least when a zero dose constraint is assigned to all surrounding normal tissues. However, this would inevitably slow down the optimization process as, for each iteration, the dose contribution from every pencil beam shown in Figure 11.2a will have to be calculated. In contrast, by using a preselection process, the number of Bragg peaks for which the calculation needs to be performed can be reduced substantially. By a similar argument, the dose calculation matrix can also be significantly reduced in size if we restrict this to the region of the target. In short, the preselection process described above is essentially an efficiency measure, using a priori knowledge of the Bragg peaks that will make a significant contribution to the target dose in order to make the subsequent optimization quicker. 11.2.5  Dose Calculations for Scanning and IMPT To get from Figure 11.2e to 11.2f, requires a dose calculation, the intricacies of which will be covered more in Chapter 12. I will therefore only very briefly review these from the point of view of pencil beam scanning.

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As with other forms of proton therapy, there are basically three classes of dose calculations that can be used for scanned proton therapy; ray casting, pencil beam (both analytical approaches), and Monte Carlo, which have been nicely reviewed and described by Schaffner, Pedroni, and Lomax (4). With the ray casting (as still used at our institute), the physical pencil beam incident on the patient is modeled as the smallest element in the dose calculation, with density heterogeneities being dealt with by a simple scaling of the water equivalent depth of each dose grid calculation point along the field direction (4). In contrast, for the pencil beam approach, the physical pencil beam is further subdivided into a number of smaller beam elements per physical pencil beam (typically 4–64, depending on the calculation accuracy required), with each beam element being weighted such that the resultant dose envelope approximates to the lateral spread of the physical beam in air. This concept is shown in Figure 11.3a. Such an approach has been described in detail by Soukup et  al. (5). An alternative to this approach was earlier described by Schaffner, Pedroni, and Lomax (4), where instead of modeling a single physical pencil beam, the total fluence from all applied pencil beams is first calculated and then modeled by the appropriately weighted set of beam elements (see Figure 11.3b). This approach has the advantage of speed in the calculation, because fewer beam elements need to be calculated over the whole field, whereas the first approach (Figure 11.3a) has obvious advantages during the optimization procedure, where the weights of the physical pencil beams (and therefore the total fluence) is changing iteration-by-iteration. In practice, most commercial treatment-planning systems for pencil beam scanning are essentially similar to that shown in Figure 11.3a. Finally, Monte Carlo techniques can also be used (6–8), whereby the physical pencil beams are each represented by many thousands of individual protons tracked through the patient a

b

FIGURE 11.3 Analytical calculations using the pencil beam model. (a) The decomposition of an individual Gaussian physical pencil beam into a subset of (Gaussian) beamlets for calculation, showing how a discrete set of such beamlets can be weighted in order to model the shape of the actual physical pencil beam. (b) The composition of a total fluence (sum of all individual physical pencil beams into a single composite fluence) and its decomposition into beamlets for the calculation. (After Schaffner et al., Phys Med Biol., 44, 27, 1999.)

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geometry, the number of protons per pencil beam then being proportional to the relative fluence (weight) of that pencil beam. As with other areas of radiotherapy, Monte Carlo calculations provide by far the most accurate results, but at considerable calculational expense. On the other hand, Monte Carlo calculations for scanned fields can, in principle, be considerably faster than for passive scattering, because the incident pencil beams can be more easily modeled without necessarily transporting particles through the treatment nozzle, and the lack of collimators and compensators means that the tracking process can start directly in the patient (see Chapter 9). 11.2.6  The Impact of Secondary Particles As described in Chapter 2, protons traversing a medium undergo a number of different processes: energy loss, scatter, and interactions with atomic nuclei (9, 10). In the latter process, about 1% of the incident protons are lost per centimeter of traversed matter through interactions with nuclei. These proton losses are not without consequence, however, and although the proton may be lost from the primary beam, a spectrum of secondary particles are produced (11). Although these include heavier and extremely low-range particles such as deuterium and tritium, secondary protons and neutrons are the most predominant. Let’s first consider the neutron contribution (see Chapter 18). This has been the subject of much controversy and discussion in the last few years. In an article published in 2006, Hall estimated the risk of secondary cancer induction as a result of radiotherapy using IMRT, passive scattered and active scanned protons (12). In that article he claimed that the neutron background resulting from passive scattering could be extremely high and if one takes into account the potential relative biological effectiveness (RBE) for neutrons, could potentially more than cancel out the significant reduced (primary) integral dose resulting from proton therapy. Although the article had a positive effect on highlighting the neutron contamination as a potentially important issue, subsequent work and more detailed analysis indicated that the problem is much smaller than initially estimated (13–18) . Nevertheless, Hall pointed out an important issue relative to active scanning: that in any case, the neutron contamination is considerably smaller than that for passive scattering. This is due to the fact that for scanning, the beam exiting the treatment nozzle can be very clean (there are very few beam-line elements that intersect with the beam close to the patient) and that no collimators are required, which are a primary source of neutron contamination for passive scattering (13). Indeed, a few years earlier, measurements made at our institute with scanned proton beams indicated that the neutron contamination lateral to the field direction was of the same order of magnitude (as in fact, somewhat lower than) the neutron contribution from a 15-MV photon field of similar size and dose (19). This is one of the major advantages of the scanning approach

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Perhaps more of an issue for active scanning, and in particular IMPT, is the secondary proton contribution. Although the fluence of secondary protons is only a few percent of the fluence of the primary beam, secondary protons have a much wider angular distribution, leading to a long, low dose tail to the lateral dose profile of the beam—the so-called halo effect. The effects of this halo on dosimetry and an analytical model for estimating its effect has previously been published by Pedroni et al. (20). If this effect is ignored in the dose calculation, it has been found that errors in absolute dose of up to 9–10% can be observed for small fields. This is due to the secondary protons essentially removing the dose from the primary field and into the tissues outside of the irradiated volume. Figure 11.4 shows this effect. In Figure 11.4, a and b, calculated profiles through a Single Field, Uniform Dose (SFUD) active scanned field (see Section 11.3.1) are shown, together with second profiles (shown as closed circles) showing the same field, but this time calculated taking into account the secondary proton halo. There is a clear (and systematic) reduction of about 2% in the dose level throughout the high-dose region and a small, but just visible, increase in dose in the tails of the profile. Figure 11.4, c and d, shows the same profiles, but this time with the full dose profile

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FIGURE 11.4 Effect of the secondary particle “halo” dose associated with scanned proton beams on the absolute dosimetry of homogenous fields. (a and b) Orthogonal dose profiles through a homogenous (SFUD) scanned proton field calculated using primary particle contributions only (solid line) and with the additional effect of the secondary halo dose (closed circles). The dose halo essentially removes dose from the primary field and adds dose to the tails of the profile. (c and d) The same profiles, but with the primary and halo dose profile (closed circles) globally increased by 2% such as to correct for the effect.

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(primary and halo dose) increased in dose globally by 2%. Although there is a slight rounding in the full dose profile in comparison to the primary dose profile, after a global increase in dose, a much improved agreement between the two is found. It is through this global scaling of absolute dose that such effects are currently dealt with at our clinic, although clearly, the best approach is to incorporate the halo effect into the dose calculation during the optimization process, an approach that is now being adopted by most proton treatment–planning manufacturers. Perhaps more significant, however, is the potential effect of this halo dose on IMPT (Intensity Modulated Proton Therapy, see Section 11.3.2) plans. Figure 11.5 shows lateral profiles through an example IMPT field. Again, Figure 11.5,

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FIGURE 11.5 Similar profiles as for Figure 11.4, but this time for a more complex, intensity-modulated proton therapy (IMPT) field. (a and b) Primary and primary+halo profiles before the dose correction. (c and d) After correction by 4% dose. Note the improved agreement in the dose peaks, but the subsequent “collection” of dose in the dose valleys due to the accumulation of halo doses in these areas. (e and f) Ionization-based measurements for two more profiles through the same field, this time showing the good agreement of measurement to the primary+halo model.

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a and b, shows the primary only profiles compared with the primary plus halo profiles. As with the SFUD example above, there is a clear and systematic underdosage throughout the profile for the primary and halo calculation, particularly in the sharp peaks of dose. Figure 11.5, c and d, then show the two profiles compared after the primary and halo dose has again been globally corrected as described above. An interesting effect can now be seen in the valleys of the dose profile. Although the corrected profile improves the correspondence between measurement and calculation in the high dose regions, the halo dose effectively collects in the valleys of the dose distribution, locally increasing the dose in these regions. As these valleys are often the result of the IMPT optimization attempting to reduce the dose into critical structures, it is important to understand this effect. In the worst case, if the halo dose is not taken into account at the optimization stage, the actual delivered dose in the low-dose valleys could be in reality a few percent higher than anticipated. Figure 11.5, e and f, shows the resulting ionization chamber measurements for both profiles, clearly showing that the effect estimated from the analytical halo model of Pedroni et al. (20) is quite accurate and reiterates the importance of the halo effect on scanned proton therapy dose distributions. 11.2.7  The Problem of Superficial Bragg Peaks Before leaving this section, one additional point needs to be made about field design (and delivery) for active scanned proton therapy: the problem of delivering superficial (low energy) Bragg peaks. This is a problem that occurs surprisingly often, is not trivial, and unfortunately is often overlooked. So what exactly is the problem? As should be clear to the reader by now, the depth of a Bragg peak in the patient is determined by the energy of the incident beam, so, if it is necessary to deliver Bragg peaks close to the surface of the patient, then proton beams of very low energy are required. Indeed, if Bragg peaks need to be delivered exactly at the surface of the patient, essentially a proton beam of close to zero energy is required. Here lies the problem. It is extremely difficult to produce low-energy proton beams from accelerators that are designed to operate at energies of 200 MeV or more. Even with synchrotrons (with which the energy can be changed pulse-to-pulse) it is difficult to extract beams with energies much less than 70–100 MeV. With cyclotrons it is even more difficult. Being fixed energy machines, the only way to reduce energy is to introduce material into the beam. This in turn causes the beam to diverge (due to multiple Coulomb scattering in the degrading material); consequently, to obtain a narrow beam after the degradation process, the beam needs to be collimated with an inevitable loss of beam fluence. This process can be horribly inefficient. As an example, at PSI, in order to degrade the 250-MeV beam produced by our super-conducting cyclotron down to 70 MeV for eye irradiations, 99.7% of the protons exiting the accelerator will be lost in this degradation process! The next question then is how often do we require such Bragg peaks? After all, when looking at the standard SOBP curve and the relative weights of the

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Bragg peaks required to produce such a curve, the low-range (and therefore low-energy) Bragg peaks have extremely low weights. Nevertheless, in many circumstances, low-range Bragg peaks can be very important. Figure 11.6a shows a slice through a large sacral chordoma, with the planning target volume (PTV) shown in yellow. Also shown are the Bragg peaks that can be delivered to this tumor from a single lateral beam, assuming a maximum energy of 177 MeV and a minimum energy of 70 MeV. As with Figure 11.2e, the colors of the crosses show the relative weights of each Bragg peak after optimization. There is a clear absence of Bragg peaks at the most proximal part of the tumor for all positions within about 3 cm of the patient surface. However, for this slice, this is not a great problem, because the tumor is thick enough along the field direction that there are at least 37 Bragg peaks stacked from the distal end; for the last few energy layers, the Bragg peaks will have extremely low weights (white crosses in the figure). a

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FIGURE 11.6 (See color insert.) An example of the importance of superficial Bragg peak positions. (a) An example slice through the PTV of a large chondrosarcoma in the pelvis region. The PTV is shown in green, and the colored crosses show the deliverable Bragg peaks if a minimum deliverable energy of about 70 MeV is assumed (3-cm range). Because of this minimum deliverable limit, there is a 3-cm strip of the PTV close to the patient surface where no Bragg peaks can be applied. (b) A second slice through the same PTV, 5 cm more superior. Here the PTV is extremely narrow and superficial, and with the minimum 3-cm range, this portion of the PTV cannot be sufficiently covered with Bragg peaks to ensure a homogenous coverage of the PTV at this level. (c and d) The resulting dose distributions at the two levels after optimization. Although the coverage at the first level is sufficient, there is a clear problem at the more superior level due to the lack of Bragg peaks in the proximal aspect of the PTV.

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Thus, the inability to deliver Bragg peaks closer to the patient surface will not be a problem at this level, because they are not required. Figure 11.6b is another slice through the same CT set and target volume, but about 5 cm more superior. Now the PTV has a completely different form, being rather narrow and very superficial. Again, the Bragg peaks for the same field are shown, assuming once again that the minimum energy that can be delivered is 70 MeV. Because of the very superficial position of the PTV at this level and the limit on the lowest energy of Bragg peaks that can be delivered, there is a significant problem in covering the target sufficiently. Indeed, by looking at the resulting dose distribution at this level (Figure 11.6d), it has not been possible to obtain a homogenous dose across the PTV because of the lack of superficial Bragg peaks. Consequently, it will be very difficult to treat such a target volume from the selected field direction without being able (in the same field) to deliver both high- and extremely low-energy beams of high fluences. For instance, taking Figure 11.6 as an example, in order to cover the PTV at all depths and all levels, it would be necessary to insert a preabsorber to deliver Bragg peaks to the last 3 cm of the target (e.g., for the portion of the field covering the target at the level shown in Figure 11.6b), but it would be unfortunate to always have the preabsorber in the beam for delivering the more deeply applied Bragg peaks (e.g., the majority at the level shown in Figure 11.6a), as it will inevitably degrade the lateral characteristics of the beam. Ideally then, from the delivery machine point of view, one wants a preabsorber that can be automatically inserted into the beam when low penetration Bragg peaks are required and a treatment-planning system that supports this feature. In addition, it would be of great advantage in such cases to be able to use field-specific collimators in combination with scanning in order to sharpen up the lateral penumbra after the inevitable degradation resulting from the preabsorber for the superficially applied pencil beams. At the time of writing, all these requirements are, sadly, lacking in most commercial scanning proton systems.

11.3 SFUD or IMPT 11.3.1  SFUD Planning In the previous section, the importance of optimization for active scanning was described, using the example of a single field. The result of this optimization process was a dose distribution in which the dose throughout the target volume was more or less homogenous (at least within ±10% of the prescription dose). Although it could be argued that one may want to have a somewhat more homogenous dose across the target for a compete plan, the result of the optimization process is nevertheless impressive and provides a result

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that is already close to a clinically acceptable dose distribution. Nevertheless, as with conventional photon treatment planning and passive scattered proton therapy, it is extremely rare that single-field plans are planned or delivered (the treatment of uveal melanomas and craniospinal axis irradiations being the exceptions). The reasons for this are twofold. First, additional fields can improve the overall dose homogeneity across the target volume and second, the robustness of the delivered plan can be improved. When one or more individually optimized and homogenous dose distributions are added together to make a composite plan, we call this a Single Field, Uniform Dose (SFUD) plan (21). An example of such a plan is shown in Figure 11.7, where the four individual field dose distributions are shown together with the combined dose of all these fields added together. As is clear from the individual fields, the dose across the target for each field is close to uniform, whereas the combination of all the fields improves both the dose homogeneity and dose conformation. The SFUD approach then, although involving an optimization and modulation of the fluence of each individual pencil beam of each field, ensures a smooth dose across the target from each field and can therefore be considered to be the scanning equivalent of treating with open fields in photon therapy, as well as passively scattered proton therapy. Indeed, although to the author’s knowledge nobody is pursuing this approach, there is no reason to believe that SFUD-type delivery with an active scanning system could not be combined with compensators and collimators in order to construct patched plans as performed routinely with passive scattering. As noted above, the use of scanning does not necessarily exclude the use of collimators and compensators, and the SFUD approach could provide a method by which, if desired, patched-field techniques could be delivered with an active scanning system.

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FIGURE 11.7 (See color insert.) A first-course SFUD (single-field uniform dose) plan to a large and complex skull-base chordoma, together with the individual field dose distributions making up the total plan (F1–F4). Note that for each field, the dose across the target volume is more or less homogenous.

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11.3.2  Intensity Modulated Proton Therapy (IMPT) Planning One reason perhaps that scanning and field patching are often thought to be mutually exclusive is because scanning provides the possibility to deliver IMPT. When one thinks about optimization in radiotherapy, one immediately thinks about IMRT. Although this name is somewhat unfortunate in many ways (1), it has become ubiquitous to describe the process of simultaneously optimizing the cross-field fluences of many, angularly separated photon fields, such as to conform the high dose to the defined target volume while additionally selectively sparing neighboring critical structures. The key to our discussions here is the phrase “simultaneously optimizing” the fluence from different fields. This is patently not what we are doing with SFUD planning where the optimization process was restricted to each field individually. However, there is no reason why the optimization process for active scanning cannot also be performed in a similar way to IMRT, that is, that the fluences of all proton pencil beams from multiple fields are optimized together in the same process. When the planning and optimization process is performed in this way, we term such treatments IMPT, simply because this is then the exact proton equivalent of IMRT with photons (21, 22). Also, as with IMRT, in IMPT planning the optimization can also be driven, not just by the requirement of delivering a therapeutically relevant dose across the tumor, but also such that selected critical structures are spared through the definition of dose constraints. An example of an IMPT plan, with its component individual field dose distributions is shown in Figure 11.8, which shows a complex (and large) skull base chordoma that is close to the brainstem, shown in red. For this plan, the optimization has been asked to cover the PTV as much as possible,

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FIGURE 11.8 (See color insert.) The second-course IMPT (intensity-modulated proton therapy) plan for the same case as in Figure 11.7. This time, IMPT has been used to cover the PTV as much as possible, while also setting a dose constraint on the brainstem, which partially overlaps with the PTV. The individual field dose distributions are also shown (F1–F4).

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while sparing the brainstem at about the 60–70% level. The difference from the corresponding SFUD plan shown in Figure 11.7 should be clear. Now, the individual field dose distributions are anything but homogenous; indeed, they are highly complex and irregular in form and individually are useless for ensuring a homogenous coverage of the target volume. However, when all these fields are combined into the final plan (shown in the center of the figure), the target is homogenously covered, while simultaneously sparing the brainstem. By carefully reviewing the individual field dose distributions, it is also possible to see how the optimization process has achieved this result. The proton pencil beams passing through the brainstem have been selectively reduced in weight for all fields, with the missing dose resulting from this process being compensated for by the other fields. This is of course the power of IMPT. As the optimization is performed simultaneously for all fields, then missing doses from one field can be easily compensated for by the other fields, a possibility that is missing in SFUD planning. However, the individual field distributions also show the potential problem of IMPT planning. The distributions are extremely irregular and complex, which can have consequences on the robustness of the plan, as we will discuss in more detail later. In this section I have deliberately made a clear distinction between SFUD and IMPT planning, and this is a distinction that we adhere to clinically at our institute. Where possible, SFUD planning is used for as many cases as possible, and IMPT plans are only used when the geometry of the case is so complex that SFUD planning becomes limited. Even in such cases, SFUD planning will be used for the first course of treatment, with an IMPT plan being used as a second or third course in order to “pull-off” the critical structures. However, there is no reason why SFUD- and IMPT-type fields could not be used in the same plan or treatment course. Although this is not something we have yet pursued (and to the author’s knowledge has not been investigated anywhere), one can imagine that a single plan could consists of one or two SFUD fields and one or two IMPT-type fields, in which the IMPT optimization takes into account the dose resulting from the SFUD field or fields. In particular, such an approach could be very interesting for simultaneous integrated boost (SIB)-type treatments, with the low dose per fraction part of the treatment delivered using SFUD and the higher dose-per-fraction boost portion being delivered using IMPTtype fields. 11.3.3  Normalizing IMPT Plans A few words need to be said about normalizing and prescribing the dose to SFUD and in particular, IMPT plans. For SFUD plans, although the dose for the full plan can be quite uniform across the target, it can nevertheless vary by at least ±5%, sometimes even more when using small numbers of fields or in anatomical areas with complex density heterogeneities (which

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can significantly distort the Bragg peak shape). Thus, normalizing/prescribing to a single point of such a plan could, in the worse case, lead to quite significant changes in the overall dose to the tumor. Given that complex IMPT plans (i.e., those in which many critical structures maybe spared through the use of constraints in the optimization process) can be even more inhomogeneous, the problem in this case can be even more severe. For this reason, we strongly recommend the recommendations of International Commission on Radiation Units and Measurements (ICRU) Report 78 (23) be followed, which states that such plans should be normalized to the median or mean dose to the prescribed target. This is certainly sufficient for SFUD plans, but there can still be a problem with IMPT plans, particularly when normalizing to the mean dose because IMPT is most often used in cases where there are neighboring, dose limiting structures. The selected target dose is often inevitably compromised in order to attain the constraint dose in the critical structures. A good example of this is shown in Figure 11.8. For this reason, at our institute, we normalize IMPT plans by calculating the mean (or median) dose to the defined target minus all overlapping critical structures. Indeed, given that there is always a finite dose gradient between the organs at risk (OAR) and the target, we actually define an expansion of 2–3 mm around each OAR for which a dose constraint has been defined and use this as the structure for which the dose is subtracted during the normalization process.

11.4  Optimization Strategies for IMPT 11.4.1  Degeneracy in IMPT Optimization It will be left to Chapter 15 to deal with optimization theory for proton treatment planning. Nevertheless, a chapter about treatment planning for scanning and IMPT cannot be complete without a discussion about the problem, and potential, of degeneracy in the optimization process. In basic terms, degeneracy simply means that there can be many, sometimes quite different solutions to the specific optimization problem being solved. In general terms, degeneracy will decrease as the number of goals and constraints defined in the optimization process increase. Thus, if the only goal of the optimization process is to achieve a uniform dose to the target volume, the problem will be highly degenerate, whereas if the problem is to achieve a sufficient target coverage while also sparing dose to multiple neighboring critical organs while also minimizing the total dose to all normal tissues, then clearly, the degree of degeneracy will rapidly decrease. Indeed, degeneracy has been recognized for many years in the optimization of IMRT plans (24–27). Given that for a typical active scanning field, many thousands of individual Bragg peaks are available to the optimization process, in most clinical situations,

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the optimization process for IMPT will generally be much more degenerate than the corresponding IMRT problem. The concept of degeneracy has led some investigators to propose alternative methods of planning, and delivering, IMPT-type treatments. For example, in Section 11.3.2, the process described for optimizing IMPT plans can be considered to be the most general approach, as it has the largest number of Bragg peaks available to the optimization process. Indeed, it has been previously categorized as 3D-IMPT by Lomax (22), in that the initial Bragg peaks available to the optimization routine are distributed throughout the target volume in three dimensions for each field. In the same publication, however, three alternative approaches to IMPT were also described, namely 2D, 2.5D, and distal edge tracking (DET). The 2D and 2.5D approaches are rather similar in concept and can be differentiated simply by the fact that the 2D approach (in which fixed extent SOBP pencil beams are modulated in the two dimensions orthogonal to the field direction) was mainly proposed as a possible method that could be implemented on existing passive scattering machines. On the other hand, 2.5D is a special case of the full 3D approach, with the difference being that the relative fluence of Bragg peaks along the field direction is predefined and is not varied as part of the optimization process. Thus, the 2.5D approach is also essentially a 2D modulation, with the main difference to the 2D approach being that for each pencil beam, mini-SOBPs are defined that match to the thickness of the target in that position (22). Although to the author’s knowledge no facility is using or planning to use the 2.5D approach, it should perhaps not be forgotten, as it could possibly have some advantages, lying as this technique does somewhere between SFUD and full 3D-IMPT in complexity. The last approach is DET, and next to 3D-IMPT it is the IMPT “flavor” that has attracted the most interest in the literature and even by some proton therapy manufacturers. This approach was first proposed by Deasy et al. (28), and the idea is quite simple. Instead of distributing Bragg peaks throughout the target volume from each direction, each field only delivers single Bragg peaks to the distal end of the selected target volume. Through the application of a number of such fields, the optimization algorithm then modulates the individual pencil beams (in two dimensions) such that a homogenous dose across the target can be achieved, even with a surprisingly small number of fields. Indeed, this is the nearest equivalent to IMRT with photons that is possible with protons. Although it has been suggested that the DET approach can be very sensitive to delivery uncertainties (29, 30), more recently the opposite has been shown for certain types of cases (31). In any case, DET has potentially a number of advantages in that of all the techniques, it uses the smallest number of Bragg peaks/pencil beams and, at least for centrally positioned tumors, it has been shown to minimize the delivered integral dose in comparison to the other IMPT approaches (28, 32).

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11.4.2  When Less Is More: Field Numbers in IMPT Planning A special consequence of the degeneracy of the IMPT optimization problem is its consequence on the selection of field arrangements and in particular the number of fields necessary to achieve a clinically acceptable solution. This has been studied by Stenecker et  al. (33) for a simple head and neck case. In this work, photon IMRT and IMPT plans were calculated using 3–9 equally spaced fields. In addition, for each field arrangement and delivery type, the dose constraints on both parotid glands were successively reduced for different plans, and the resultant mean dose to these structures then was plotted against the resulting dose inhomogeneity in the PTV. Such curves were produced for 5- and 9-field IMRT plans, and 3-, 5-, and 9-field IMPT arrangements. An example of such a plot for one case is shown in Figure 11.9. For IMRT, it is quite clear that, as the number of fields available to the optimizer increases, the quality of the plans improves. That is, the curve of parotid dose against PTV dose inhomogeneity moves toward the bottom left (indicating lower parotid dose and a lower dose heterogeneity in the PTV). However, it also clearly shows that there is always a “play-off” between parotid dose and PTV coverage. Even for the nine field plans, as parotid dose is reduced, dose heterogeneity in the PTV increases. For the IMPT plans, however, the results are quite different. To begin with, for all IMPT plans, the doses to the parotids are always substantially lower than the IMRT plans for the same (or better) dose homogeneity in the PTV. More interestingly, and also more relevant to the discussion here, there seems to be little advantage in moving from 3- to 5- or 9-field plans. Indeed, the curves relating parotid and PTV dose are more or less superimposed on one another, indicating that, at least from the point of view of parotid sparing, 3-field IMPT plans are just as effective as 9-field IMPT plans. As stated at the beginning of this section, this is also a result of the degeneracy factor available to 3D-IMPT plans and after a little thought should not come as a great surprise. After all, we know from SFUD planning that for not too complex cases, a single actively scanned field direction can be optimized such that it delivers a more-or-less homogenous dose to the target. Although the addition of more fields improves dose homogeneity and conformation, the gain factor is still only relatively small. The same is true for the IMPT plans represented in Figure 11.9. The problem for the optimizer in this case was not too complex (as homogenous a dose as possible across the PTV while sparing both parotid glands) and thus, as we add in fields, the problem becomes more and more degenerate. For the case shown, it appears that just three equally spaced proton field directions provide enough Bragg peaks to the optimizer to provide equally good results compared with those resulting from many more field directions. This is borne out in clinical practice at our institute. In the 14 years we have been treating patients using both SFUD- and IMPT-based proton treatments, we have not yet found it necessary to deliver any more than four fields per plan (34).

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Mean bilateral parotid dose FIGURE 11.9 (See color insert.) (a and b) Example IMPT (three-field) and IMRT (nine-field) plans to a simple head and neck case. (c) Plots of target dose homogeneity plotted against mean dose to both parotid glands for different IMRT and IMPT plans. Each point on the plot corresponds to one plan, consisting of different numbers of fields (indicated by the lines) and decreasing constraints on the parotid glands. With IMPT, similar (if not better) target dose homogeneity can be achieved for much lower doses to the parotids than for any of the IMRT plans, and little difference is observed between three-, five-, and nine-field IMPT plans.

11.4.3  Bragg Peak Numbers, Beam Sizes, and Bragg Peak Placement For completeness when talking about degeneracy, we should also mention that, in addition to the position and relative fluence of individual Bragg peaks, other parameters can potentially be modulated as part of the optimization process. Examples include the number of Bragg peaks, the size of the pencil beam, and the placement of Bragg peaks in relation to the target volume. These issues will be briefly reviewed here. Given that, at least for not too complex treatments, 3D-IMPT and DET (almost the two extremes of the IMPT spectrum, but see below) can provide extremely similar dose distributions, there is clearly a whole spectrum of solutions in between. Searching this solution space could be quite interesting, particularly when only a limited number of field directions are available

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or desired (remember that to obtain a uniform dose across the target volume with the DET approach, a number of angularly spaced fields are required, because a single DET-type field can never provide a uniform dose across the target). For instance, even for an SFUD field, do we need to have Bragg peaks distributed completely over the whole target volume? Figure 11.2e shows an example. After the optimization, the majority of Bragg peaks within the target have very low relative weights (the white crosses in Figure 11.2e). Do we need to deliver all these, or are many redundant? In a study we performed a few years ago, it was found that by building a spot-reduction option into the optimization algorithm (35, 36) the number of delivered Bragg peaks could be reduced by up to 85%. When using the same approach for IMPT (multiple-field) optimization, the number of Bragg peaks could be reduced even more, as would be expected perhaps when comparing the 3D-IMPT and DET approaches. Interestingly however, when applying the spot reduction approach to a simple cylindrical target volume, it was even found that DET is not necessarily the optimum approach for reducing Bragg peak numbers. Figure 11.10 shows the Bragg peak positions resulting from the spot reduction approach for this case. As can be seen, only distal Bragg peaks in the central portion of the sphere are actually needed to ensure a homogenous dose across the target when planning using five IMPT fields. The more lateral distal peaks have been successfully removed. For this solution, 20% fewer Bragg peaks are required than for the DET solution! a

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FIGURE 11.10 (See color insert.) (a–c) Dose distributions for five-field plans to a cylindrical target volume. (a) 3D-IMPT; (b) DET; (c) using the spot-reduction algorithm explained in the text. (d–f) The corresponding Bragg peak positions and weights for the posterior field of each plan only, with the colors representing the relative weight of the individual Bragg peaks. The corresponding number of non-zero weighted Bragg peaks for each approach is also shown. Using a spot reduction scheme directly in the optimizer, a substantial reduction in the number of Bragg peaks required for dose coverage can be achieved, and this approach even finds a solution where fewer Bragg peaks than the DET approach are required (120 peaks per field as opposed to 150 peaks per field for the DET approach).

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So, do such methods for reducing the number of Bragg peaks bring any advantages from the point of view of delivery? Surprisingly, not as much as one may expect. When the potential reduction in delivery time for these cases was calculated (and subsequently measured) it was found that the reduction in delivery time for 80% reduction in the number of delivered Bragg peaks was only of the order of 6%. When analyzed, this was found to be due to the fact that, although the total dead time for the field (the time to move from Bragg peak to Bragg peak position) was somewhat reduced, this only accounts for about 40% of the total treatment time (at least on our delivery system), whereas the total beam-on time (i.e., the total number of protons that have to be delivered) remains the same. That is, although the number of Bragg peaks can be significantly reduced, the average fluence per delivered Bragg peak increases. This is of course also the case for DET plans. On the other hand, reduced numbers of delivered Bragg peaks per field could have some indirect advantages from the point-of-view of delivery. As the average fluence per delivered pencil beam increases, this could allow one to deliver the treatment using higher beam intensities. This in turn would result in significant reductions in the time required to deliver each field. On a similar note, it is often discussed whether there are any advantages to varying the lateral beam size within a delivered field, rather than using a constant beam size. Again, using Figure 11.2d above as an example, the argument goes as follows. If we have so many low-weighted Bragg peaks filling in the dose in the central and proximal portion of the target volume, is it not possible to replace at least some of these with a much smaller number of larger Bragg peak or pencil beams? In principle the answer is likely to be yes, at least to a point. However, this author is not convinced that the quality of the resulting plan can ever be as good as that resulting from the delivery of many smaller Bragg peaks and is also not completely convinced that such an approach brings much in the way of advantages. In principle, using varying beam sizes is similar in concept to the Bragg peak reduction schemes discussed above. In the end, at least with a constant intensity source, the total number of protons that need to be delivered will be about the same, with the only gain coming from a possible reduction in the dead time for the treatment, as less pencil beams need to be delivered. If intensity can be varied however, then perhaps, as with Bragg peak reduction, some more gains could be made. Despite some reservations about the usefulness of this approach, it is nevertheless an undoubtedly interesting area for future research. Finally in this section, I will discuss Bragg peak placement as a planning parameter for SFUD and IMPT planning. In Figure 11.2b, the Bragg peaks (indicated by the crosses) have been calculated and selected based on a regular (and rectilinear) starting grid. That is, orthogonal to the direction of the incident field, the delivered pencil beams are separated by 5 mm in both directions. Also, in depth, although the Bragg peaks are irregularly spaced in the patient (due to the differences in densities through different parts of the patient), they are nevertheless regularly spaced in water equivalent depth

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(in the case of Figure 11.2d, with a separation of 0.46 cm). As the Bragg peaks are distributed on such a grid, the consequence is that, in order to cover the selected target volume completely, Bragg peaks up to 5 mm outside of the selected target volume have to be selected as well, as are clearly visible in Figure 11.2d. If these additional external Bragg peaks are not selected, then, in the worse case, the nearest Bragg peak to the surface of the target volume could be up to 5 mm inside the target volume, with obvious consequences for dose coverage of the target (see Figure 11.11a). Thus, although a rectilinear placement of Bragg peaks is certainly the simplest, it is not necessarily the best. As an alternative, one can imagine selectively placing Bragg peaks directly on the surface of the target volume and then filling-in the remaining Bragg peaks internally to the target as required (in this case on an irregular grid, see, e.g., Figure 11.11b). Such an approach should certainly improve dose falloff outside the target volume and could potentially lead to a more efficient delivery. However, to achieve this, a fine spatial resolution is required in the placing of pencil beams both orthogonally to the field direction (which with modern magnets should not be too challenging) but also in depth, which requires a fine resolution in the energy selection system. Nevertheless, irregular and contour-based Bragg peak positioning will certainly be a a

b

FIGURE 11.11 A schematic comparison of spot placement on a rectilinear and regular grid (a) and the gain that could be achieved by “optimizing” Bragg peak/pencil beams such that placement is performed first on the target surface, and then pencil beams/Bragg peaks are “filled-in” in the internal region (b). In theory, this should significantly improve penumbra around the target volume.

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requirement and perhaps will even be standard in future active scanning delivery and treatment-planning systems. 11.4.4  The Importance of Starting Conditions in IMPT Optimization In the previous sections, we have looked at various consequences of degeneracy in IMPT planning. Whether this is forcing the solution to one requiring fewer delivered Bragg peaks (as in the DET approach) or the fact that in some circumstances satisfactory plans can be achieved with small number of fields, I hope that it is clear that there are many different solutions to the IMPT problem that give similar dose distributions. So how do we search this immense space of possible solutions, or indeed how do we decide which of the many similar solutions we actually want for our final plan? (See also Chapter 15.) Hard core optimizers will argue that a comprehensive optimizer will find any of these solutions if sufficient constraints to the optimization algorithm are defined, and the answer we achieve should be driven by defining the full problem to the optimizing engine. There is certainly much merit in this approach. However, one could also ask, why let the optimizer do this (with the associated time-cost function) when in many cases, it is absolutely clear that the optimization can be helped by defining starting conditions? The specific solution of DET is, after all, achieved by defining the starting conditions as being just those Bragg peaks that are delivered to the distal edge of the target, and de-selecting (or not selecting at all) the Bragg peaks internal to the target volume. However, the DET solution is just a special case of 3D-IMPT, and if this is indeed the most optimal result (or the most desired), then a good optimizer should be able to find its way to this solution. Such an approach was attempted in our example of spot reduction above. By adding a spot reduction algorithm to the optimization, we could show that the solution could be driven toward the DET solution, and even beyond (see Figure 11.10). So why is DET still referred to as a particular approach? Because, in the end, it is much easier to get to the DET solution by defining the starting conditions of the optimization than to start with a full 3D distribution of Bragg peaks across the target (or why not across the whole patient?) and then to get the optimizing algorithm to work out that DET is the result that is required. In other words, the definition of starting conditions for the IMPT optimization is a way in which the user (the treatment planner) can already impart his or her knowledge of the case or of previous similar cases in order to achieve the desired result. As in other chapters of this book, the reader will certainly find counter arguments to this, let’s have a look at the starting condition issue in somewhat more detail. Although many sophisticated optimization algorithms are available (Chapter 15), it is still very much the case that many of the optimization algorithms used in commercial and research treatment-planning systems are rather simple in concept. Although there are certainly exceptions, most

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algorithms are gradient based and are based on rather simple dose or dosevolume constraints to the target volume (or volumes) and multiple OAR’s. Given that the problem for the optimizer is then overdefined (or degenerate), such algorithms will inevitably find the nearest solution to the starting conditions that best fits all the constraints. There is no reason for it to do anything else, as the algorithm will likely find the nearest local minimum in the solution space. Thus, in many systems, a definition of the starting conditions is a “must” for users if they want to impose other conditions on the final plan. Take as an example Figure 11.12, which shows a schematic representation of a simple two-field, parallel opposed plan to a centrally placed target volume. Now, let’s assume that the only constraint for this plan is to obtain a homogenous dose across the target volume and that we are going to perform an IMPT plan as defined in Section 11.3.2 (i.e., the Bragg peaks from both fields will be simultaneously optimized and the only requirement is that the dose a

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FIGURE 11.12 A schematic representation of two possible solutions to the definition of Bragg peak weights along the beam direction for a simple, parallel opposed field plan. (a) The resulting dose profile along the beam direction as a result of the use of a set of preweighted Bragg peaks delivering a mini-SOBP along the field direction. (b) The dose profile resulting from the same optimization of the same fields, but assuming that the first “guess” for Bragg peak weights along the beam direction is a constant set of weights. (c) The dose profiles from the two solutions superimposed on top of each other.

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from both plans combine to deliver a homogenous dose across the target volume). Figure 11.12a shows one possible solution for this problem. As a starting condition for both fields, a set of Bragg peaks has been used that is already weighted such that the resultant dose profile in depth is a mini-SOBP. It is clear then, that when these two fields combine, the resulting dose will already be very close to uniform across the target, and the optimizer will perhaps only have to fine-tune Bragg peak weights in order to achieve the desired result. In the case of Figure 11.12b, the initial set of Bragg peak weights has been defined such that the weights are the same regardless of their relative depth along the beam direction (i.e., all Bragg peaks have the same initial relative weight). If we calculate the resultant depth–dose curve for such a weighting, then this actually gives a linear wedge profile in depth, with the maximum dose at the proximal end and the dose reducing toward the distal end. However, the field from the opposite side has a similar arrangement, and when both are combined, similarly to Figure 11.12a, the resultant dose across the target volume is once again more-or-less uniform. Again, the optimizer has to do little work in order to obtain a uniform dose across the target. Indeed, if target dose uniformity is the only criterion for the optimization (as stated above), the optimizer in the second case has no reason to do anything else. So in Figure 11.12 we have two possible IMPT solutions for delivering a uniform dose to the target volume. Are they equivalent? Well, yes and no. They are equivalent if one is only interested in target dose uniformity, but not in other aspects. Take for example Figure 11.12c, where we have overlaid the combined dose profiles of the two fields on top of each other and have normalized them such that the dose to the target is the same. It is now clear that in the entrance regions of the two fields, there is a clear difference in dose between the two solutions. Solution A (the predefined SOBP approach) results in a significantly lower dose in the entrance channels than solution B (the constant weight approach), and I think most readers will agree that solution A is the more desirable. If the example shown above appears to be rather artificial, then consider Figure 11.13, which shows two plans for a prostate case, using conventional field directions (parallel opposed lateral fields) for prostate treatments with proton therapy (37). The plan in Figure 11.13a and c, has been optimized using the mini-SOBP starting conditions described above, whereas in Figure 11.13b and d, the plan uses the constant weight approach, also described above. Despite similar coverage and dose uniformity in the target, the additional dose in the entrance channel for the constant weight approach is clearly visible in comparison to the mini-SOBP approach. Figure 11.13c and d, shows the single-field distributions for the right-hand field of each plan after optimization. Because of the irregular nature of the target volume, although there is some clear variation of dose across the target for both fields, there is nevertheless a clear trend in the two fields. The mini-SOBP approach has resulted in a relatively uniform coverage of the target from the single field (similar to the result one would expect from using the SFUD approach), whereas the

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FIGURE 11.13 (See color insert.) Dose distributions for the complete plans and one example field for lateral opposed field plans for a prostate case, (a and b) calculated using the preweighted, SOBP approach and (c and d) calculated using the constant weight approach. As in Figure 11.12, the constant weight approach leads to single-field distributions with a clear and distinct dose gradient from the proximal to distal end. This in turn leads to a clear increased dose to the normal tissues lateral to the target volume in comparison to the preweighted approach.

constant weight approach results in a single-field distribution with a clear dose gradient from the proximal-to-distal end of the target, demonstrating an in-depth profile similar to that shown in Figure 11.12b. The dose distributions in Figure 11.13 have been calculated using the optimization algorithm of the PSI planning system (22, 36), which is a gradientbased method. However, such fields have been calculated by the author on at least two commercial systems with similar results, indicating that the choice of starting conditions can be an important issue. Indeed, even if a more sophisticated optimizer (e.g., one that finds a global minimum) is used, the result will be the same if target uniformity is the only defined goal. To get to solution A (if starting from solution B), one has to define more parameters about the dose to the normal tissues. For the example described here, this would certainly make sense, but the point is, a sophisticated optimization engine is only as good as the input parameters (constraints) defined for it. So if we did want to get to a DET solution, what would we define to the optimizer? If we wanted to use larger spots in the internal portion of the target, how would this be expressed? If we only want to use two fields instead of four, how do we incorporate this into the optimizer? This is not to say that these cannot be done through optimization alone, but only is to emphasize

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that for many cases the definition of starting conditions is a logical and perhaps somewhat easier approach to achieving the desired result.

11.5  Dealing with Uncertainties Having looked in some detail at some of the characteristics of the optimization problem for IMPT, and in particular at the problems, and potential, of degeneracy, I now move on to a potential area where that degeneracy could well be utilized to advantage: to help design plans that are robust to potential delivery errors (see Chapters 13–15). 11.5.1  Magritte’s Apple A famous painting by Belgian artist Rene Magritte is entitled Ceci n’est pas une pomme (This Is Not an Apple). Although the image is clearly a very beautiful painting of an apple, Magritte’s point was exactly that—it is just a painting of an apple and not a real apple. In many ways, the same can be said of dose distributions calculated (and displayed) by treatment-planning systems. Although they are quite accurate representations of the estimated deposited dose, they are exactly that: just representations and estimates. What will actually be delivered to the patient will be, at many different levels, inevitably different. Thus, a dose distribution displayed by a treatmentplanning system is just an image of the (to be) delivered dose and is not the true delivered dose. This may all seem overly pedantic, but an appreciation of how a treatment may vary from that calculated by the treatment-planning system is an important criteria in designing and evaluating treatment plans, and every type of treatment will be subject to many, very different treatment uncertainties. In this section, we will look at different ways of dealing with such uncertainties and how to analyze and display these when analyzing treatment plans. 11.5.2  Sources of Delivery Uncertainties Before looking at the management of uncertainties, let’s first look at the possible uncertainties associated with modern radiotherapy, and in particular, proton therapy. These can be divided into four categories: clinical, spatial, calculational, and delivery based. Clinical uncertainties result from initial diagnosis through to the definition of the target volume to be irradiated. Although certainly one of the potentially most grave uncertainties would be a complete misdiagnosis of a tumor, there is little that can be done at the treatment planning/delivery stage to rectify this, so we will skip over this. The other main clinical

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uncertainty is uncertainty in the definition of the target volumes and critical structures. Again, although it has been well documented that this could be one of the largest sources of uncertainty in radiotherapy, various tools such as multimodality imaging and fusion, international standards on the definition of target volumes (i.e., GTV/CTV concepts) hopefully help to keep these to a minimum (38, 39). In any case, once the targets and OARs have been defined, it is the author’s opinion that these have to be accepted as correct, and then it is the treatment planner’s job to design a plan that best meets the criteria defined by the responsible clinician. So let’s move onto the second category of errors: spatial errors. These can come from errors and uncertainties in the imaging process such as image distortions (although with modern imaging equipment this is perhaps less of a problem nowadays than a few years ago); however, more relevant from the point of view of treatment planning and delivery, is the impossibility of positioning a patient in exactly the same place every day of a fractionated treatment and the impossibility of keeping a patient perfectly still for the duration of each delivered fraction. Depending on the site being treated, the type of immobilization used, and the patients themselves, these errors can easily be the order of millimeters to centimeters in magnitude and need to be seriously considered in the planning process. Although many values can be found for these errors in the literature, they are largely of little use, as positioning errors will be very dependent on the working practices of each individual center. Nevertheless, such errors can (and should) be separated into random errors (those that vary day to day with a resulting spread of values over the whole treatment) and systematic errors (those that may be the same for every fraction). The reason to separate these different types of uncertainty is simple. Random errors will generally have a blurring effect, whereas systematic errors can lead to large, constant errors. From the point of view of uncertainty management, systematic errors are by far the most important, and particularly for proton therapy, there is an additional spatial error that needs to be considered, exactly because in most circumstances it is a systematic error. That is, the uncertainty in the range of protons in the patient. In other words, the uncertainty in where the Bragg peak actually stops. The sources and estimated magnitudes of these uncertainties are covered in detail in Chapter 13, but they can easily reach 3% from imaging and calibration uncertainties alone (40, 41) and much greater values when taking into account reconstruction artifacts due to metal implants or changes in patient anatomy (42, 43). 11.5.3  To PTV or Not to PTV? That Is the Question Uncertainty management is nothing new in radiotherapy. In the 1980s, Goitein and coworkers recommended including error estimates as part of the routine planning process, in the form of maximum and minimum plans in addition to the nominal distribution, to encapsulate possible variations of the

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dose distribution about the nominal values (44, 45). Unfortunately these ideas were never successfully incorporated into commercial treatment-­planning systems, and these innovative ideas have not as yet caught on. Instead, uncertainties have been managed using the concept of the PTV as defined in ICRU reports 50 and 62 (38, 39), where the PTV is defined as a spatial expansion of the clinical or gross tumor volume, with the margin for the expansion being defined by the likely uncertainties associated with the treatments. This has led to the concept of margin recipes, where statistical analysis has been applied to the PTV expansion concept in order to more precisely define (and standardize) margin expansions. The most well known of these is that defined by van Herk et al. (46), which defines the margin based on a separation of the uncertainties into random and systematic components. However, most of this work has been concentrated on photon-type treatments, and little work has been published for margin recipes for proton therapy. However, should there be a difference between PTV definitions and margin recipes between proton and photon therapy? The answer is certainly yes. The problem lies in the additional uncertainty relating to the calculation of the range. Although the effect of positioning errors on the PTV in proton therapy are similar to those for conventional therapy (after all, there should not be any difference in random and systematic positioning uncertainties between different treatment modalities if the same fixation devices are used), there is essentially no concept of range uncertainty in photon therapy. As noted above, range uncertainty is almost certainly systematic in nature, and there is no reason to believe that the magnitude of uncertainties in range are the same as (or are even correlated to) the positioning uncertainties orthogonal to the beam direction. Thus, because range uncertainties will be different from and most likely larger than positional errors, and additionally range errors are likely to be systematic, a significantly different margin expansion for the PTV will be required at the distal end of the target than lateral to the field direction. Consequently, a single PTV expansion for the whole target that is valid for all fields is not necessarily valid for proton therapy. Much more likely is that a field-specific PTV is required, with a different expansion being used along the beam direction to that laterally. Very few (if any) planning systems allow for such an expansion. Indeed, most facilities with passive scattering take a very different approach for exactly this reason. As described by Moyers et al. (47), the typical approach to allowing for errors is to expand the aperture lateral to the field by an amount determined from the estimated positional errors, while modifying the compensator by shaving-off a fixed amount of material to ensure a controlled overshoot of Bragg peaks at the distal end. The amount shaved-off is then determined from the estimated uncertainties associated with the range. As the two uncertainties are dealt with differently, and independently, then this approach is equivalent to a field-specific PTV, without actually defining a PTV. Indeed, it is important to realize that when building the margins into the field-specific hardware devices (apertures and compensators), a PTV should not be used,

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because the uncertainty management is built directly into the field hardware rather than being incorporated into a target volume expansion. For scanning, the approach adopted for passive scattering is not valid because generally, and as discussed above, scanning does not require fieldspecific apertures or collimators. Thus, other methods of uncertainty management need to be adopted. At PSI, we use a single PTV expansion similar to conventional therapy, with the margin mainly being determined either by an assessment of the positioning errors or from the range uncertainties (48). However, this is not necessarily the best approach. For instance, if the PTV concept is to be used, then it would be more reasonable to define a PTV per field (as described above), as this is the nearest analog to the approach generally adopted for passive scattering. Alternatively, it is conceivable that the PTV concept is preserved to deal with positional errors, and other methods are adopted for the range errors. We have previously looked into the possibility of building range uncertainty into the optimization, by simply performing the Bragg peak selection and optimization on a modified CT data set in which all CT voxels have an artificially increased Hounsfield unit (HU) value (e.g., by +3%, the estimated uncertainty in the range). When the optimized set of Bragg peaks are then used to calculate the final dose on the nominal, unmodified CT, this leads to a systematic overshoot of the dose to the PTV by about 3%. An example of this approach is shown in Figure 11.14a. This SFUD plan has been calculated to a PTV expanded by 3 mm around the CTV and with a planned overshoot of 3%. This can be compared to a plan with an isotropic margin expansion of 5 mm (our typical value for such a case) for which no planned overshoot was used (Figure 11.14b). The 3-mm expansion with planned overshoot delivers a % 109

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lower dose to the normal tissues than the 5-mm expansion, while being just as robust to both positional and range errors as the 5-mm expansion. For this case, the differences are not huge, but this should illustrate that there is still a lot of work to be done in the development of PTV concepts for scanning proton therapy. 11.5.4  Robust Optimization The concept of planned overshoot described above is essentially a “trick” in the optimization to “fool” the algorithm that all tissue densities are somewhat more dense than in reality. However, would it not be more elegant to incorporate all delivery uncertainties into the optimization, such that the degeneracy of the optimization problem can be utilized to generate fundamentally “robust” plans? This is an area that is attracting more and more interest in the literature in the form of robust optimization. There are two approaches, in analog to the discussion about optimization above. One is by manipulating the starting conditions of the optimization in order to point the optimization in the correct direction toward a robust solution; the other is to incorporate uncertainties directly into the optimization process itself (49–51). The latter of these is covered in more detail in Chapter 15, and will not be described further here. We will thus concentrate in this chapter on robust planning through manipulation of the starting conditions of the optimization process. In a previous publication, we have shown that, even for extremely simple cases, IMPT plans can be less robust than SFUD plans for the same case, at least to range uncertainties (30). However, in the first IMPT case reported in the literature, IMPT was actually used to improve plan robustness against that that could be achieved with a single SFUD field plan (52). For this case, the full target volume was split into two subvolumes, with each field of the three-field plan covering a different subvolume. The way in which these subvolumes were defined resulted in a solution in which no highly weighted Bragg peaks were delivered against the spinal cord, which lay at the distal end of the PTV. Consequently, even if range errors of 10% were assumed, the IMPT plan still kept the spinal cord below the defined tolerance, whereas a single SFUD field applied to the same PTV under the same error conditions would overirradiate the spinal cord significantly. The definition of these subvolumes was, of course, essentially a definition of the starting conditions for the optimization that ensured a robust solution. Indeed, this approach to robustness is not new. It is exactly the same concept that is used in field patching in passive scattering, where many fields are patched around a critical structure in order to avoid using the steep distal falloff of the Bragg peak that will be particularly sensitive to range errors. More recently, we have studied the relative robustness of 3D-IMPT and DET plans to a number of different uncertainties (29, 30) and found, at least for the cases studied, that 3D-IMPT was generally more robust than DET and that

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the more complex the IMPT plan (i.e., the more modulation there is in each IMPT field) the more sensitive (less robust) is the plan. This work has been followed up by Albertini, Hug, and Lomax (31), who have investigated the relative robustness of different IMPT flavors through the manipulation of the starting conditions for a number of different cases. In that work, it is shown that clear differences in the robustness of the plans can be demonstrated, but also that 3D-IMPT is not always necessarily better than DET. Depending on the geometry of the case, DET could sometimes give a more robust plan (at least to range uncertainty) because in some cases, neighboring critical structures are spared only using the lateral edge of delivered pencil beams, and not the distal edge, as is sometimes the case for the 3D-IMPT approach. Although this may sound confusing and maybe makes the choice between different IMPT techniques seem rather difficult, it is hoped that these studies can provide pointers to case solutions that, depending on the geometry of the cases being planned can be defined, will allow the planner to make informed decisions about the type of IMPT to use in order to make a robust plan. 11.5.5  Tools for Evaluating Plan Robustness As outlined in the previous section, robust planning and optimization is a growing area of research in proton therapy. It is therefore interesting to note that, despite these developments, there is still little in the way of tools for actually evaluating the robustness of a plan. Given the importance put on this aspect in this chapter, and in the proton therapy community generally, this is a rather strange omission. As has already been mentioned, such tools were suggested by Goitein in the 1980s (44), but have unfortunately not been generally adopted. However, given the complexity of (in particular) IMPT plans, it seems to the author that simple tools for evaluating the robustness of treatment plans should be standard tools in any treatment-planning system. Without such tools, how can the efficacy of robust planning techniques actually be determined? Or how will it be possible, in the degenerate world of IMPT planning, to differentiate between two IMPT solutions with very similar resulting dose distributions but for which robustness may be very different (i.e., between a 3D and DET-type solution)? In the last few years, we have tried to follow on from the work of Goitein et  al. (44) and develop tools for representing robustness to the treatment planner. The worse-case distribution has already been mentioned above (29, 53). More recently, we have developed the concept of error-bar distributions, which essentially display as a 3D distribution the width of the twosided error bar associated with the nominal dose at every point of the 3D distribution. The full details of this approach can be found in Albertini, Hug, and Lomax (54), and just one example will be shown here. Figure 11.15a and b, shows the nominal dose distributions of two plans to a paraspinal case; one is an SFUD plan (a and c), the other an IMPT plan (b  and  d). Field directions for the two cases are the same. Figure 11.15, c

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FIGURE 11.15 (See color insert.) Example application of “error-bar” distributions to display potential dose errors for proton treatment plans. (a) A three-field (1 lateral and 2 superior lateral obliques) SFUD plan to a skull base chordoma. (b) A four-field (right and left lateral anterior and posterior oblique) IMPT plan to the same case with a strict dose constraint on the brainstem. (c and d) Composite error-bar distributions for the two plans, which combine random and systematic errors into a single error-bar distribution (see text for a fuller explanation). The potential variation of dose within the CTV (inner yellow contour) for the IMPT is clearly much higher than that for the SFUD plan, whereas the opposite is true for the brainstem (spared in the optimization process for the IMPT plan).

and  d, shows the resultant error-bar distributions, which here are the socalled composite distributions that combine the possible random effects of positional spatial errors with the systematic effects of range errors into a single error distribution. In these figures, the colors now show the possible variation in dose at each point about the nominal value and within a certain confidence limit (in this case the 85% confidence limit). In a similar way to dose distributions, cumulative error bar–volume histograms (EVHs) can also be calculated for any delineated structure, which then indicate the amount of dose variance that can be anticipated in any structure. These can be interpreted like normal tissue DVHs, in that the more the curves are toward the bottom left-hand corner of the plot, the less dose variance there will be in that structure and the more robust is the plan for this structure. The corresponding EVH plots for the two plans shown in Figure 11.15 are shown in Figure 11.16.

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There are some subtle, but maybe significant differences in the dose variance distributions. Directly at the border of the high-dose region with the brainstem, the dose variance of the IMPT plan is actually somewhat smaller than that of the SFUD plan, indicating that the IMPT plan could, in this case, be a little more robust than the SFUD plan when considering dose to the brainstem. This is confirmed somewhat by the EVHs, where the IMPT reduces the volume of the brainstem that could experience large dose variances. Although it could be argued that the differences here are insignificant, this example has been chosen for the following reason. The variance distributions are clearly different, indicating that there could well be differences in the robustness of the two plans to delivery errors and that such differences can never be inferred from the nominal dose distributions alone. Only when looking at the variance distributions do some differences become

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apparent, perhaps then aiding the decision process on which of these two plans is preferable. In other words, evaluating robustness using tools such as those suggested here provide an additional criterion by which the planner can more accurately navigate through the degenerate world of SFUD and IMPT plans.

11.6  Case Studies To finish this chapter, I will briefly present two typical cases that have been treated using SFUD and IMPT at PSI, in order to give the reader a flavor of what can be achieved using active scanned proton therapy. 11.6.1  Case 1: Nasopharynx Carcinoma The first case is a sinonasal undifferentiated carcinoma. Figure 11.17 shows two slices through the PTV1 at the level of the eyes and optic structures. The volume of PTV1 is 300 ml and of PTV2 284 ml. The prescription for the case was 54Gy(RBE) to PTV1 and 70 Gy(RBE) to PTV2. As with all our plans, a global RBE value of 1.1 has been assumed. Figure 11.17 shows two of three series and the composite dose (the combined dose from all plans) delivered to this patient. Plan 1 is an SFUD plan to PTV1 (delivered from 0 to 30Gy[RBE]), whereas plan 2 is an IMPT plan to PTV1 with dose constraints defined to the brainstem, optic structures, and cochleae (30–54Gy[RBE]). Plan 3 (not shown) is an IMPT plan to PTV2, with the same dose constraints to the same OARs as for plan 2. Four fields were used for each plan using the same field geometry for all plans: right and left lateral beams with a 15° table kick, an anterior-superior oblique field, and a posterior-superior oblique field. Even for the large and rather complicated PTV1, the SFUD first series plan provides a relatively homogenous and conformal plan. The PTV is well encompassed by the 95% dose level (the red color wash in the figure), and there is a good dose homogeneity (absolute maximum dose in the plan is 107%). For the second series plan (Figure 11.17, c and d), an IMPT plan calculated to PTV1 was used to already start pulling dose off the main dose limiting critical structures (those to which a dose constraint was defined in the IMPT plan), as can be clearly seen in the slice between the eyes, as well as somewhat in the region of the brainstem and cochleae. In addition, because of the selective sparing of the critical structures, the maximum dose in the plan increased a little (from 108 to 114%), which is typical for such IMPT plans. This was somewhat more increased in the third series IMPT plan, despite the fact that the constraints and field geometry are identical. However, this is a feature that we often see with our IMPT plans when the volume reduces somewhat. Nevertheless, this plan is perfectly acceptable.

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FIGURE 11.17 (See color insert.) Case study 1: sinonasal undifferentiated carcinoma. (a and b) Two slices through the first series, four-field SFUD plan (0.0–30.0 Gy). (c and d) The same slices through the second series, four-field IMPT plan (30.0–54.0 Gy). (e and f) The composite dose for the complete treatment (up to 70 Gy) including a third series to PTV2 from 54.0 to 70.0 Gy (not shown).

The final, composite distribution shown in Figure 11.17, e and f, indicates the quality of the full treatment, which provides precision, homogeneity, and conformality to a particularly large and complex tumor situated between a number of sensitive critical structures. 11.6.2  Case 2: Sacral Chordoma Figure 11.18 shows the individual series plan and composite treatment for a relapsing sacral chordoma. The PTV in this case is 1.4 liters, and this volume was treated to a total of 74 Gy(RBE) using two series. The first series (Figure 11.18, a and b) is a two-field SFUD plan using angles of ±15° away from the

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FIGURE 11.18 (See color insert.) Case study 2: a relapsing sacral chordoma. (a and b) Two slices through the first series, two-field SFUD plan (0.0–36.0 Gy[RBE]). (c and d) The same slices through the second series two-field IMPT plan (36.0–74.0 Gy[RBE]). (e and f) The composite dose for the complete treatment (74.0 Gy[RBE]).

vertical (posterior) and that was delivered from 0 to 36 Gy(RBE). Again, two different slices through this complex case are shown, the first rather more superior and at the level of the cauda equina, and the second more inferior and at the level of the rectum. Note the almost total sparing of dose in the abdominal region and pelvic space. Figure 11.18, c and d, shows the second series IMPT plan, delivered from 36 to 74 Gy(RBE). This is also a two-field plan, but with the fields now separated from the vertical (posterior) by ±30°. In this case, IMPT has been used in order to reduce the dose to the cauda and the nerve roots, which are visible just anterior to the cauda. The ability to form donut-like dose holes around centrally spaced critical structures from an extremely narrow field

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arrangement is a unique ability of IMPT. Even in this case, the doses to the abdomen, rectum, and pelvic space are extremely low. Finally, Figure 11.18, e and f, shows the composite dose distribution for the whole treatment (to 74 Gy[RBE]). This case graphically illustrates the power of scanned proton therapy for delivering highly conformal dose distributions to large volumes while minimizing the integral dose to all normal tissues outside of the target volume, and its ability to selectively spare smaller critical structures embedded directly in the target volume with the use of very small numbers of fields. Indeed, this allows for very large doses to be delivered to large volumes with little in the way of acute side effects to the patient.

11.7  Summary Proton therapy is currently experiencing what can only be called a boom period. Particularly in Europe and the United States, a number of hospitalbased sites are nearing completion, are in a late stage of planning, or are currently being seriously discussed. In Japan, many centers are already operational and are well established. Although at the time of writing, the vast majority of centers are mainly based on the passive scattering approach, and only four centers worldwide are currently treating with scanned proton beams (PSI, Villigen, Switzerland; University of Texas MD Anderson Cancer Treatment Center, Houston, TX; Rinecker Proton Therapy Center, Munich, Germany; and Massachusetts General Hospital, Boston, MA), of the new centers currently being planned, many are planning on either treating a substantial number of their patients using scanning or treatment will be exclusively based on scanning. The reasons for this are clear. As we have tried to outline in this chapter, scanning provides the most flexible method for delivering proton therapy, either for achieving improved dose conformation per field or, perhaps more importantly, allowing for IMPT. The latter approach truly allows the treatment planner to fully exploit the advantageous characteristics of protons in ways that are not possible with photon-based techniques or with passive scattering (see, e.g., case study 2 in Section 11.6.2). However, as we have also tried to explain here, this flexibility does not come without consequence. In particular, great attention must be paid to the characteristics of the delivery device in order to get the most out of scanning. Clearly, because the maximum lateral penumbra that can be achieved is determined on the scanned pencil beam size, it is imperative that the delivery machine minimizes this as much as possible. In addition, and as described in detail in Section 11.2.7, much attention must also be paid to the problem of the delivery of superficial Bragg peaks, a problem sadly overlooked by many manufacturers. Then in treatment planning, given the

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degeneracy of the problem, there is a great potential for either exploiting this to the maximum or ignoring this and leaving the user frustrated with suboptimal plans. Although it is tempting to think that existing IMRT optimization methods will suffice for scanned protons, the additional degrees of freedom available to the optimizer, together with the characteristics of protons mean that already in the planning system, special care needs to be paid to these factors, for instance, by the use of multiple-criteria planning approaches (as described elsewhere in this book) and/or the ability for the treatment planner to set the starting conditions to drive the result of the optimization in a desired direction (as described in Section 11.4.4 of this chapter). Finally, although plan robustness is a sadly underevaluated characteristic of any radiotherapy treatment, it is certainly true that, due to their finite range, this aspect is more important for proton therapy than it is for conventional therapies. Although much of this aspect can be gained through experience and good training of staff, it is also an aspect that should be more closely incorporated into the planning and quality assurance aspects of proton therapy. For this, tools must be provided by both the treatment planning and delivery machine manufacturers by which the consequences of delivery uncertainties can be estimated at the time of planning and their magnitudes determined during treatment. For this, uncertainty analysis tools should be provided in the treatment-planning systems, as well as advanced imaging and verification tools at the treatment machine. As such, there is much interesting and important technological research and development still to be done in the field of scanned proton therapy.

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41. Schaffner B, Pedroni E. The precision of proton range calculations in proton radiotherapy treatment planning: experimental verification of the relation between CT-HU and proton stopping power. Phys Med Biol. 1998; 43:1579–92. 42. Jäkel O, Reiss P. The influence of metal artefacts on the range of ion beams. Phys Med Biol. 2007; 52:635–44. 43. Albertini F, Bolsi A, Lomax AJ, Rutz HP, Timmerman B, Goitein G. Sensitivity of intensity modulated proton therapy plans to changes in patient weight. Radiother Oncol. 2008; 86:187–94. 44. Goitein M. Calculation of uncertainty in the dose delivered in radiation therapy. Med Phys. 1985; 12:608–12. 45. Urie M, Goitein M, Doppke K, Kutcher G, LoSasso T, Mohan R, et al. The role of uncertainty analysis in treatment planning. Int Radiat Oncol Biol Phys. 1991; 47:1121–35. 46. van Herk M, Reneijer P, Rasch C, Lebesque JV. The probability of correct target dosage: dose-population histograms for deriving treatment margins in radiotherapy. Int J Radiat Oncol Biol Phys. 2000; 47:1121–35. 47. Moyers MF, Miller DW, Bush DA, Slater JD. Methodologies and tools for proton beam design for lung tumors. Int J Radiat Oncol Biol Phys. 2001; 49:1429–38. 48. Bolsi A, Lomax AJ, Pedroni E, Goitein G, Hug EB. Experiences at the Paul Scherrer Institute with a remote patient positioning procedure for high-throughput proton radiation therapy. Int J Radiat Oncol Biol Phys. 2008; 71:1581–90. 49. Unkelbach J, Chan TC, Bortfeld T. Accounting for range uncertainties in the optimization of intensity modulated proton therapy. Phys Med Biol. 2007; 52:2755–73. 50. Pflugfelder D, Wilkens JJ, Oelfke U. Worst case optimization: a method to account for uncertainties in the optimization of intensity modulated proton therapy. Phys Med Biol. 2008; 53:1689–700. 51. Unkelbach J, Bortfeld T, Martin BC, Soukup M. Reducing the sensitivity of IMPT treatment plans to setup errors and range uncertainties via probabilistic treatment planning. Med Phys. 2009; 36:149–63. 52. Lomax AJ, Boehringer T, Coray A, Egger E, Goitein G, Grossmann M, et  al. Intensity modulated proton therapy: a clinical example. Med Phys. 2001; 28:317–24. 53. Lomax AJ, Pedroni E, Rutz HP, Goitein G. The clinical potential of intensity modulated proton therapy. Z Med Phys. 2004; 14:147–52. 54. Albertini F, Hug EB, Lomax AJ. Is it necessary to plan with safety margins for proton scanning plans? Phys Med Biol. 2011; 56:4399–413.

12 Dose Calculation Algorithms Benjamin Clasie, Harald Paganetti, and Hanne M. Kooy CONTENTS 12.1 Pencil Beam Algorithms............................................................................ 382 12.1.1 Rationale........................................................................................... 382 12.1.2 Physics Model.................................................................................. 383 12.1.2.1 Elastic Scatter in Medium............................................... 383 12.1.2.2 Large Scattering Events................................................... 386 12.1.3 Dose to Patient................................................................................. 388 12.1.4 Beam Representation...................................................................... 389 12.1.4.1 SOBP Beams...................................................................... 389 12.1.4.2 SOBP Production Model................................................. 391 12.1.4.3 Scanning Beams............................................................... 393 12.1.4.4 Implementation................................................................ 394 12.1.5 A Scatter-Only Monte Carlo.......................................................... 396 12.2 Monte Carlo Algorithms............................................................................ 398 12.2.1 Statistical Resolution in a Clinical Setting.................................. 398 12.2.2 Improving Monte Carlo Efficiency............................................... 399 12.2.3 CT Conversion................................................................................. 399 12.2.4 Absolute Dose.................................................................................. 401 12.2.5 Dose-to-Water and Dose-to-Tissue............................................... 401 12.2.6 Impact of Nuclear Interaction Products on Patient Dose Distributions.................................................................................... 402 12.2.7 Differences between Proton Monte Carlo and Pencil Beam Dose Calculation.............................................................................403 12.2.8 Clinical Implementation................................................................ 405 12.2.9 Simplified Monte Carlo Dose Calculations................................. 407 Acknowledgments............................................................................................... 407 References..............................................................................................................408

381

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12.1  Pencil Beam Algorithms 12.1.1  Rationale Pencil beam dose calculation models are the most pragmatic representation for empirically modeling dose transport in medium. The pencil beam model is a convenient representation of a piecewise geometric and physical approximation to the exact model where each pencil beam allows a sufficiently accurate approximation of all dose-depositing processes in the patient by local effects, those along the axis of the pencil beam. Pencil beam algorithms use the mathematical concept of a set of narrow beams that, as a composite, (1) model all the degrees of freedom of the radiation field, (2) fill the physical space of the radiation field, and (3) provide a good approximation of modeling the patient as a set of interactions of the pencil beam in a “slab” geometry around the pencil beam axis. Interactions in laterally infinite slab geometry are well understood, and its application in pencil beam models is only limited by the lateral extent of the pencil beam itself. That is, the pencil beam local model is insensitive to heterogeneities lateral to its bounding envelop. Pencil beam models introduce the concept of modeling fluence, ϕ, transport along the pencil beam axis as a function of radiological depth, ρ, combined with a lateral energy diffusion kernel, K. Energy released in medium, and quantified  as dose to water, for a set of pencil beams, p, is E( x , d) = ∑ p ( ρ(d))K (r , ρ(d )) A , where ρ is the radiological depth, r is the distance from the pencil beam axis   to the point at x, and dA is the “area” of the pencil beam. The kernels, K, are x generated by, for example, Monte Carlo as dose-to-water. The kernels are radially symmetric and spatially invariant in compliance with the slab geometry assumption. More accurate kernels include polar angular dependencies and corrections for heterogeneities along the displacement, r. The nature of the kernel is fundamentally different between photon and charged particle dose models. For photons, the kernel is superimposed on a point on the pencil beam axis and transports the energy liberated at that point (i.e. the KERMA, within the medium). For protons, the kernel quantifies the diffusion of the pencil beam protons relative to the pencil beam axis. The pencil beam model was first applied in electron dose calculations (1). The electron field was subdivided in rectangular pencil beams and each pencil beam modeled the electron fluence diffusion in medium in the presence of heterogeneities as quantified on computed tomography (CT) data. Figure 12.1 shows a simple pseudocode description of a pencil beam model implementation where the line (1) creates an initialized set of dose calculation points, containing the position based on the CT data set and accumulates dose at that position; (2) sets up the computation given a decomposition of the field into mathematical pencil beams; (3) creates a trace object that maintains the geometry and state necessary to resolve the physics interactions as a function of depth; (4) places the points in the coordinate system of

Dose Calculation Algorithms

1 2 3 4 5 6 7

383

points = new_matrix(sizeof(CT), bounds); for each pencil-beam P in field F { trace = new_trace(P); points_p = place_and _sort_point_in(trace, points); while inside(trace, CT) { trace = trace_to_z_of_next_p(trace, CT); kernel = compute_kernel(kernel, trace, physics_model); points_p = compute_dose(kernel, points_p); } }

FIGURE 12.1 Pseudocode implementation of a pencil beam algorithm. The algorithm collects the calculation points (points) and sorts the points along the axis of each pencil beam P (points_p) to permit direct step-wise tracing to the depth of each point. At each point, the algorithm computes the extent of the pencil beam and computes the dose to the affected points.

the pencil beam with the z-axis along the pencil beam axis and where each trace is to the depth of the next point sorted in depth, now, along the pencil beam axis; (5) traces the pencil beam through the volume in increments; (6) computes the local kernel given the results from the trace and the physics model; and (7) adds dose as a consequence of the kernel convolution. The performance of an algorithm implementation is of course of primary significance. The above algorithm scales obviously as O(P), linearly with the number of pencil beams, but the performance of the super position of the kernel on the points will be very sensitive to the details of its implementation. It is of course the evolution of the kernel and its convolution on the dose point geometry that are the key to the efficiency of the algorithm implementation. Pencil beam models are well suited to model the transport of protons through the patient because a narrow beam of protons is itself a pencil beam. The fact, however, that a physical proton beam is well approximated by a mathematical pencil beam does require special implementation considerations as described below. 12.1.2  Physics Model 12.1.2.1  Elastic Scatter in Medium The physical processes involved in traversal of protons through medium are well understood (see Chapter 2). The primary mode of interaction is through elastic scatter of the proton in the electric field of the atoms in the medium. These numerous scattering events have the statistical consequence that the density of protons lateral to the mean direction approximates a Gaussian distribution. The Gaussian approximation is rigorous, according to the central limit theorem, if every scattering event occurs at a small angle. The proton scattering events, however, have an angular distribution governed, effectively, by the small-angle Rutherford form, dσ/dΩ ≈ 1/θ4, which means that the lateral distribution will be Gaussian for small angles but will trend

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toward a scattering tail distribution, 1/θ4. A complete multiple Coulomb scattering (MCS) theory was published by Molière in 1947 (2). We want to derive a model for the evolution of a beam with initially zero emmittance (i.e., zero lateral width and zero angular spread) in medium whose stopping power is characterized relative to water. The latter is in compliance with the definition of the dose kernels in water that we apply to the water equivalent representation of the patient. This evolution is largely described by the Gaussian widening of the proton distribution and the involved volume in which those protons will interact. Fermi-Eyges theory (3) describes the evolution of spatial and angular distributions of particles propagating through matter with the assumption that the particles undergo many small-angle scattering events. It was initially applied in pencil beam algorithms for electron beams (1) and more recently, although not in the Fermi-Eyges form, to proton (4) and heavy-ion beams (5). The theory is more accurate for protons and heavy ions because these particles scatter through small angles in interactions with the atoms in the medium. The Fermi-Eyges theory predicts that the lateral spread of a parallel and infinitesimally narrow proton beam as a function of depth in water, z (in centimeters), is Gaussian in shape with width given by (6) z

2 x MCS ( z) = σ 2x , MCS ( z) = ∫ ( z − z′)2 T ( z′) dz′  [ cm2 ]



0

(12.1)



N

2 where x MCS ( z) = ∑ xi2/N is the lateral variance of the beam (equal to σ2x , MCS ( z), i =1

the square of the standard deviation of the Gaussian profile, in the limit of many events) and T ( z) ≡ d θ2/dz is the scattering power. Gottschalk (7) gives a parameterization of the scattering power that is accurate almost within experimental errors for protons in water, thin slabs, and high-Z materials. The parameterization, called the improved nonlocal formula, is given by T ( z) = TdM = [0.524 + 0.1975 log 10 (1 − ( pv/p1 v1 )2 ) + 0.2320 log 10 ( pv/MeV )) 2

E  1 − 0.0098 log 10 ( pv/MeV )log 10 (1 − ( pv/p1 v1 ) )] ×  s   pv  LR 2



(12.2)

where pv [MeV] is the product of the proton momentum and velocity and is a function of z, p1v1 is the initial product of momentum and velocity, Es = 15.0 MeV, and LR is the radiation length (36.1 cm for water). Most treatment-planning algorithms, however, use the Highland formula for calculating the spread of proton beams in water, which is accurate within ±5% (4). The Highland scattering angle is integrated along the beam axis, and the result for the lateral standard deviation at z is (8) σ

2 x , MCS

 1  z ( z) = 1 + log 10   LR  9

2 2   1   z  14.1 MeV × ( z − z′)  dz′ (12.3)   ×  ∫0  pv      LR

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where ρ = 1 g/cm3 is the density of water and where the MCS is multiple Coulomb scattering. The Highland approximation and Fermi-Eyges theory with the improved nonlocal formula are given in Figure 12.2 for proton beams in water and the two parameterizations agree within 7%. Each pencil beam evolves in water according to σ x , MCS (z). At z, the total distribution is the convolution of two Gaussian functions: the initial or unperturbed Gaussian beam shape and the additional spreading from MCS in medium. The beam spread at z for an initially thick beam with zero angular spread is therefore 2 2 2 xthick ( z) = x MCS ( z) + xthick (0)



(12.4)

2 thick

where x (0) is the initial variance of the thick Gaussian beam. If the initial beam has nonzero angular spread, then 2 2 2 xthick ( z) = x MCS ( z) + xvac ( z)



(12.5)

2 2 2 where xvac ( z) = xthick (0) + 2 ⋅ z ⋅ x θthick (0) + θthick (0) ⋅z 2 is the spread of the beam in

N

2 a vacuum at z, xθthick (0) = ∑ xi θi/N is the initial covariance (6), and θthick (0) = N

∑ θ /N i =1

2 i

i =1

is the initial angular variance.

1

1

0.8

0.8 σx, MCS(R) [cm]

σx, MCS(z) / σx, MCS(R)

Proton pencil beam dose calculations determine the MCS lateral spread for each pencil beam in a field at each depth, and because a typical field consists of thousands of pencil beams, corresponding to the spatial and energy subdivisions, and hundreds of dose calculation depths, the spread calculation algorithm must be fast and accurate. The use of a look-up table for the results

0.6 0.4

0.4 0.2

0.2 0

0.6

0

0.2

0.4

z/R

0.6

0.8

1

0

0

10

20 R [cm]

30

40

FIGURE 12.2 Left: the normalized Gaussian spread in water vs. normalized depth, z/R, where R is the range of protons to stop in water (cm). This relation is independent of R between 0.1 and 40 cm and is the same for both Equations 12.1 and 12.3. Right: the Gaussian spread at maximum depth (i.e., z = R) for Equation 12.1 (dashed line) and Equation 12.3 (solid line).

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in Figure 12.2 can improve the speed of the dose calculation; see appendices in Hong et al. (4). Computational results in water are extended to heterogeneous media by assuming the media is water-like. That is, the physical depth, z, is converted to a water equivalent depth along the central ray of the pencil beam, and the media are assumed to have the radiation length of water. A general purpose Monte Carlo simulation should be used to check dose calculations for treatment plans in media that are not water-like. 12.1.2.2  Large Scattering Events Dose deposited outside of the central Gaussian region, from large-angle elastic scattering events and secondary particles, is called the beam halo. This leads to extended tails in the spatial and angular distributions of the beam. No correction for this effect is needed for uniform fields typical of those produced in scattering systems or uniform scanning systems because there is equilibrium of the lateral scattered dose and the effect is implicitly included in either measurement or model (9). On the other hand, nonhomogeneous fields are implicit in proton pencil beam scanning and the beam halo can not be ignored in the calculation of absolute dose. This effect has been studied by Pedroni et al (10), Soukup, Fippel, and Alber (11), and Sawakuchi et al. (12, 13), and ignoring the halo in treatment planning can lead to errors on the order of 5%. The halo contribution to the proton spread is characterized by a much larger radial effect. Figure 12.3 shows the buildup of dose measured on the central axis of square fields for a pencil beam of range 25 cm in water. The effect extends up to a distance on the order of 7 cm as shown in Figure 12.3 where full build-up is achieved in a square field of 15 cm. The halo is not easily described a priori. In practice, however, the halo can be well parameterized as a second Gaussian pencil beam with a fraction, f H, relative to the total beam. This weight is slowly varying as a function of depth, d, and range, R, and a simple parameterization is adequate to describe dose deposited by the halo, such as



1 − f H ( d , R) =

D∞M (R , d) = a0 (R) + a1 (R)t + a2 (R)t 2 T D∞ (R , d)

(12.6)

where t equals d/R, D∞M (R , d) is the MCS depth–dose component integrated over an infinitely broad lateral field, D∞T (R , d) is the same for the total measured depth dose. The fraction, f H, is derived from measurement and used, subsequently, to decompose measured depth doses into MCS depth doses and halo depth doses (Figure 12.4). In our implementation, we parameterize the coefficients in Equation 12.6 for f H as

ai (R) = b0 , i + b1, i R + b2 , i R 2

(12.7)

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R = 25 g/cm2, Depth of water = 17.4 cm

Dose (a.u.)

1.02 1

0.98 0.96 5

10

25

30

15 20 Full width of square (cm)

25

30

R = 25 g/cm2, Depth of water = 22.4 cm

1.02

Dose (a.u.)

15 20 Full width of square (cm)

1

0.98 0.96 5

10

FIGURE 12.3 Observed dose build-up in the center of a square field as a function of field width. The square field is delivered by a set of mono-energetic, 25 cm in water, pencil beams that populate the field area uniformly. The blue markers are measurement, and the red line is the model described in the text (Equations 12.6 and 12.7 and Table 12.1). Dose (Y-axis) is normalized to a 10 × 10 square field central dose. Depth dose R = 16 cm

Gy cm2 Gp–1

101 100

10–1 10–2 10–30

MCS 2nd p

2

4

6

Fraction of dose due to 2nd p 0.12 0.1 0.08 fH 0.06 0.04 0.02 0

8 10 12 14 16 18 20 Depth/cm

1

0.8

0.6 0.4 t = d/R 0.2

0 5

30 20 25 15 10 R cm water

FIGURE 12.4 The total measured depth dose (left) is decomposed into its component from MCS protons (top curve) and from secondary scattered halo protons (bottom curve). The decomposition (Equation 12.6) can be characterized as a second-order polynomial surface as a function of range-scaled depth t = d/R and Range (right).

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TABLE 12.1 Fit Parameters for Equation 12.7 to Obtain the Coefficients ai for the Computation of the Depth-Dependent Fraction f H in Equation 12.6

b0, i b1, i b2, i

a0

a1

a2

1.002 −5.900e-04 0

2.128e-03 −2.044e-02 3.178e-04

−2.549e-03 2.125e-02 −3.788e-04

These values characterize the beam at MGH (2010).

where the values for b are given in Table 12.1. This parameterization is derived from measurements of dose build-up in, for example, the center of circular rings of proton pencil beams of increasing radius and as a function of depth and energy. The parameterization allows a decomposition of a measured pristine peak depth dose in terms of elastic and inelastic dose contributions as a function of energy and depth (see Figure 12.4). Finally, the spread of the halo appears to be sufficiently constant (in the beam at the Massachusetts General Hospital [MGH]) as a function of depth as

σΗ (R) = 6.50 − 0.34R + 0.0078R 2 .

(12.8)

The halo model quantification is sensitive to the details of the measurements and beam conditions. The primary concern, however, is to characterize the energy flow away from our primary dose component characterized by f H because the redistribution of this secondary scattered energy is very homogeneous compared with the primary energy distribution in the patient. 12.1.3  Dose to Patient The dose to a point p in the patient from a proton pencil beam can now be stated as follows: D( p) =

 rp2 W exp  − 2 2 πσ2  2σ

  D∞ (ρp ) 

(12.9)

where W is the dosimetric “weight” of the pencil beam (physically propor− M tional to the number of protons in the pencil beam), ρp = ρW ∫0 SW (t)dt is the water equivalent depth along the pencil beam axis of u to the point p, σ is the total spread of the pencil beam at depth ρp , and rp is the shortest distance from p to the pencil beam axis. The same mathematical form in Equation 12.9 can be used to model the dose from the primary, multiple Coulomb, or halo components as defined by the depth dose, D, and the appropriate spread.

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389

12.1.4  Beam Representation The dose contribution from a specific beam must now be represented in terms of the pencil beam computational units in Equation 12.9. We have two classes of proton beams: scattered fields (Chapter 5) and pencil beam scanning fields (Chapter 6). These differ, fundamentally, in their means of producing dose distributions. Scattered fields are limited to dose distributions which, by design and in water, have a uniform dose region between the distal range and proximal range (defined as the modulation width). These fields are referred to as spread-out Bragg peak (SOBP) fields as a consequence of the production method in which a single pristine Bragg peak is modulated in fixed energy intervals to create the uniform profile. The set of energies, distributed between a distal-to-proximal range value, of pristine peaks determines the modulation width, whereas the relative contribution of each pristine peak produces the uniform dose over the modulation width. SOBP fields were used from the very beginning of proton radiotherapy as both the energy interval set and the pristine peak weights could be combined in a mechanical range modulator, typically constructed as a rotating wheel where an angular interval encoded both the range and relative contribution by its thickness and its angular width (Chapter 5). The incoming beam of a given energy would pass through these intervals, where the interval thickness reduced the beam energy and the angular width its beam-on time, to produce the characteristic SOBP dose distribution. SOBP fields require an aperture to provide lateral conformation of the SOBP field and a range compensator to achieve distal conformation, while they always produce a uniform lateral dose profile, by design, in water defined by the modulation width and the lateral extent. Scanning fields, in contrast, can achieve any dose distribution in the patient without the need of such devices, although the use of these devices could have some benefit. Note that SOBP fields can also be produced by uniform scanning beams, where the beam intensity is constant during an energy layer. Functionally, such SOBP fields are equivalent to those produced in scattered systems. 12.1.4.1  SOBP Beams Algorithmically, there are some considerations: (1) the apertures and range compensators need to be modeled, (2) the stacking of the pristine peaks needs to be accurately modeled, and (3) some properties of the production system may need to be considered explicitly. In general, an SOBP field is produced in a scattering system (see Chapter 5). The use of a scattering system results in a field that appears to emanate from a “virtual” source. Such a field has an intrinsic inverse square relationship in its depth–dose distribution. The source position can be inferred by measuring the increase in width of a collimated field as a function of distance. Thus,

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a decomposition of a scattered field requires the use of an inverse-square scaled depth–dose distribution in Equation 12.9. The scattering system produces a source with a size correlated to the amount of scattering material in the beam. Thus, there is an intrinsic penumbra associated with the field analogous to that in electron scattered fields (1). The penumbra is quantified by measuring the penumbral edge as a function of distance (from the source) and projecting the penumbral edge at the source position. The projected penumbral width is modeled as a Gaussian spread contribution σs from the “virtual” source to the total pencil beam width. The source size in a proton scattering system is significant and on the order of 5 cm. This source size effect is mitigated by placing the source as far away from the patient as possible (and one reason for the large proton gantry diameter; the other being the significant size and mass of the bending magnet) and to place an aperture as close to the patient as possible. The source size, and σs, is thus demagnified by the ratio of distances. The source size contribution at the calculation point p is  zA − zp  σ s ( zp ) =   σs  SAD − zA 



(12.10)

where zp is the z-position (along the central axis of the SOBP field) of the point p, zA is the z-position of the aperture, and SAD is the distance from the isocenter to the source. SOBP fields use, invariably, a range compensator that shifts the initial range across the field area to that range necessary to “just” place the distal edge of the field beyond the distal target volume surface. The range compensator thus presents various thicknesses of material (typically Lucite) along the lateral extent of the beam. Protons passing through a particular thickness t will scatter as a consequence and introduce an additional contribution σR equal to σR = Lp θR (t)



(12.11)

where θR(t) can be computed by Equations 12.1 and 12.2, or tabulated as in Hong et al. (4), and Lp is the distance from the range compensator intersection point to the calculation point p along the ray from the source to p. The total spread of a pencil beam at the depth of point p is (including Equation 12.3) σT2 = σS2 + σ2R + σ2MCS



(12.12)

Thus, for scattered SOBP fields, produced by set of pristine peaks of energies, R, the dose to a point p becomes



D( p) = ∑ R

 rp2 1 exp −  2 2 πσT2  2 πσT

2

 R  SAD − zp   D∞ (dp )    SAD  

(12.13)

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Dose Calculation Algorithms

where the inverse square correction accounts for the intrinsic divergence of the field and hence each pencil beam. Dose distributions in treatment planning programs are typically obtained through the application of Equation 12.13. The model holds up well compared to Monte Carlo (14, 15) and fails in predictable areas of high-Z materials and distal of heterogeneities. 12.1.4.2  SOBP Production Model There are multiple means of creating SOBP fields. The most common method is to use a rotating modulator wheel with angular segments of widths and thicknesses corresponding to the pullback and weight of individual pristine peaks that comprise an SOBP field (Figure 12.5). The construction of such As Track step

Beam size

105

100

100

% Dose

120

80 % Dose

No BCM modulation With BCM modulation Decreased SSD

Stop angle

60 40 20 0 0

95

220

0 mm 9 mm

101

50 55 60 Depth/mm

180 140 100

20

40

60 80 Depth/mm

100

120

20 40 60 80 Modulation (90-98%)/mm

FIGURE 12.5 The SOBP is constructed from the weighted superposition of a single pristine peak, pulled back (shown as the individual pristine peak depth doses) by successively increasing step thickness on a rotating modulator wheel. The wheel weights are adjusted by modulating the beam current as a function of wheel rotation angle (with BCM modulation curve). In absence of this modulation, the wheel produces the SOBP (no BCM modulation curve). The SOBP is designed to be flat at the nominal SSD of SAD-30 mm (proximal of the distal edge); other SSD values create a slope in the SOBP. The figure in the top right shows the effect of the source size, where the 0-mm line is the SOBP proximal falloff for an infinitesimal spot, whereas the 9-mm line corresponds to the observed softening of the proximal “knee” as a consequence of the source size. The figure in the bottom right shows the stop angle (expressed as an 8-bit value) to achieve the desired modulation. The above SOBP has a range (modulation) equal to 110 (80).

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modulator wheels is an art and, in theory and practice, only achieves a “perfect” uniform SOBP plateau for the design energy. We demonstrate the production and modeling for a rotating modulator wheel corresponding to the system used by IBA (IBA Ltd, Louvain la Neuve, Belgium) in their double-scattering system design. This design has a set of fixed range modulator wheels (implemented as up to three concentric tracks on a single modulator wheel) where the thickness of a track step is a combination of a high-Z (lead) and low-Z (carbon/Lexan) material such that the scattering angle remains constant, independent of total (water equivalent) thickness. The beam subsequently passes through one (of three) scatterer (see Chapter 5) to produce a uniform field up to a 25-cm diameter. The clinical range of energies range from 5 to 30 cm in water and require the use of eight combinations, dubbed options, of track and scatterer. Each of the eight options is further subdivided into three suboptions. Thus, a suboption covers about 1 cm of energy interval over which the energy effect on the shape of the SOBP is assumed negligible. The track rotates at 10 Hz and produces a full SOBP dose distribution in the patient 10 per second. In our clinical practice we achieve SOBP plateaus with a ±0.5% uniformity when the isocenter is positioned slightly (~3 cm) from the distal falloff: SSD = SAD – R + 3, where SSD is source-to-skin difference and Sad is sourceto-axis difference. This requirement is well beyond any theoretical ability to design the proper track thicknesses and angular intervals. The IBA system, however, uses beam current modulation as a function of rotation angle to modulate the track contributions for each pristine peak produced by the track. This modulation as a function of rotation angle (i.e., as a function of position along the track) allows an increase or decrease of current to correct any design limitations. The track is designed up to a maximum modulation width (corresponding to the maximum track step thickness). The current modulation allows any modulation up to the maximum track thickness by turning the current off before the rotation completes. Thus, modulation is a function of rotation angle, referred to as the “stop angle” in this context. The track has discrete steps, and the finite source size (approximately the track width) causes incomplete contributions of the pristine peak dose when the source stops at a junction (see Figure 12.5). Thus an SOBP is not a simple superposition of discrete energy pristine peaks. A model for such a track system specifies, for each track, a base pristine peak depth–dose distribution (defined at a range R equal to the maximum energy of an option), its current modulation distribution, its source size on the track, and its thickness and angular width for each track step (typically on the order of 30 steps). This base pristine peak depth dose is not trivial to obtain. The scattering system inside the housing of the gantry nozzle presents a complex geometry in which the scattered beam is not easily, if at all, characterized. In addition, the measurement has to be done while the modulator wheel is rotating. A simple approach has been to measure only the protons that pass through the first, thinnest step of the track by, essentially,

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Dose Calculation Algorithms

producing an SOBP of zero modulation. The use of this pristine peak, however, fails to produce SOBPs that compare well with measurements. Lu and Kooy (16) describe a rigorous experimental method to measure the pristine peak while the wheel is rotating. This pristine peak does produce an excellent correspondence between calculations and measurements. The SOBP is computed as follows:

D(d) = Q0 ∑ P0 (d − Ti )∫ i

θi θi−1

BCM(θ)A(σQ , θ)dθ



(12.14)

where Q 0 is the total charge delivered in a rotation over the angle θ, P0 is the SOBP depth–dose distribution at the maximum range defined for a track option, BCM is the (relative) beam current modulation over the rotation, and A(σQ, θ) is the fractional area of the beam spot (relative to the total spot area), with spread σQ at the rotation angle. Figure 12.5 shows the result of the model in Equation 12.14 to produce an SOBP at the design SSD and the relevance of the beam current modulation and source size modeling. In clinical practice, the SOBP is specified only in terms of its distal range, typically the 90% (relative to the plateau) range R90, the modulation width from R90 to the proximal falloff, and its dose expressed in monitor units (MUs, the units of the ionization reference chamber). The latter was, by convention, also defined as the 90% value. This, however, leads to a definition of modulation values larger than the range. The latter, in turn, leads (at least in our practice) to issues in beam delivery and field output specification in terms of Gy/MU (9). Therefore, a more consistent definition is the modulation width between the distal R90 and the proximal 98% falloff. This definition, however, does require an accurate description of this proximal falloff and the implementation of Equation 12.14. Its absence can result in a 5-mm error. 12.1.4.3  Scanning Beams Proton pencil beams scanned by orthogonal dipole magnets can irradiate arbitrary field areas without the need for a mechanical collimating aperture. Variation of the pencil beam energy allows control of the pristine peak position within the patient and thus also removes the absolute need for a range compensator. Finally, varying the intensity (expressed as total charge) of the pencil beam allows for dose modulation throughout the target volume. Thus, scanned beams have three degrees of control: energy, position, and charge (intensity). The size of the beam tends to be fixed in current scanning system implementation, although there will be an energy dependence. Pencil beam− scanning systems are generally assumed to deliver their dose in patient in discrete energy layers as changes in energy may require a mechanical manipulation of the beam and “slow” changes in beam-line magnetic systems. Much effort, however, is focused on removing this limitation.

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In a pencil beam−scanning field, the “pure” pencil beam emerges from the beam-line transport system and traverses one or more foils that separate vacuum from air and one or more ionization chambers required for registering current and position. Thus, the overall “thickness” of space between the beam line and the patient is small, on the order of 4 mm. The pencil beam is thus little perturbed. The algorithmic representation of the pencil beam is thus as a “cone” of protons with an elliptical spread (expressed in (σx, σy ) in the reference plane of the beam). By and large the focusing of the pencil beam is ignored and the pencil beam is assumed nondivergent. The use of a range compensator is not excluded and thus the spread will include σR (Equation 12.12). The effect of including an aperture has not been well studied but is expected to improve the penumbral edge for “large” spot size. An elliptical spot size may rotate as a function of gantry angle, which introduces an implementation requirement. The dose from a set of proton pencil beams, R, is



D( p) = ∑ R

 rp2 1 exp  − 2 2 πσT2  2 σT

 R  D∞ (dp ). 

(12.15)

Note the absence of the inverse square correction for the depth dose because the pencil beam is not diverging. The beam will, however, have an inverse square behavior if one or both axes of the pencil beam pivot around a scanning magnet bending source. This effect manifests itself in the ray-tracing of the pencil beam axes through the volume and computationally expresses itself in the computation of rp in Equation 12.15. There are beam configurations where, in fact, one axis is at infinite SAD as a consequence of the beamline magnet layout or where the beam is only scanned in a line as in one of the gantry systems at the Paul Scherrer Institute (PSI, Villigen, Switzerland). 12.1.4.4  Implementation Physical proton pencil beams have the nice mathematical form of Equation 12.15. This, however, may lead to the assumption to directly model the physical pencil beams, spots in the discussion below, produced in a proton delivery system by Equation 12.15. These spots, however, have sizes (3–10 mm σ) that exceed the computational need for resolution. Instead, the correct approach is to first transport infinitesimally narrow mathematical proton pencil beams through the patient to satisfy the need for spatial accuracy in patient and subsequently superimpose the spots. We define these mathematical pencil beams as bixels and define the bixel set B, each with unit number of protons, that covers the required patient volume including targets and organs-at-risk for each treatment beam. We subsequently superimpose the spots, deliverable by the equipment for each field, on top of this bixel space (see Figure 12.6).

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k(j+1)

2∆X

Yk1

Fj(k)

k(j)

Yk0 j

(xj, yj)

j+1

j

Xk0

Xk1

FIGURE 12.6 The transport of spots, physical pencil beams j, through the patient first transports “small” bixels (hatch bar in Gaussian, left) through the patient. The bixels have initial 0 spread and thus only spread as a consequence of in-patient scatter. Each spot j contributes to k(j) bixels proportional to the area of bixel k under the spot j. The subdivision ensures that the transport in patient is at the highest lateral resolution, limited by the bixel area and the bixel spread at depth, and removes the dependency on spot spread on the calculation resolution and performance.

The calculation in patient thus becomes



 D(x) = ∑ S GS 2     1 ×  ∑ K   exp  − 2 S , K dAK   2 ∫  2 πσO (RS , z)   2 σO (RS , z)   

× 

2    K ( x) − exp   2 2   2 πσ p (Rs , ρ)  2 σ p (Rs , ρ) 

DR∞s (ρ)

(12.16a) (12.16b)

(12.16c)

where the first term (12.16a) is the number of protons GS (in units of billions, or Giga-protons Gp) in a pencil beam spot from the set S, the second term (12.16b) is the apportionment of these GS protons, given the optical spread σO2 (RS , z) of the spot, over the set of computational pencil beams K. This set of computational pencil beams K in Equation 12.16c is defined at the highest resolution necessary to accurately represent the dose in the patient. Equation 12.16c models the diffusion of the number of protons, given by the product of (12.16a) × (12.16b), in the patient given the scatter spread σP(RS, ρ) in the patient due to MCS. In a pencil beam–scanning system, the spot spread σO2 (RS , z) in Equation 12.16b is determined by the optical properties of the system and is a function of the spot range RS and position z along the pencil beam spot axis. The parameter ΔS,K denotes the position of a point in the computational pencil beam area AK with respect to the spot coordinate system. The final term (12.16c) follows Pedroni et al. (10), where DR∞ ( z) (in units of Gy·cm2·Gp−1) is the absolute measured depth dose per proton integrated over an infinite plane at depth z, σP(R S, ρ) is the total pencil beam spread at radiological depth ρ caused by MCS in the patient (see Hong et al. [4]), and

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 ( x) is the displacement from the calculation point to the K pencil beam

axis. Equation 12.16 is a phenomenological description of the distribution in patient of protons delivered by the set of spots S. Finally, the product of (12.16b) and (12.16c) is a convenient computational unit in the pencil beam– scanning optimization algorithms and maintained as a look-up table, often dubbed “Dij,” to map the number of protons (12.16a) to dose to a point. The use of mathematical pencil beam bixels increases the computation performance significantly. The main computational burden in a pencil beam algorithm is the part of the algorithm that, at each step along the pencil beam axis, finds the points that are within the Gaussian envelop (line 7 in Figure 12.1). This search time is proportional to the area (i.e., O(σ2)). Thus, tracing the narrowest possible pencil beams, the bixels, improves computational performance. An efficient search algorithm will rely on ensuring that points are efficiently ordered with respect to the pencil beam to ensure that points are indexed as a function of distances along and lateral to the pencil beam axis. 12.1.5  A Scatter-Only Monte Carlo Pencil beam implementations suffer from the assumption that interactions along the central axis are representative within the whole Gaussian envelop. This makes pencil beam models insensitive to heterogeneities near the pencil beam axis, reduces the lateral sensitivity to that of the Gaussian width, and overemphasizes dosimetric diffusion as a consequence of upstream heterogeneities on the pencil beam axis. The intrinsic physics pencil beam model for primary and secondary scatter of protons suffices for clinical modeling of the dose distribution. This allows the definition of a simple Monte Carlo implementation where scatter is modeled on a voxel basis for a proton traversing the voxel. This implementation (pseudocode in Figure 12.7) uses two random numbers: one to select the scattering mechanism based on Equation 12.6 and one to select the azimuthal angle (0–2 π) of scatter along the direction of the incoming proton. The polar angle is the mean scattering angle, either from MCS or halo interactions, based on the voxel density. The large number of voxels assures that this approximation converges to the correct overall scatter in the medium. The Monte Carlo transports individual protons through a volume represented by a rectangular 3D grid of voxels. Each voxel has the relative (to water) stopping power, Sv, obtained, in practice, from CT Hounsfield units (17). We score the dose to a voxel as the sum of energy depositions along the individual proton tracks that traverse the voxel and divide by the voxel mass. A proton, of energy ES, enters a voxel on one of its faces and exits on another. The model computes the (unscattered) exit point along the incoming proton direction (u, v, w) and the distance L between the entrance and this projected exit point. The mean polar MCS scatter angle in the voxel is θ = θ0 (ES)√Sv, whereas the mean polar halo scatter angle is θ = θH (ES)√Sv and the azimuthal angle is randomly uniform between 0 and 2π. The mean scatter

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while E > 0 { 1. Compute current voxel position; 2. If outside of volume, exit; 3. Look up MCS or Halo scattering angle; 4. Generate random azimuth angle; 5. Compute new direction; 6. Estimate traversal distance in voxel; 7. Compute energy loss; 8. Deposit energy in voxel; 9. Reduce current energy; 10. Compute voxel exit point;}

Ei

d = (Ei-Eρ)/pV (θ,ϕ) (s,ρ,) Eo

150

100

50

–25

0 Lateral/mm

25

FIGURE 12.7 Top: pseudocode for the transport of protons through a set of voxels. Only MCS and secondary scattered protons are considered, each with a mean scattering angle scaled to the voxel dimension and density. The resultant code implementation is well suited to a GPU architecture because of its compactness and its lack of secondary particles. Bottom: two pencil beams traversing a medium with alternating high- and low-density regions.

angle θ0(Es) is derived and quantified by Gottschalk (7). The mean scatter angle θH(Es) is fitted to reproduce the observed spread (Equation 12.8). The fraction of protons that scatter with the halo scatter angle and the azimuthal angle are the random variables. The proton direction is adjusted to (u’, v’, w’) given the scattering angles and the actual exit point is computed. The energy loss of the proton along the mean voxel track length 〈L〉 is SV <λ >



∞ W

(E) = T (R , dp ) ×

SW

ρV ρW

× ρV × L .

(12.17)

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The use of a mean track length 〈L〉 serves solely to reduce computational overhead. Computed pristine peak Bragg peaks using Δ〈L〉(E) and their range compared to the original projected range (from PSTAR from the National Institute of Standards and Technology) show excellent agreement. The simplicity of the model offers excellent opportunities for a GPU (graphics-processing unit) implementation. In our implementation of the model in CUDA, on an entry-level nVidia FX1700 card, it achieves a performance of 2,000,000 protons/100 cm2 in 10 s in 1283 voxels. This is compared to our analytic pencil beam algorithm implementation, which computes the same distribution in 30 s. Thus, it is clear that at least a simple Monte Carlo, yet improved compared to a pencil beam model, now outperforms significantly traditional algorithmic model implementations.

12.2  Monte Carlo Algorithms The principles of Monte Carlo simulations are outlined in Chapter 9. This section describes the specific aspects of using Monte Carlo for dose calculation purposes. 12.2.1  Statistical Resolution in a Clinical Setting Other than with analytical methods, the accuracy of the dose calculation with Monte Carlo depends on the calculation time. The more histories that are being tracked the lower the statistical uncertainty. For clinical dose calculations it is important to estimate the number of histories needed. This number depends on the field parameters, for example, on the beam energy and treatment volume. If the whole treatment head is being considered (i.e., if the simulation is not based on a phase space distribution) the required number of histories also depends on the efficiency of the treatment head. For pencil beam scanning, the efficiency of the treatment head is typically more than 90%, whereas for passive scattering it is typically in the order of 3–30%. For passive scattered delivery, a typical number of proton histories for a given patient field is ~25 million at the treatment head entrance to reach ~2% statistical accuracy in the target for a single field based on the treatment planning grid resolution (based on the treatment head at the MGH). This number is quite low compared to photon therapy due to the higher proton LET. If an analysis is done for the entire plan (i.e., not field specific), fewer protons per field may be sufficient. Note that a certain statistical accuracy in the target volume does not guarantee the same accuracy in the organs at risk. However, the impact of statistical deficiencies is less for dose-volume analysis in organs at risk because the dose distribution is less homogeneous (18, 19).

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12.2.2  Improving Monte Carlo Efficiency There are several techniques to improve the computational efficiency of Monte Carlo for proton beams in patients (20, 21). Furthermore, Monte Carlo codes have been specifically designed for fast patient dose calculations using approximations to improve computational efficiency (22–25). One method is to implement track-repeating algorithms in which precalculated proton tracks and their interactions in material are tabulated. The changes in location, angle, and energy for every transport step and the energy deposition along the track are recorded for all primary and secondary particles and reused in subsequent Monte Carlo calculations (26). Particle tracking in a voxel geometry is computationally inefficient because in a standard Monte Carlo code, each particle has to stop when a boundary between two different volumes is crossed. Thus, the maximum step size is limited. This limitation even occurs when two adjacent voxels have the same material composition. Algorithms have been developed to tackle this problem (27, 28). Such algorithms are based on an image segmentation that compromises the regular voxel geometry. The efficiency (and potential compromise in accuracy) depends on the CT resolution. The speed of the Monte Carlo simulation depends on the grid size, but assuming that a step size above 1 mm is typically not warranted: a larger grid size does not translate into a huge gain. Nevertheless, to decrease the statistical uncertainty one might be tempted to interpolate the CT grid to a larger grid. Furthermore, treatment planning algorithms often present dose distributions on a more coarse grid than the one provided by the patient’s CT scan. The problem with resampling the CT grid is that averaging of material compositions is not well defined. Thus, to avoid resampling, the Monte Carlo should operate on the actual CT scan, which is typically in the order of 0.5 to 5 mm. That of course also implies that the Monte Carlo simulations might be required to operate on a nonuniform CT grid as often used clinically (20). Resampling to improve statistical uncertainty can still be done after the dose calculation, where weighting of doses that contribute to a given voxel on a grid can be done accurately based on volume averaging. To improve the computational efficiency smoothing or de-noising algorithms have been suggested to reduce statistical variations in Monte Carlo dose calculation (29–33). These methods need to be applied with caution because regions of low signal are, other than in imaging, not noise but valid information. Some de-noising techniques tend to soften dose falloffs, which could have a negative impact when used in proton therapy. Furthermore, one has to keep in mind that, other than in photon therapy, dose is not directly proportional to particle fluence in proton therapy. 12.2.3  CT Conversion The patient geometry is typically available as a Digital Imaging and Communications in Medicine (DICOM) stream (34). The grid under which

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CT data are stored can be regular or with a nonequidistant slice spacing because regions of greater interest are often scanned with a smaller slice thickness. With a software interface, Monte Carlo codes can use DICOM directly (35–37). Analytical (e.g., pencil beam) dose calculation algorithms in photon therapy use electron density because the dominant energy loss process is interaction with electrons. Protons lose energy by ionizations, MCS, and nonelastic nuclear reactions. Because each interaction type has a different relationship with the material characteristics obtained from the CT scan (38, 39), relative stopping power is being used to define water equivalent tissue properties in proton therapy. Monte Carlo dose calculations are based on a more specific tissue description, that is, material compositions and mass densities. In addition, mean excitation energy for each tissue can be obtained by using Bragg’s rule and the atomic weight of the elements. Mean excitation energies are subject to uncertainties that might be in the order of 5–15% for tissues, which can lead to uncertainties in predicting the correct proton beam range (40). Mean excitation energies for various elements are tabulated by the International Commission on Radiation Units and Measurements (ICRU) (41). Averaged values for tissues are also given directly by the ICRU (42, 43). The accuracy of dose calculations, not only for Monte Carlo methods, is affected significantly by the ability to precisely define tissues based on CT scans (44, 45). CT numbers reflect the attenuation coefficient of human tissues to diagnostic x-rays and may be identical for several combinations of elemental compositions, elemental weights, and mass densities (46). In CT conversion schemes, tissues are grouped into different tissues that share the same material properties (i.e., elemental composition and ionization potential), which are typically between 5 and 30 different tissues (i.e., distinct material compositions are being used) (20, 44, 47). For better accuracy, independent of the number of tissues, the number of densities is typically the same as the number of grey values (CT numbers) (20). Models based on tissue materials or animal tissues have been used to determine the correspondence between Hounsfield numbers and human tissues (45). Stoichiometric calibrations of Hounsfield numbers with mass density and elemental weights allow accurate CT conversion (46). Several conversion schemes have been published (17, 46, 48). A robust division of most soft tissues and skeletal tissues can be done, but soft tissues in the CT number range between 0 and 100 can only be poorly distinguished because CT numbers of soft tissues with different elemental compositions are similar. A conversion table can be extended to higher Hounsfield units in order to deal with high-Z implant materials in the patient (47). Discrepancies in mass density assignments and assignments in elemental compositions can lead to dose uncertainties (44). A relationship between a certain CT number and a combination of materials is not unique, and various fits can lead to a feasible result (46, 49). Not only can the absolute dose

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vary, but also the proton beam range might depend on the accuracy of the CT conversion. For head and neck treatments it was shown that CT conversion schemes can influence the proton beam range in the order of 1–2 mm (49). Any conversion scheme is valid only for the CT scanner used for the underlying measurements. A normalization for the Monte Carlo can be done by either doing a separate stoichiometric calibration or, as an approximation, by simulating relative stopping power values in the Monte Carlo based on a existing CT conversion and then by comparing the results with the planning system conversion curve that had been validated during the commissioning process. Based on this a slight correction of material compositions (or even less cumbersome), mass densities can be done (15, 20, 50). 12.2.4  Absolute Dose Monte Carlo dose calculation results are often presented as relative doses. Absolute doses are typically reported as cGy per MU (15, 51). Absolute dose prediction can be done based on simulations of the ionization chamber readings (Chapter 9). In a segmented ionization chamber the volume used for absolute dosimetry can be quite small (e.g., 1–2 cm in diameter). This causes low statistics when simulating the chamber response (energy deposition events) and thus requires a large number of histories to be simulated. The method is thus not efficient for routine use. An alternative method for simulating absolute doses with Monte Carlo is to simply relate the number of protons at treatment head entrance to the dose in an SOBP in water for a given field specification. With an accurate model of the treatment head this method is equivalent to a direct monitor unit simulation because instead of relating the dose to the impact of the beam at a given plane in the treatment head (in an ionization chamber), one relates the dose to a specific number of protons at treatment head entrance. 12.2.5  Dose-to-Water and Dose-to-Tissue Dose in radiation therapy is traditionally reported as dose-to-water. Analytical dose calculation engines, e.g., pencil beam algorithms, calculate dose by modeling physics relative to water (using the relative stopping power). There is an open discussion whether doses in radiation therapy should be reported as dose-to-water or dose-to-tissue (52). The advent of Monte Carlo is in part responsible for this question. Arguments in favor of using dose-to-water include the fact that clinical experience is based on dose-to-water, that quality assurance and absolute dose measurements are done in water, and that tumor cells in the human body consist mostly of water. Dose constraints in treatment planning are based on our experience with dose-to-water. Monte Carlo dose calculation engines are not based on stopping power relative to water. Instead, they are based on material properties, which are converted from CT numbers: material composition, mass density, and mean

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excitation energy. Naturally, Monte Carlo dose calculation does result in dose-to-tissue. A conversion of Monte Carlo results into dose-to-water thus disregards one of the advantages of Monte Carlo simulations. Nevertheless, to allow a proper comparison between Monte Carlo– and pencil beam–­ generated dose distributions, one has to convert one dose metric to the other. This can be done in Monte Carlo simulations based on known relationships for proton energy–dependent relative stopping powers and on a nuclear interaction parameterization (53). It has been shown that in most cases it is sufficiently accurate (within ~1%) to do a conversion to dose-to-water retroactively by simply multiplying the dose with energy independent relative stopping powers (53). Dose-to-water can be higher by ~10–15% compared to dose-to-tissue in bony anatomy. For soft tissues the differences are typically on the order of 2% (Figure 12.8). Because the difference in mean dose roughly scales linear with the average CT number, a rough scaling based on the CT numbers might be sufficient, depending on the desired precision (53). 12.2.6 Impact of Nuclear Interaction Products on Patient Dose Distributions

(Dw(mean)-Dm(mean))/Dw(mean) [%]

Analytical algorithms are typically based on measured dose distributions and thus include all relevant dose contributions naturally. For Monte Carlo dose calculation one needs to decide which interactions to include. Protons lose energy not only via electromagnetic but also via nuclear interactions. The latter needs to be taken into account, specifically in the entrance region of the Bragg curve (39, 54–57), where it can be well over 10% of the total dose. Monte Carlo simulations need to explicitly generate all secondary particles in order to ensure proper energy balance. Although generating all secondary 12 10 8 6 4 2 0 –2 0

200

400 600 CT number

800

1000

FIGURE 12.8 Percentage difference between dose to water, Dw, and dose to medium, Dm, as a function of the mean Hounsfield unit, CT number, in the volume. Circles, organs at risk; squares, target structures. (From Paganetti, Phys Med Biol., 54, 4399, 2009. With permission.)

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Dose Calculation Algorithms

particles is necessary, it might not be necessary (depending on the application) to track them (Chapter 9). If the range of the particles is smaller than the region of interest (e.g., the size of a voxel in the patient), it might be sufficient to deposit the energy (dose) locally. For patient-related dose calculations, typically only secondary protons from nuclear interactions need to be tracked. Nuclear interaction cross sections show a maximum at a proton energy of about 20 MeV and decrease sharply if the energy is decreased (Chapter 9). As a rule of thumb, the average proton energy in the Bragg peak is about 10% of the initial energy. The contribution of dose due to nuclear interactions becomes negligible close to the Bragg peak position of a pristine Bragg curve because of the decreasing proton fluence and a sharply decreasing cross section. Secondary protons cause a dose build-up in the entrance region of the Bragg curve because of forward emission of secondary protons from nuclear interactions. For an SOBP, nuclear interactions still play a role in the peak because dose regions proximal to the Bragg peak contribute. This leads to a tilt of the dose plateau if their contribution is neglected (57). Figure 12.9 shows the dose contribution from secondary protons compared to the total dose for a treatment field used to treat a spinal cord astrocytoma. Consideration of nuclear interactions is particularly important for pencil beam scanning because each pencil is surrounded by a long-range nuclear halo (Chapter 11). The dose distribution is small for each pencil, but can be significant for a set of pencils delivering dose to the target volume or in the sharp dose gradient at the distal falloff (12, 58). 12.2.7 Differences between Proton Monte Carlo and Pencil Beam Dose Calculation Differences between Monte Carlo–based dose calculation and analytical methods in proton therapy have been demonstrated extensively (11, 15, 24, 59–62). Error analysis can be applied when comparing Monte Carlo and analytical dose calculation and optimization methods (63).

10 30 50 70 90 95 100 102

1 3 5 7 9 9.5 10

FIGURE 12.9 (See color insert.) Dose distribution for one treatment field in a patient treated for a spinal cord astrocytoma. Left: prescribed dose (in %). Right: dose due to secondary protons generated in nuclear interactions (in % of the prescribed dose).

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Pencil beam algorithms are less sensitive to complex geometries and density variations: bone–soft tissue, bone–air, or air–soft tissue interfaces (64). Most pencil beam algorithms project the range based on the water equivalent depth in the patient calculated for individual beam spots. This neglects the position of inhomogeneities relative to the Bragg peak depth (59, 65, 66). Even small discrepancies in local energy deposition can result in changes in range over the entire beam path (20). If a proton beam passes through complex heterogeneous geometries a phenomenon called range degradation occurs (58, 67), which is correctly predicted using Monte Carlo only. Note also that some pencil beam models do not consider aperture-edge scattering, which can cause dose errors for the first few centimeters entering the patient (68). One of the areas where pencil beam algorithms specifically show weaknesses is in the presence of lateral heterogeneities (11, 60, 61). Figure 12.10 demonstrates the inaccurate consideration of interfaces parallel to the beam path with a pencil beam algorithm due to the treatment of multiple scattering in heterogeneous media. It is noteworthy that large density gradients that can be tangential to the beam do not only occur in the patient but also in range compensators. Treatment planners are typically aware of dose calculation uncertainties and take these into consideration when prescribing fields, for example, by avoiding pointing a beam toward a critical structure and by applying safety margins (see Chapter 10). Because of such precautions, differences between pencil beam algorithms and Monte Carlo dose calculations turn out to be

1 Gy(RBE) 3 Gy(RBE) 5 Gy(RBE) 7 Gy(RBE) 9 Gy(RBE) 11 Gy(RBE) 13 Gy(RBE) 15 Gy(RBE) 17 Gy(RBE) FIGURE 12.10 (See color insert.) Axial views of dose distributions calculated using a commercial planning system based on a pencil beam algorithm (right) and a Monte Carlo system (15) (left). The patient was treated for a spinal cord astrocytoma with three coplanar fields (same as Figure 12.9). The figure only shows one of the fields. The Monte Carlo dose calculation was based on a CT with 176 × 147 × 126 slices with voxel dimensions of 0.932 × 0.932 × 2.5/3.75 mm3 (variable). The yellow circle indicates the dosimetric impact of an interface parallel to the beam path. Doses are in Gy(RBE).

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small when analyzing dose volume histograms from carefully designed plans. It appears that the differences are not always clinically significant (15, 61). More accurate dose calculations might however lead to the reduction of margins. A heterogeneity index parameterizes lateral tissue heterogeneities for a beam spot and might be useful to decide if significant differences between pencil beam algorithm and Monte Carlo algorithm are to be expected (64). Here, the radiological depth of each voxel is calculated. Next, a disk of radius 3σ0 orthogonal to the pencil beam axis around the Bragg peak position is defined, where σ0 is the initial lateral spread. The homogeneity index is defined as the standard deviation of fluence weighted radiological depths on this disc. A slight variation of this method was used to analyze proton dose calculations (61). It was shown that the dose error (variation of the relative mean systematic error) between pencil beam– and Monte Carlo–generated dose calculation depends on the heterogeneity index. Monte Carlo simulations have been used to benchmark analytical algorithms (11, 15, 69) or to help commissioning planning systems (70, 71). Monte Carlo is also the method of choice in special geometries. For example, tantalum markers used to stabilize bony anatomy after surgery or as markers for imaging can lead to significant dose perturbations typically not predicted accurately by pencil beam algorithms (72). It is likely that the future of dose calculation lies in Monte Carlo. Currently the computational efficiency of most Monte Carlo codes is not optimized for routine clinical use. Monte Carlo can be used for recalculation of pencil beam–optimized dose distributions (with subsequent fine-tuning) or for Monte Carlo treatment planning including iterative dose calculation for optimization. If Monte Carlo treatment planning is to be done, it needs to be incorporated into a framework for treatment plan optimization (61, 73). A compromise would be to utilize a Monte Carlo dose engine only at a limited number of checkpoints during the optimization process. 12.2.8  Clinical Implementation If proton Monte Carlo dose calculation is not part of commercial treatment planning systems, one might be interested in implementing an in-house Monte Carlo system in the clinic, which can then be used for routine dose calculation as well as for research purposes (e.g., the Monte Carlo system used at MGH (15, 76), see Figure 12.11). To facilitate data flow between the planning system and the Monte Carlo, the CT information and planning information needs to be imported from the planning system, and input files for the Monte Carlo phase space and dose calculation have to be created. Simulations of phase spaces is common practice when using Monte Carlo in radiation therapy even though in proton therapy it is unlikely that

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FIGURE 12.11 (For color image, see cover) Protons tracked through a treatment head (left), particle tracks in a volume-rendered CT (middle), and dose (right) in a volume-rendered CT simulated with the TOPAS Monte Carlo system (76) combined with the graphics system gMocren (75).

identical beam settings are prescribed for different patients and thus reusing a phase space is unlikely. However, the separation of the phase space calculation from the dose calculation might be done because the treatment head may overlap with the patient CT volume (depending on the size of the air gap)  (15). Overlapping geometries can cause ambivalent situations in a Monte Carlo transport environment and should be avoided. A phase space distribution can thus be used as a starting point for simulations inside the CT volume. If the planning system prescribes the settings of treatment head components (e.g., the modulator wheel), the phase space can be simulated accordingly. If the planning system prescribes solely range and modulation width, the translation into treatment head settings is typically done by the treatment control software for the actual treatment. Consequently, this algorithm needs to be incorporated into the Monte Carlo code (15, 74). Aperture and compensator are also prescribed by the planning systems and can be modeled in the Monte Carlo using the milling machine files (see Chapter 9). For proton beam scanning, the planning system will most likely provide a matrix of beam spot energies, beam spot weights, and beam spot positions, which can be translated into Monte Carlo settings in a straightforward manner. Whether a complex beam model is needed to prescribe the distribution of these parameters within each spot depends on the delivery system (see Chapter 9). The patient’s CT image can be imported in at least two ways, either by importing a DICOM stream directly in the Monte Carlo (35, 36) or by importing CT information based on a planning system–specific format (15, 50). The latter has the advantage that all Monte Carlo related input data can be imported from the planning system instead of importing patient data as DICOM from an external database. Within the Monte Carlo the CT image might be translated into a Monte Carlo–specific format, and the calculations can be done on grids identical or different from the CT grid or the grid used for treatment planning.

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Besides the radiation field and the patient geometry other vital information is needed to simulate a patient treatment. These are the gantry angle, the patient couch angle, the isocenter position of the CT in the coordinate system of the planning program, the number of voxels and slice dimensions in the CT coordinate system, the size of the air gap between treatment head and patient, and the prescribed dose (15). Also, couch and gantry rotations have to be applied. The different coordinate systems (treatment control system, treatment head, planning system, and CT system) have to be converted into a common simulation coordinate system. A user interface tailored to the planning system might be needed to facilitate the data flow from the planning system to the Monte Carlo system. Results of the Monte Carlo simulation might be analyzed in the planning system (if this is agreed upon with the vendor) or using a standalone visualization tool. 12.2.9  Simplified Monte Carlo Dose Calculations There are hybrid methods that combine aspects of Monte Carlo simulation and analytical algorithms (see 12.1.5). There are many ways to improve the accuracy of pencil beam algorithms by adding Monte Carlo components (e.g., using spot decomposition), which are often associated with significantly decreased computational efficiency (11, 61). One obvious use of Monte Carlo in dose calculation algorithms without the disadvantage of long calculation times is the implementation of Monte Carlo–generated kernels to be used as look-up tables (61). Precalculated depth–dose curves in water can serve as input for pencil beam algorithms. Simplified Monte Carlo methods using measured depth–dose curves in water or other materials as input have also been proposed (25). A significant speed improvement compared to codes like Geant4 and FLUKA (see Chapter 9) has been reported for VMCpro (22). Here, various approximations were introduced, for example, a simplified multiple-­ scattering algorithm and density-scaling functions instead of actual material compositions. Nuclear interactions are treated as a correction to electromagnetic interactions by using parameterizations and distribution sampling, and it was shown that these are valid for dose calculations, at least for broad beams.

Acknowledgments The authors thank Dr. Bryan Bednarz for proofreading parts of the manuscript and Dr. Jan Schümann for help with the figures.

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References

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20. Jiang H, Paganetti H. Adaptation of GEANT4 to Monte Carlo dose calculations based on CT data. Med Phys. 2004;31:2811–8. 21. Yepes P, Randeniya S, Taddei PJ, Newhauser WD. Monte Carlo fast dose calculator for proton radiotherapy: application to a voxelized geometry representing a patient with prostate cancer. Phys Med Biol. 2009 Jan 7;54(1):N21–N28. 22. Fippel M, Soukup M. A Monte Carlo dose calculation algorithm for proton therapy. Med Phys. 2004 Aug;31(8):2263–73. 23. Kohno R, Takada Y, Sakae T, Terunuma T, Matsumoto K, Nohtomi A, et al. Experimental evaluation of validity of simplified Monte Carlo method in proton dose calculations. Phys Med Biol. 2003;48:1277–88. 24. Tourovsky A, Lomax AJ, Schneider U, Pedroni E. Monte Carlo dose calculations for spot scanned proton therapy. Phys Med Biol. 2005;50:971–81. 25. Kohno R, Sakae T, Takada Y, Matsumoto K, Matsuda H, Nohtomi A, et al. Simplified Monte Carlo dose calculation for therapeutic proton beams. Jpn J Appl Phys. 2002;41:L294–97. 26. Li JS, Shahine B, Fourkal E, Ma CM. A particle track-repeating algorithm for proton beam dose calculation. Phys Med Biol. 2005 Mar 7;50(5):1001–10. 27. Sarrut D, Guigues L. Region-oriented CT image representation for reducing computing time of Monte Carlo simulations. Med Phys. 2008 Apr;35(4):1452–63. 28. Hubert-Tremblay V, Archambault L, Tubic D, Roy R, Beaulieu L. Octree indexing of DICOM images for voxel number reduction and improvement of Monte Carlo simulation computing efficiency. Med Phys. 2006 Aug;33(8):2819–31. 29. Deasy JO. Denoising of electron beam Monte Carlo dose distributions using digital filtering techniques. Phys Med Biol. 2000;45:1765–79. 30. Deasy JO, Wickerhauser M, Picard M. Accelerating Monte Carlo simulations of radiation therapy dose distributions using wavelet threshold de-noising. Med Phys. 2002;29:2366–73. 31. Fippel M, Nuesslin F. Smoothing Monte Carlo calculated dose distributions by iterative reduction of noise. Phys Med Biol. 2003;48:1289–304. 32. Kawrakow I. On the de-noising of Monte Carlo calculated dose distributions. Phys Med Biol. 2002;47:3087–103. 33. De Smedt B, Vanderstraeten B, Reynaert N, De Neve W, Thierens H. Investigation of geometrical and scoring grid resolution for Monte Carlo dose calculations for IMRT. Phys Med Biol. 2005;50:4005–19. 34. ACR-NEMA. Digital Imaging and Communications. ACR-NEMA Standards Public­ation, National Electrical Manufacturer’s Association, Washington, D.C. 1985;300. 35. Kimura A, Tanaka S, Aso T, Yoshida H, Kanematsu N, Asai M, et al. DICOM interface and visualization tool for Geant4-based dose calculation. IEEE Nuclear Science Symposium Conference Record. 2005;2:981–4. 36. Kimura A, Aso T, Yoshida H, Kanematsu N, Tanaka S, Sasaki T. DICOM data handling for Geant4-based medical physics application. IEEE Nuclear Science Symposium Conference Record. 2004;4:2124–7. 37. Van Riper KA. A CT and MRI scan to MCNP input conversion program. Radiat Protect Dosim. 2005;115:513–16. 38. Matsufuji N, Tomura H, Futami Y, Yamashita H, Higashi A, Minohara S, et al. Relationship between CT number and electron density, scatter angle and nuclear reaction for hadron-therapy treatment planning. Phys Med Biol. 1998;43:3261–75.

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39. Palmans H, Verhaegen F. Assigning nonelastic nuclear interaction cross sections to Hounsfield units for Monte Carlo treatment planning of proton beams. Phys Med Biol. 2005;50:991–1000. 40. Andreo P. On the clinical spatial resolution achievable with protons and heavier charged particle radiotherapy beams. Phys Med Biol. 2009 Jun 7;54(11):N205–15. 41. ICRU. Stopping Powers and Ranges for Protons and Alpha Particles. International Commission on Radiation Units and Measurements, Bethesda, MD. 1993;Report No. 49. 42. ICRU. Tissue Substitutes in Radiation Dosimetry and Measurement. International Commission on Radiation Units and Measurements, Bethesda, MD. 1989;Report No. 44. 43. ICRU. Photon, Electron, Proton and Neutron Interaction Data for Body Tissues. International Commission on Radiation Units and Measurements, Bethesda, MD. 1992;Report No. 46. 44. Jiang H, Seco J, Paganetti H. Effects of Hounsfield number conversions on patient CT based Monte Carlo proton dose calculation. Med Phys. 2007;34:1439–49. 45. Schaffner B, Pedroni E. The precision of proton range calculations in proton radiotherapy treatment planning: experimental verification of the relation between CT-HU and proton stopping power. Phys Med Biol. 1998;43:1579–92. 46. Schneider W, Bortfeld T, Schlegel W. Correlation between CT numbers and tissue parameters needed for Monte Carlo simulations of clinical dose distributions. Phys Med Biol. 2000;45:459–78. 47. Parodi K, Paganetti H, Cascio E, Flanz JB, Bonab AA, Alpert NM, et al. PET/ CT imaging for treatment verification after proton therapy: a study with plastic phantoms and metallic implants. Med Phys. 2007 Feb;34(2):419–35. 48. du Plessis FCP, Willemse CA, Loetter MG, Goedhals L. The indirect use of CT numbers to establish material properties needed for Monte Carlo calculation of dose distributions in patients. Med Phys. 1998;25:1195–201. 49. Espana Palomares S, Paganetti H. The impact of uncertainties in the CT conversion algorithm when predicting proton beam ranges in patients from dose and PET-activity distributions. Phys Med Biol. 2010;55:7557–72. 50. Parodi K, Ferrari A, Sommerer F, Paganetti H. Clinical CT-based calculations of dose and positron emitter distributions in proton therapy using the FLUKA Monte Carlo code. Phys Med Biol. 2007 Jun 21;52(12):3369–87. 51. Paganetti H. Monte Carlo calculations for absolute dosimetry to determine output factors for proton therapy treatments. Phys Med Biol. 2006;51:2801–12. 52. Liu HH, Keall P. Dm rather than Dw should be used in Monte Carlo treatment planning. Med Phys. 2002;29:922–4. 53. Paganetti H. Dose to water versus dose to medium in proton beam therapy. Phys Med Biol. 2009;54:4399–421. 54. Carlsson CA, Carlsson GA. Proton dosimetry with 185 MeV protons. Dose ­buildup from secondary protons and recoil electrons. Health Phys. 1977; 33:481–84. 55. Laitano RF, Rosetti M, Frisoni M. Effects of nuclear interactions on energy and stopping power in proton beam dosimetry. Nucl Instrum Methods A. 1996;376:466–76. 56. Medin J, Andreo P. Monte Carlo calculated stopping-power ratios, water/air, for clinical proton dosimetry (50-250 MeV). Phys Med Biol. 1997;42:89–105.

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57. Paganetti H. Nuclear Interactions in proton therapy: dose and relative biological effect distributions originating from primary and secondary particles. Phys Med Biol. 2002;47:747–64. 58. Sawakuchi GO, Titt U, Mirkovic D, Mohan R. Density heterogeneities and the influence of multiple Coulomb and nuclear scatterings on the Bragg peak distal edge of proton therapy beams. Phys Med Biol. 2008 Sep 7;53(17):4605–19. 59. Petti PL. Evaluation of a pencil-beam dose calculation technique for charged particle radiotherapy. Int J Radiat Oncol, Biol Phys. 1996;35:1049–57. 60. Schaffner B, Pedroni E, Lomax A. Dose calculation models for proton treatment planning using a dynamic beam delivery system: an attempt to include density heterogeneity effects in the analytical dose calculation. Phys Med Biol. 1999;44:27–41. 61. Soukup M, Alber M. Influence of dose engine accuracy on the optimum dose distribution in intensity-modulated proton therapy treatment plans. Phys Med Biol. 2007;52:725–40. 62. Szymanowski H, Oelfke U. Two-dimensional pencil beam scaling: an improved proton dose algorithm for heterogeneous media. Phys Med Biol. 2002;47:3313–30. 63. Jeraj R, Keall PJ, Siebers JV. The effect of dose calculation accuracy on inverse treatment planning. Phys Med Biol. 2002;47:391–407. 64. Pflugfelder D, Wilkens JJ, Szymanowski H, Oelfke U. Quantifying lateral tissue heterogeneities in hadron therapy. Med Phys. 2007 Apr;34(4):1506–13. 65. Petti PL. Differential-pencil-beam dose calculations for charged particles. Med Phys. 1992;19:137–49. 66. Urie M, Goitein M, Wagner M. Compensating for heterogeneities in proton radiation therapy. Phys Med Biol. 1984 May;29(5):553–66. 67. Urie M, Goitein M, Holley WR, Chen GTY. Degradation of the Bragg peak due to inhomogeneities. Phys Med Biol. 1986;31:1–15. 68. Titt U, Zheng Y, Vassiliev ON, Newhauser WD. Monte Carlo investigation of collimator scatter of proton-therapy beams produced using the passive scattering method. Phys Med Biol. 2008 Jan 21;53(2):487–504. 69. Sandison GA, Lee C-C, Lu X, Papiez S. Extension of a numerical algorithm to proton dose calculations. I. Comparisons with Monte Carlo simulations. Med Phys. 1997;24:841–49. 70. Koch N, Newhauser W. Virtual commissioning of a treatment planning system for proton therapy of ocular cancers. Radiat Protect Dosim. 2005;115(1-4):1 59–63. 71. Newhauser W, Fontenot J, Zheng Y, Polf J, Titt U, Koch N, et al. Monte Carlo simulations for configuring and testing an analytical proton dose-calculation algorithm. Phys Med Biol. 2007 Aug 7;52(15):4569–84. 72. Newhauser W, Fontenot J, Koch N, Dong L, Lee A, Zheng Y, et al. Monte Carlo simulations of the dosimetric impact of radiopaque fiducial markers for proton radiotherapy of the prostate. Phys Med Biol. 2007 Jun 7;52(11):2937–52. 73. Moravek Z, Rickhey M, Hartmann M, Bogner L. Uncertainty reduction in intensity modulated proton therapy by inverse Monte Carlo treatment planning. Phys Med Biol. 2009 Aug 7;54(15):4803–19. 74. Paganetti H, Jiang H, Lee S-Y, Kooy H. Accurate Monte Carlo for nozzle design, commissioning, and quality assurance in proton therapy. Med Phys. 2004;31:2107–18.

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13 Precision and Uncertainties in Proton Therapy for Nonmoving Targets Jatinder R. Palta and Daniel K. Yeung CONTENTS 13.1 Introduction................................................................................................. 414 13.2 Range Uncertainties in Clinical Proton Beams...................................... 415 13.2.1 Inherent Uncertainties in Linear Stopping Power..................... 415 13.2.2 Uncertainties in the Formation of Broad Clinical Proton Beams (Laterally and In-Depth)................................................... 416 13.2.3 Uncertainties in the Determination of Radiological Thicknesses of Bolus/Compensator Materials and Accessories....................................................................................... 417 13.3 Range Degradation in Patients................................................................. 417 13.3.1 Patient Alignment and Setup in the Treatment Beam.............. 418 13.3.2 Relative Motion of Internal Structures with Respect to the Target Volume................................................................................. 418 13.3.3 Misalignment of the Apertures and Compensator (If Present) with the Target Volume and Critical Organs......... 419 13.4 Impact of Tissue-Density Heterogeneities.............................................. 419 13.4.1 Bulk Heterogeneities Intersecting the Full Beam...................... 420 13.4.2 Bulk Heterogeneities Partially Intersecting the Beam.............. 421 13.4.3 Small but Complexly Structured Heterogeneities Intersecting the Beam....................................................................422 13.5 CT Conversion Uncertainties....................................................................423 13.6 Planning and Delivery Uncertainties...................................................... 425 13.6.1 Patient Selection.............................................................................. 425 13.6.2 Beam Delivery Techniques............................................................ 426 13.6.3 Positioning, Immobilization, and Localization.......................... 426 13.6.4 Imaging for Treatment Planning.................................................. 427 13.6.5 Proton Treatment Planning........................................................... 427 13.6.6 Uncertainty in Planning and Delivery........................................428 13.7 Considering Uncertainties in Planning and Delivery........................... 430 13.8 Summary......................................................................................................430 References.............................................................................................................. 432

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13.1  Introduction Proton therapy allows for conformal dose distributions with sharp dose falloff for complex target volumes and unprecedented lower doses in normal tissue as compared to state-of-the-art conventional radiotherapy. Unlike three-dimensional conformal radiotherapy (3DCRT), the precision and accuracy of both the treatment planning and delivery of proton therapy are greatly influenced by random and systematic uncertainties associated with the delineation of volumes of interest in 3D imaging, imaging artifacts, tissue heterogeneities, patient immobilization and setup, inter- and intrafractional patient and organ motion, physiological changes, and treatment delivery. Furthermore, the locations, shapes, and sizes of diseased tissue can change significantly because of daily positioning uncertainties and anatomical changes during the course of radiation treatments. Transient intrafractional changes, such as rectal and bladder filling status, in the treatment of prostate cancer, can also introduce uncertainties in dose delivery. Because of these changes, the 3D computed tomography (CT) images used for radiation treatment planning do not necessarily correspond to the actual position of the anatomy at the delivery time of each treatment fraction or even to the mean treatment position. Therefore, the traditional assumption that the anatomy discerned from 3DCT images acquired for planning purposes is applicable for every fraction is treated with suspicion in proton therapy. The published literature concerning acceptable planning and delivery precision and accuracy in proton therapy is sparse. However, the dose-response curve in radiation therapy is quite steep in certain cases, and evidence suggests that a 7–10% change in the dose to the target volume may result in a significant change in tumor-control probability (1). Similarly, such a dose alteration may also result in a sharp change in the incidence and severity of radiation-induced morbidity. Surveying the evidence on effective and excessive dose levels, Herring and Compton (2) concluded that a therapeutic system should be capable of delivering a dose to the tumor volume within 5% of the dose prescribed. The International Commission on Radiation Units and Measurements (ICRU) Report 24 (1) lists several studies in support of this conclusion. Because the finite range of protons makes proton therapy more susceptible to tissue-­ density uncertainties than photon therapy, achieving the aforementioned dose accuracy in proton therapy is a challenge. The primary effect of interfractional variations in the shapes, sizes, and positions of anatomical structures; tissue heterogeneities; uncertainties in the conversion of CT numbers to relative electron densities; imaging artifacts; and beam delivery uncertainties in conventional photon therapy is that they smear dose distribution in a patient (3–5). On the other hand, similar uncertainties in proton therapy can result in significantly compromised target coverage and/or normal-­tissue sparing, which limit the full potential of proton therapy. This chapter describes

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precisions and uncertainties associated with proton therapy for nonmoving targets; it also provides strategies for mitigating some of these uncertainties.

13.2  Range Uncertainties in Clinical Proton Beams Proton beams are used in radiation therapy because of the physical characteristics of energy loss by protons as they penetrate into matter, namely, (1) protons have a finite depth of penetration into material, the magnitude of which depends on their energy and on the stopping power of irradiated material; (2) protons exhibit a Bragg peak with negligible dose at the end of their range; and (3) the dose from a proton beam falls off sharply, both laterally and distally. Figure 13.1 shows the relationship between the protonbeam energy and its maximum penetration in water. However, the clinical proton beams are not mono-energtic and do not exhibit the same relationship as shown in Figure 13.1. Clinical proton beams have energy and angular spread, which is a result of energy losses and scattering in beam-modifying devices, in dosimetric equipment in beam line, and in the air gap. Therefore, the factors that contribute to range uncertainties in clinical proton beams include the following: • Inherent uncertainties in linear stopping power • Uncertainties in the formation of broad clinical proton beams (laterally and in-depth) • Uncertainties in the determination of radiological thicknesses of bolus/compensator materials and accessories 13.2.1  Inherent Uncertainties in Linear Stopping Power In a recent publication (6), Andreo explained that the range of I-values for water and tissue-equivalent materials stated in ICRU reports 37, 49, and Range in water / cm

120 100 80 60 40 20 0

0

100 200 300 400 Proton energy / MeV

FIGURE 13.1 Proton range in water as a function of energy.

500

416

dE/dz (MeV/g cm2) per incident particle

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4

3

122 MeV Protons on water: Iw- dependence 0.3 g/cm2

P122Iw = 67eV P122Iw = 75eV P122Iw = 80eV

2

1

0 9.5

Peak spread is .7 g/cm2 for 230 MeV protons

10.0

11.0 10.5 Depth in water (g/cm2)

11.5

FIGURE 13.2 Variation of the depth of Bragg peak for the I-values of water 67, 75, and 80 eV for a 122-MeV proton beam. (From Andreo, Phys Med Biol., 54(11), N205, 2009. With permission.)

73 (7–9) for the collision stopping-power formulas, namely 67, 75, and 80 eV, yield a spread of the Bragg peak’s depth as well as a spread of up to 3 mm for a 122-MeV proton beam (Figure 13.2). He also found that the uncertainty in the Bragg peak is energy dependent due to other energy-loss competinginteraction mechanisms. Although accurate depth–dose distribution measurements in water can be used when empirical dose-calculation models are developed, the energy dependence of range uncertainties causes substantial limitations. In the case of in vivo human tissues, where distribution measurements are not feasible, a spread of the Bragg peak’s depth due to the various soft-tissue compositions is of the same magnitude or more than that of water. This finding indicates that the inherent uncertainty in the computation of linear stopping power of water and tissue equivalent material can result in an uncertainty of ±1.5%–2.0% in the range calculation of a clinical proton beam. 13.2.2 Uncertainties in the Formation of Broad Clinical Proton Beams (Laterally and In-Depth) A broad proton therapy beam can be formed by passive scattering or by dynamic scanning of a pencil beam both laterally and in-depth. In passive scattering, the placement of scattering material in the beam provides a nearuniform dose within the field; a variable thickness propeller that rotates in the beam gives uniform dose in-depth. In beam scanning, lateral and indepth uniform dose distribution is achieved by scanning a pencil beam or a spot both laterally and in-depth (by changing its energy). The lateral

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positions and weights of each pencil beam or spot of a particular energy level determine the lateral distribution for proton energy; weighting the pencil beams or spots at each position within the field determines the distribution in-depth. In either method, the range of protons is changed either by inserting absorbers into the beam path or by changing the beam energy upstream. Typically, proton-beam energy uncertainty introduces a systematic range of uncertainty of ±0.6–1.0 mm; however, because of the physical introduction of beam-modifying devices in the beam line, the reproducibility of the range is ±1.0 mm for passively scattered proton beams. 13.2.3 Uncertainties in the Determination of Radiological Thicknesses of Bolus/Compensator Materials and Accessories Passively scattered proton beams utilize physical range compensators to achieve distal conformance of the dose distribution to the target volume. The thickness profile of the compensator is calculated based on the difference between the distal ranges of the given ray to that of the global maximum for the beam. Based on the stopping power of the compensator material used, the water equivalent thicknesses necessary for the range pullbacks are converted to physical thicknesses. The compensator is milled out of acrylic, wax, or other low atomic number (Z) materials to minimize additional scatter increased penumbra from the compensator. The nonuniformity of stock compensator materials introduces small uncertainties in their relative stopping power, which in turn affects the range of protons. Sharp gradients in the compensator-thickness profile can also induce fluence perturbation as protons are preferentially scattered away from the thicker part toward adjacent thinner areas. This scattering can result in hot and cold spots of 10%– 20% in dose near such gradients and minor range degradation. Furthermore, nonuniformities in the thickness and/or composition of the accessories (e.g., immobilization devices, tabletops, and head holders) can also increase range uncertainties. Range uncertainties introduced by both compensators and accessories are generally systematic and ±1.0 mm.

13.3  Range Degradation in Patients Proton beams have a finite and controllable penetration in-depth, which is strongly affected by the stopping-power characteristics of the tissues through which they pass. Therefore, patient-tissue heterogeneities and their interfractional variability in the beam path during treatment add to random uncertainties in range; thus, they contribute to range degradation. In clinical practice, two key parameters, the range and modulation, are required to select the proton beam energy and spread-out Bragg peak

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(SOBP) width for adequate proximal and distal coverage of the target volume. Proton treatment–planning systems typically perform dose calculations based on a pencil beam grid with a resolution of the order of 1–3 mm. The range and modulation width is then computed based on the most proximal and distal points at which each pencil beam intercepts the target volume. Afterwards, ray tracing is performed through the 3D image set to calculate the total water equivalent thicknesses between these two points, which in turn yields the proximal and distal ranges for each pencil beam. The factors that contribute toward range degradation in clinical proton beams include the following: • Patient alignment and setup in the treatment beam • Relative motion of internal structures with respect to the target volume • Misalignment of the apertures and compensator (if present) with the target volume and critical organs 13.3.1  Patient Alignment and Setup in the Treatment Beam If one wants the high-dose volume to cover the target up to its distal surface over the entire field, patient alignment and setup must be very precise. Conformance of the dose distribution with the distal edge of the target volume, often referred to as “distal edge conformance,” depends on the location of the distal target surface and on the presence or absence of intervening tissue heterogeneities. Therefore, uncertainties in patient alignment and proton beam setup directly translate into range degradation. The degree of range degradation is highly variable and is dependent on tissue heterogeneities in the treatment field and the surface contour of the patient. Selecting “good” beam directions is essential in proton beam therapy. One should avoid beam directions that pass through complex or high-Z heterogeneities and large air cavities that may change due to patient motion or misalignment or that are tangential to the patient surface. 13.3.2 Relative Motion of Internal Structures with Respect to the Target Volume The finite penetration of protons creates “distal edge conformance.” However, the relative motion of internal structures with respect to the target volume (e.g., due to bladder and rectal filling, tumor growth or shrinkage, and movement of bony structures and/or air cavities along the beam path) results in the degradation of high-dose conformation to the distal surface of the target volume. The clinical consequences of this effect can be variable and potentially severe. Hence, one should avoid beam directions that require protons to stop directly in front of critical structures. Non-coplanar beam directions

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that avoid critical structures directly, such as vertex or superior oblique fields in treatments of the brain and the base of the skull, are common and often advantageous in proton therapy. 13.3.3 Misalignment of the Apertures and Compensator (If Present) with the Target Volume and Critical Organs In passive beam scattering and uniform scanning, a brass or cerrobend aperture controls lateral coverage, whereas a compensator that shifts the SOBP upstream along each ray line achieves the distal range pullback. Unfortunately, this approach has weaknesses. It does not allow for possible misalignment between the compensator and the patient because of to patient-setup uncertainties and the motion of internal structures. It also ignores multiple Coulomb scattering (MCS). One can mitigate the scattering problem by avoiding beam angles that result in sharp gradients in the compensator, such as a tangential approach to bony ridges, large air cavities, or thick metal implants. Alternatively, one can smear the compensator laterally so that its thickness at any point is the least thickness within its neighborhood defined by the specified smearing radius (see Chapter 10). The consequence of the smearing process is that it assures target coverage, even in the face of setup error and patient motion. This approach, however, has two major drawbacks: (1) it exaggerates the vertical walls in the compensator design, which can cause significant dose overshoot and undershoot, and (2) it degrades distal dose conformance, limiting the ability to spare adjacent critical structures distal to the target. Smoothing can be used to thin and smooth out the compensator thickness profile in the field-margin area. This technique helps remove sharp gradients and allows for adequate penetration even in the case of misalignment or patient motion but only at the expense of less distal conformance. Because of misalignment of the apertures and compensators, range degradation varies. One solution is to avoid proton beam orientations that exacerbate the effect of aperture and compensator misalignment. These approaches to compensation for distal conformance of the target volume work reasonably well for most tissues in the human body; however, they are not adequate when dense high-Z heterogeneities, such as metallic implants, are in the beam’s path. Beam scanning can overcome some of these issues. For example, intensity-modulated proton therapy, which allows for conformal avoidance of such implants, is a possible alternative.

13.4  Impact of Tissue-Density Heterogeneities The influence of and compensation for heterogeneities on dose distribution is far more critical for protons than photons. Heterogeneities alter the

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penetration and lateral scattering of protons in the patient. The dosimetric impacts of these two effects in the presence of heterogeneities in proton beams, relative to what occurs in a homogeneous medium, can potentially be substantial because of the sharp dose falloff characteristics of protons. When designing treatment beams, one must account for the presence of heterogeneities proximal to or within the target volume by not only calculating their influence on target volume coverage but also compensating for range modifications. The influence of heterogeneities varies by clinical situation. Three potential scenarios are possible: (1) the heterogeneity extends through the entire proton beam; (2) the heterogeneity intercepts part of the proton beam in the lateral direction; or (3) the heterogeneity is small and complexly structured in the proton beam. 13.4.1  Bulk Heterogeneities Intersecting the Full Beam A proton beam’s energy loss in a section of material of a particular areal density (g/cm 2) is similar for all materials with the exception of highly hydrogenous substances (in which Z/A > 0.5) and high-Z elements (in which Z/A < 0.5). Protons lose energy in a medium primarily through electromagnetic interactions with atomic electrons. Because the mass of protons is large compared with the mass of electrons, they lose only a small fraction of their energy and are deflected very little in each interaction. Although the probability of nuclear interactions increases with energy of protons, its impact in the therapeutic energy range is small except for the shape of the Bragg peak. Nuclear interactions essentially decrease the intensity of protons in the beam by producing secondary particles. These particles may be important from the biological point of view because of their higher relative biological effectiveness (RBE) values but their impact on physical dose distribution is negligible. Therefore, interposing a material composed of a substance other than that of the surrounding medium primarily increases or decreases the beam’s range but does not affect the shape of the depth dose in the region distal to the heterogeneity. The change in a beam’s range (ΔR) in such a situation (measured in units of length and not medium-equivalent density) is altered by an amount given by



(

)

R = t ρmedium − ρeqslab / ρwater , eq

(13.1)

where t is the physical thickness of the interposed slab, ρmedium is the water eq equivalent density of the interposed slab, and ρeqslab is the water equivalent density of the surrounding medium. The water equivalent density is estimated by comparing the mass stopping power of the material in question with the mass stopping power of water at the energy of therapeutic

Precision and Uncertainties in Proton Therapy for Nonmoving Targets

421

interest. Alternatively, it can be obtained by measuring the change in residual range in water of protons passing through a water tank with and without a physical thickness, t of the interposed slab. These relationships hold equally when the interposed slab replaces the entire surrounding medium. The interposed slab also affects the beam’s penumbra because penumbras are largely caused by upstream multiple scattering, which is dependent on the chemical composition of the interposed material; however, this phenomenon has little effect on tissue-equivalent materials and can be ignored. 13.4.2  Bulk Heterogeneities Partially Intersecting the Beam The influence of bulk heterogeneity that partially intersects the proton beam is primarily limited to the interface between the two media. The beam penetration is altered in the shadow of the heterogeneity and decreases if the water equivalent density of the interposed heterogeneity is greater than that of the medium. Equation 13.1 calculates the magnitude of this decrease. The penetration is the same in the region not shadowed by the heterogeneity. However, the differences in MCS of protons from materials of various densities result in a perturbation of the dose at the interface (i.e., a hot and cold spot at the interface). When any material of density different from that of the surrounding medium is interposed in the beam cross section, the beam penetration is altered in the shadow of the material just as for the case of a fully intersecting heterogeneity and is unchanged in the region not shadowed by the heterogeneity. However, at the interface region, differences in MCS in the two adjacent materials create a hot spot on the low-density side and a cold spot on the high-density side. As a consequence of this effect, dose perturbation in air at the interface can be as high as 50% in tissue:air interface (10). However, if one side of the interface is not air, but rather the interface is between two materials of different scattering powers, then the dose perturbation is much reduced; in the case of a bone:tissue interface, from ±50% to approximately ±9% (10). It is important to note that the magnitude of hot and cold spots diminishes with depth in phantom due to increasing angular distribution of the protons. Figure 13.3 illustrates the impact of introducing a compensator with sharp edges in a 150-MeV proton beam. The difference in MCS of tissue equivalent compensator material and air creates hot and cold spots of the order of almost 10% at a mid-range depth in water. This is probably the worst case scenario of dose perturbation at an interface in clinical proton beams. The dose perturbation in the presence of bulk heterogeneity partially intersecting the beam within a patient is often much smaller, especially if one side of the interface is not air, but rather the interface is between two materials of different scattering powers. For example, in the dose perturbation in the case of a bone, the tissue interface is much smaller than for air:tissue interface.

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Proton Therapy Physics

Measurement

–10 –5

100

120 100 80 60 40 20

0 5 Y [cm]

10

Depth 8.7 cm

120

5 cm

Depth [cm.H2O]

2 4 6 8 10 12 14

6 cm.H2O

Relative dose [%]

3 cm.H2O

80 60 40

Eclipse (raw) Eclipse (convolved) Measurement (diode)

20 0 –10

–5

0 Y [cm]

5

10

FIGURE 13.3 (See color insert.) Illustration of an edge-scattering effect. A 150-MeV proton beam traversing through a tissue equivalent compensator with sharp edges introduces hot-and-cold spots of the order of 10%. Note that the treatment-planning system can predict these hot-and-cold spots within a few percent.

13.4.3 Small but Complexly Structured Heterogeneities Intersecting the Beam In most clinical situations, the patient presents a complex pattern of heterogeneities. The most extreme scenarios are found in the region at the base of skull where protons may be directed along extended bone surfaces or in a complex bone–tissue–air structure such as the petrous ridge or the paranasal sinuses. These complex heterogeneities create range perturbations and MCS-induced dose nonuniformities. Urie et al. (11) studied the influence of these types of heterogeneities on proton beams and concluded that MCS is the main cause of Bragg peak degradation. They concluded that Bragg peak degradation cannot be predicted by simply using the stopping powers of the materials composing the heterogeneities. They also suggested that Bragg peak degradation can be diminished by increasing the angular divergence of the beam but only at the expense of widening the lateral falloff. More recently, Sawakuchi et al. (12) carried out systematic Monte Carlo simulation studies to understand this phenomenon. Their Monte Carlo simulation data (Figure 13.4) confirmed the findings of Urie et al. and showed a trend of increasing distal falloff width with increasing complexity of heterogeneities. They concluded that MCS is the primary cause of Bragg peak degradation, nuclear scattering contributes approximately 5% to the distal falloff of the Bragg peak, and the energy spectra of the proton fluence downstream of various heterogeneity volumes are well correlated with Bragg peak distal falloff widths. Most treatment planning algorithms that use analytical models cannot

Precision and Uncertainties in Proton Therapy for Nonmoving Targets

1.0

423

D (MeV cm2 p1)

0.06 0.05 0.04

D (rel. units)

0.8

0.03 0.02

0.6 0.4 0.2

0.01

MCS/NS on 1×1 6×6 16 × 16 64 × 64

0.0 21.5

22.0

0.00 21.5

22.0 22.5 z (cm)

23.0

23.5

24.0

6 × 6 16 × 16 64 × 64

22.5 23.0 z (cm)

23.5

24.0

FIGURE 13.4 Degradation of a normalized Bragg peak distal falloff from a 230-MeV proton beam traversing different density heterogeneities. The inset shows the absolute Bragg peak distal falloff. For these simulations, both multiple Coulomb scatting and nuclear scattering were turned on. Black areas shown in the inset represent compact bone (density = 1.85 g/cm3) in a mosaic-type symmetrical geometries for equal total bone mass in each slab. (From Sawaguchi et al., Phys Med Biol., 53(17), 4605, 2008. With permission.)

explicitly account for this effect; thus, there is a potential uncertainty in distal edge degradation of ±1.0 mm.

13.5  CT Conversion Uncertainties CT imaging remains the de facto standard in radiotherapy treatment planning. It provides a spatially accurate map of a patient’s anatomy together with quantitative tissue measurements. CT Hounsfield unit (HU) numbers vary in value from −1000 for air to 0 for water and positive values for materials with greater attenuation than water. These are derived directly from linear x-ray attenuation coefficients. Although linear attenuation coefficients are functions of the x-ray energy spectrum, HU numbers can be experimentally correlated to electron densities of known materials for a particular scanner and radiographic technique with acceptable accuracy for megavoltage x-ray treatment planning. Unfortunately, the theoretical relationship between protons’ relative-linear stopping powers (RLSP) and linear x-ray attenuation coefficients is complicated and difficult to evaluate analytically with clinically acceptable accuracy. The RLSP values depend on physical density, elemental composition, and mean excitation energy (I-value) of the material. Yang et al. (13) show that physical density and elemental composition have

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a large effect on RLSP. For example, a 4% change in density results in a 4% change in RLSP. Furthermore, data on human tissue densities and elemental compositions are sparse; therefore, for proton therapy, HU numbers, and relative stopping power correlations are established either through the stoichiometric method proposed by Schneider et al. (14) or the direct-fit method proposed by Kanematsu et al. (15). The stoichiometric method utilizes the chemical composition of test materials in conjunction with a simplified version of the Bethe-Bloch formula to compute RLSP. The HU numbers are then assumed to be represented by an equation with three terms that correspond to photoelectric effect, coherent scattering, and Compton scattering. Each term has a different Z-dependence and includes a multiplicative constant. The goal of the calibration is to fit the equation to the HU numbers for a given CT scanner for a large variety of tissue equivalent test materials of known chemical composition and, from the fit, deduce the values of the three constants. Given the constants, one can predict the HU number for any other material of known chemical composition. In the direct-fit method, measurements of a wide variety of tissue equivalent materials are made in both a CT scanner and a proton beam. These data are then fit with a series of straight lines; typically, 3–4 straight lines cover the whole range of HU numbers. Recent measurements at University of Florida Proton Therapy Institute (UFPTI; Jacksonville, FL; S. Flampouri, personal communication) showed that several parameters, including field of view (FOV), imaging kilovoltage peak (kVp), beam-hardening filters, reconstruction filters, and patient size, influence the accuracy of HU numbers and RLSP correlation. The phantom size has the most impact on the HU numbers and RLSP correlation. This is primarily attributed to how image reconstruction algorithms handle beam hardening through patients in CT scanners. Figure 13.5 1.8 1.6 Relative stopping power

Plot area

1.4 1.2 1.0 0.8 0.6

Large phantom Small phantom Medium phantom

0.4 0.2 0.0 –1000

–500

0

500 HU

1000

1500

2000

FIGURE 13.5 Conversion of CT number to relative linear stopping power based on the stoichiometric method (14). Data sets are obtained on a small, medium, and large phantoms containing ICRU tissues. (Based on ICRU, Report 49, 1993.)

Precision and Uncertainties in Proton Therapy for Nonmoving Targets

100

300

80

250

# Beamlets

350

# Beamlets

120

200

60

150

40

100

20 0 0.2

425

50 0.25 0.3 0.35 Range difference (% range)

0.4

0 0.2

0.4 0.6 0.8 1 1.2 Range difference (% range)

1.4

FIGURE 13.6 Range uncertainties computed for a small pediatric and a large prostate patient. The discrepancies in the proton range varied 0.4–0.7% and 0.6–1.2% for the prostate and pediatric patient, respectively. Please note that these uncertainties are only due to the phantom size. Other uncertainties such as position within the phantom, FOV, filtration, tissue composition, etc. are not included. However, those uncertainties are much smaller in magnitude compared to the phantom size.

illustrates that the HU number can vary by as much as 150 HU for different size phantoms, especially for higher-density materials. This variance implies that a single direct-fit method can result in large uncertainties in RLSP. ICRU Report 78 (10) notes that the overall accuracy of the conversion from HU number to water equivalent density is of the order of 2%–4% (1 standard deviation); Moyers et al. reported similar numbers (16). However, Figure 13.6 indicates that the overall accuracy can be improved to 1%–2% by using the direct-fit method for each CT imaging protocol.

13.6  Planning and Delivery Uncertainties Although protons allow for control of dose deposition along and laterally across the beam, the potential of dose uncertainties in proton therapy can be quite large if adequate attention is not paid to the treatment planning and delivery processes. In particular, one must consider patient selection; beam delivery techniques; positioning, immobilization, and localization; imaging for treatment planning; proton treatment planning; and uncertainty in planning and delivery. 13.6.1  Patient Selection Proton therapy is an ideal option for patients for whom dose to normaltissue and/or organs at risk that surround the target volume pose a

426

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problem. Examples include spinal cord irradiation in pediatric patients and skull-based tumors that are close to sensitive normal tissues, such as the brainstem and optical chiasm. On the other hand, proton therapy is not optimal if there are large heterogeneities in the beam’s path, great potential for uncertainties in patient positioning and intrafractional internal-organ motion, or significant possibility of physiological changes throughout treatment. Therefore, all potential candidates for proton therapy must be carefully screened and evaluated using relevant imaging studies that establish the clinical appropriateness of this treatment modality. 13.6.2  Beam Delivery Techniques Proton beams are delivered by scattering, scanning, or wobbling (a special case of beam scanning; see Chapters 5 and 6). Scattered beams produce uniform-­dose distributions within the target volume for each beam, whereas scanned beams can either produce uniform-dose distributions or highly non-uniform-dose distributions with variable intensity within the target volume. In both cases, dose distributions are sensitive to materials interposed upstream in the beam. All available beam delivery techniques must be fully characterized in a treatment-planning system, and their inherent uncertainties must be adequately documented to develop appropriate margin definition strategies. 13.6.3  Positioning, Immobilization, and Localization The accuracy of beam placement relative to the patient, that is, relative to the target volume(s) and the organ(s)-at-risk, is far more important in proton therapy than in photon therapy. The sharp dose falloff in proton beams is a double-edged sword. A small positioning inaccuracy can result in no dose or too much dose at the point of interest. On the other hand, a small beam-­ placement inaccuracy in photon beam therapy has very little effect; it just smears the dose distribution. Therefore, the full advantage of protons can only be achieved if there is good registration between the real or virtual compensator and any heterogeneity within the patient. Placement accuracies of 1–2 mm or even less are essential in proton therapy; indeed, the emphasis on the beam-placement accuracy has less to do with target-volume conformation (the target-volume definition by itself has the largest uncertainty) than with the conformal avoidance of nearby critical structures. Achieving the desired placement accuracy of 1–2 mm requires excellent immobilization of the patient and accurate localization of the patient relative to the treatment equipment. The latter is usually accomplished by the localization of bony landmarks or implanted fiducials as seen in diagnostic quality orthogonal-planar radiographs. Selecting an appropriate surrogate

Precision and Uncertainties in Proton Therapy for Nonmoving Targets

427

for the target volume on a planar radiograph is essential. Timmerman and Xing document that in some disease sites bony landmarks may not serve as a good surrogate for the target; thus, the only possible solution is volumetric imaging (17). At the present time, proton therapy systems do not include on-board volumetric imaging for more accurate localization. Hence, strategies for quantifying residual uncertainties in target localization for each disease site need to be developed and implemented in each clinic. 13.6.4  Imaging for Treatment Planning Multimodality volumetric imaging is essential in all advanced radiotherapy techniques, especially in proton therapy. Developing a realistic patient model is far more important in proton therapy than in conventional radiation therapy. A quality volumetric CT image set without contrast is required for treatment planning and accurate characterization of tissue densities and heterogeneities. A volumetric cine magnetic resonance imaging (MRI) set is needed for better definition of soft-tissue anatomy and to create a patient-specific motion model. Some clinical situations such as lung may require a positron emission tomography (PET) image for more accurate delineation of clinical target volumes. Each imaging modality has its own limitation (e.g., high-Z material artifacts in CT, image distortion in MRI, and poor resolution in PET). As a result, multimodality registration is bound to have residual uncertainties. The magnitude of these uncertainties is reported to be 0.5–6 mm and is technique and disease-site dependent (18); consequently, each clinic should independently quantify these uncertainties. 13.6.5  Proton Treatment Planning Proton therapy planning is inherently an inverse process (see Chapters 10 and 11). The proton range, around which proton scattering causes hot and cold spots, is dramatically altered in the shadow of tissue heterogeneities. Therefore, designing a real or virtual compensator to alter the proton beam to account for these heterogeneities is essential. The effects of heterogeneities cannot always be accurately predicted. For example, misregistration of the compensator relative to the patient introduces both random and systematic uncertainties; beam scattering makes perfect compensation impossible; and location of the heterogeneity can change. Therefore, one must be aware of and mitigate the effect of possible hot-and-cold spots due to lateral scattering effects as well as account for uncertainties associated with possible misalignment of the compensator with the patient or internal organs and tissues. These effects cannot be completely avoided, but their clinical consequence can be mitigated with the selection of appropriate margins around the target and critical structures. As suggested by Goitein (19), angular and

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depth feathering with multiple beams is another way of minimizing the effect of heterogeneities, but it makes the planning and delivery process more complex. In addition, metallic prostheses and surgical clips can cause problems in more than one way. First, they cause severe artifacts in the CT scans, which can contribute to large dose computation errors. Second, the calculations of these metallic devices’ water equivalent thicknesses in vivo have large uncertainties. The best solution is to override the HU numbers of the imaging artifacts on treatment planning CT datasets with that of water equivalent tissue and avoid proton beams being directed through the metallic implants. 13.6.6  Uncertainty in Planning and Delivery As we have shown, inherent and patient-specific planning and delivery uncertainties have far more dire consequences in proton therapy than in photon therapy. Consequently, one must seek to understand the sources of uncertainty and reduce them whenever possible as well as understand the magnitude and implications of the inevitable residual uncertainties. The mere process of identifying the sources and magnitudes of uncertainties can be quite instructive and useful in establishing safe clinical practices. In particular, one must recognize that overall uncertainty estimates tend to be local. In other words, a local clinical environment that includes patient immobilization, imaging protocol, delineation strategy and protocol, treatment planning strategy, treatment localization, plan evaluation, and treatment delivery equipment and technique has far greater influence on the overall uncertainty in proton therapy planning and delivery than inherent uncertainties in the physics of proton therapy. Thus, each proton therapy clinic should estimate the sources and magnitude of residual uncertainties in each step of the proton therapy process and develop mitigation strategies. Table 13.1 illustrates an example of such an uncertainty analysis for nonmoving clinical targets and summarizes the source and magnitude of each uncertainty. These uncertainties can only be mitigated with better physics data; otherwise, the only solution is to account for them in the margin recipes. However, other systematic uncertainties in the proton range that are attributed to the reproducibility of the delivery system, CT calibration uncertainties, compensators, and accessories, among other elements, can be substantially minimized through rigorous quality assurance (QA) (see Chapter 8). Finally, patient-specific uncertainties can only be minimized by enforcing rigorous patient selection criteria and better clinical protocols. Patients who have poor clinical dispositions and significant heterogeneities or implants in the treatment area should not be considered for treatment with protons. If proton therapy is clinically warranted for such a patient, then appropriate margins should be selected based on anticipated uncertainties in the planning and deliver of proton therapy.

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TABLE 13.1 Summary of Estimated Uncertainties in Treatment Planning and Delivery of Nonmoving Targets with Proton Therapy Source of Uncertainty

Uncertainty before Mitigation

Mitigation Strategy

Uncertainty after Mitigation

Inherent range uncertainty (pristine Bragg peak)a Inherent range uncertainty (spread out Bragg peak)a Range reproducibility Compensator

±1.3 mm

None

±1–3 mm

±0.6–1.0 mm

None

±0.6–1.0 mm

±1.0 mm ±1.0 mm

±0.5 mm ±0.5 mm

Accessories (table top, immobilization jig, etc.) CT

±1.0 mm

Patient setup

±1.5 mm

Intrafraction patient motion Compensator position relative to patient Range uncertainty (straggling) due to complex heterogeneities CT artifacts

Variable

Rigorous QA Rigorous QA of compensator material Rigorous QA of all accessories Site-specific imaging protocols Rigorous patient selection criteria Rigorous patient selection criteria Rigorous patient selection criteria Rigorous patient selection criteria

±1.0 mm

Range computation in water in a TPS

Variable

Range computation in tissue of known composition and density in a TPS Multimodality image registration

±0.5 mm

Rigorous patient selection criteria Rigorous patient selection criteria and image edits None

±0.5 mm

Treatment delivery (target coverage uncertainty) Treatment delivery (dosimetric uncertainty)

±1–3 mm

Treatment delivery (dosimetric uncertainty)

±1–3.0%

Better dose computation algorithms Site-specific image registration protocols Rigorous site-specific delivery technique selection Rigorous QA

a

±3.5% of range

Variable ±1 mm

Variable

±1 mm

±1–3 mm

±0.5 mm ±1–2.0% of range ±1.0 mm ±1.0 mm ±1.0 mm ±0.5 mm

±0.5 mm

±0.5 mm

±1–2 mm ±1 mm

±1.0%

Inherent uncertainty in the particle range determination caused by uncertainty of stopping powers and its basic components, notably the mean excitation energy or I-value of a substance.

430

Proton Therapy Physics

13.7  Considering Uncertainties in Planning and Delivery Understanding and managing uncertainties are of extreme importance in proton therapy for controlling tumors and reducing complications. These uncertainties are often a result of the complex interplay of a variety of error sources. Historically, the estimation and reporting of uncertainties has been at best implicit. Experienced physicians recognize that “what you see in the treatment plan is not what you get in the patient.” Currently available radiotherapy treatment planning systems cannot explicitly show the consequences of uncertainties on displayed plans. As a result, physicians make mental assessments of the magnitude of the known uncertainties and their dosimetric consequences. Such an assessment is acceptable if the physician is able to discern all potential uncertainties and their consequences. Unfortunately, these assessments become exceedingly difficult when greater geometric accuracy in dose delivery is warranted. A novel method to estimate the uncertainty limit associated with a particular treatment was originally described almost 30 years ago (20, 21). Goitein (20) proposed three separate dose calculations to set higher and lower doses at any point using extreme values for a few parameters, whereas Leong (21) introduced a convolution method for blurring the planned dose with a normal distribution of spatial displacement to investigate the effects of random geometrical treatment uncertainties. However, these techniques were never implemented into treatment-planning systems. More recently, attempts have been made to predict the standard deviation of a planned dose distribution (3, 22). These authors have demonstrated that with a comprehensive knowledge of spatial and dosimetric uncertainties in planning and delivery, one can compute and display confidence-weighted dose distribution (with a preset confidence interval), confidence-weighted dosevolume histograms, and dose-uncertainty-volume histograms. Examples of these plan evaluation tools are given in Figure 13.7. ICRU (10) has also described several other approaches for presenting uncertainty in proton therapy and provides specific recommendations for reporting proton therapy uncertainties.

13.8  Summary The rationale for the use of proton beams in radiotherapy, which is based on their ability to provide uniform dose to the target while sparing the surrounding tissue, is very compelling. This rationale is simply a consequence of the physical characteristics of energy loss by protons as they penetrate into matter. Protons have a finite depth of penetration in material; the magnitude

Precision and Uncertainties in Proton Therapy for Nonmoving Targets

Dose volume histogram

Norm. volume

(b) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

431

Lower 95% Upper bound bound

0

1000 2000 3000 4000 5000 6000 Dose (cGy)

(c) 100

Case 1 Case 2

80 60 (a)

40 20 0

0

1 2 3 4 5 6 7 Dose uncertainty (%)

FIGURE 13.7 (See color insert.) Illustration of confidence-weighted dose distribution (CWDD), confidence-weighted dose-volume histogram (CWDVH), and dose-uncertainty volume histogram (DUVH). The CWDD (a) is comprised of isodose lines with thicknesses proportional to the local dose uncertainty, whereas the dose-uncertainty distribution was applied to the calculated dose distribution to make the upper and lower bounds of CWDVH (b). Finally, the DUVH (c) is an accumulated histogram of dose uncertainty as a function of volume. (After Jin et al., Int J Radiat Oncol Biol Phys., 78(3), 920, 2010.)

of this penetration depends on the protons’ energy and the density of the irradiated material. This distinct advantage can turn into a double-edged sword if adequate consideration is not given to the potential sources of uncertainties in proton therapy. One must recognize that uncertainties are an inevitable part of the planning and delivery of radiotherapy. In this way, protons are no different from radiotherapy delivered with photons; however, the impact of these uncertainties is much more profound in proton therapy. For ­example, patient-positioning error, patient motion, misalignment of beam modifiers, changes in tissue characteristics, and dosimetric errors in planning and delivery can result in a dose that is very different from what is planned on being delivered to a patient. Therefore, we recommend the following procedures for each patient considered for treatment with proton therapy: • Analyze potential sources of uncertainty for each patient by evaluating their 3D/4D imaging data and clinical disposition. • Make an effort to minimize the sources of uncertainties to the extent possible. • Document the magnitude of the residual uncertainties.

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• Develop strategies for the analysis, quantification, and display of residual uncertainties. • Implement a QA program that ensures that treatment can be given with a confidence level that is established for the patient. For example, a 95% confidence level will give a 95% assurance that the patient receives the prescribed dose distribution.

References

1. International Commission on Radiation Units. International Commission on Radiation Units and Measurements: Stopping powers and ranges for protons and alpha particles. Report 24. 1976. 2. Herring DF, Compton DMJ. The degree of precision required in the radiation dose delivered in cancer radiotherapy. Computers in radiotherapy. Br J Radiol Special Report. 1971; 5(10):51–58. 3. Jin H, Palta J, Suh TS, Kim S. A generalized a priori dose uncertainty model of IMRT delivery. Med Phys. 2008; 35(3):982–96. 4. Yan D, Xu B, Lockman D, Kota K, Brabbins DS, Wong J, et al. The influence of interpatient and intrapatient rectum variation on external beam treatment of prostate cancer. Int J Radiat Oncol Biol Phys. 2001; 51(4):1111–19. 5. Yan D, Lockman D. Organ/patient geometric variation in external beam radiotherapy and its effects. Med Phys. 2001; 28(4):593–602. 6. Andreo P. On the clinical spatial resolution achievable with protons and heavier charged particle radiotherapy beams. Phys Med Biol. 2009; 54(11):N205–15. 7. International Commission on Radiation Units. International Commission on Radiation Units and Measurements: Stopping powers for electron and positrons. Report 37. 1984. 8. International Commission on Radiation Units. International Commission on Radiation Units and Measurements: Stopping powers and ranges for protons and alpha particles. Report 49. 1993. 9. International Commission on Radiation Units. International Commission on Radiation Units and Measurements: Stopping powers of ions heavier than helium. Report 73. 2005. 10. International Commission on Radiation Units. International Commission on Radiation Units and Measurements: Prescribing, recording, and reporting proton beam therapy. Report 78. 2007. 11. Urie M, Goitein M, Holley WR, Chen GT. Degradation of the Bragg peak due to inhomogeneities. Phys Med Biol. 1986; 31(1):1–15. 12. Sawakuchi GO, Titt U, Mirkovic D, Mohan R. Density heterogeneities and the influence of multiple Coulomb and nuclear scatterings on the Bragg peak distal edge of proton therapy beams. Phys Med Biol. 2008; 53(17):4605–19. 13. Yang M, Virshup G, Clayton J, Zhu XR, Mohan R, Dong L. Theoretical variance analysis of single- and dual-energy computed tomography methods for calculating proton stopping power ratios of biological tissues. Phys Med Biol. 2010; 55:1343–62.

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14. Schneider U, Pedroni E, Lomax A. The calibration of CT Hounsfield units for radiotherapy treatment planning. Phys Med Biol. 1996; 41(1):111–14. 15. Kanematsu N, Matsufuji N, Kohno R, Minohara S, Kanai T. A CT calibration method based on the polybinary tissue model for radiotherapy treatment planning. Phys Med Biol. 2003; 48(8):1053–64. 16. Moyers MF, Miller DW, Bush DA, Slater JD. Methodologies and tools for proton beam design for lung tumors. Int J Radiat Oncol Biol Phys. 2001; 49(5):1429–38. 17. Timmerman RD, Xing L. Image-Guided And Adaptive Radiation Therapy. Philadelphia, PA: Lippincott Williams & Wilkins, 2009. 18. Brock KK. Results of a multi-institution deformable registration accuracy study (MIDRAS). Int J Radiat Oncol Biol Phys. 2010; 76(2):583–96. 19. Goitein M. Radiation Oncology: A Physicist’s-Eye View (Biological and Medical Physics, Biomedical Engineering). New York: Springer Press, 2008. 20. Goitein M. Calculation of the uncertainty in the dose delivered during radiation therapy. Med Phys. 1985; 12(5):608–12. 21. Leong J. Implementation of random positioning error in computerised radiation treatment planning systems as a result of fractionation. Phys Med Biol. 1987; 32(3):327–34. 22. Jin H, Palta JR, Kim YH, Kim S. Application of a novel dose-uncertainty model for dose-uncertainty analysis in prostate intensity-modulated radiotherapy. Int J Radiat Oncol Biol Phys. 2010; 78(3):920–28.

14 Precision and Uncertainties in Proton Therapy for Moving Targets Martijn Engelsman and Christoph Bert CONTENTS 14.1 Introduction................................................................................................. 435 14.2 Motion from a Clinical Perspective.......................................................... 437 14.2.1 Over the Course of Treatment....................................................... 437 14.2.2 Interfractional Motion.................................................................... 438 14.2.3 Intrafractional Motion.................................................................... 438 14.3 Magnitude of the Dosimetric Effect of Target Motion.......................... 439 14.3.1 Density Variations..........................................................................440 14.3.2 Interplay Effect................................................................................ 441 14.4 Dealing with Motion..................................................................................443 14.4.1 The Importance of Motion Monitoring.......................................443 14.4.2 General Treatment-Planning Considerations.............................444 14.4.3 Motion Reduction...........................................................................445 14.4.4 Rescanning......................................................................................447 14.4.5 Tracking............................................................................................449 14.4.6 Adaptive Radiotherapy.................................................................. 451 14.5 Quality Assurance for Moving Tumors................................................... 452 14.5.1 Treatment-Planning Quality Assurance..................................... 453 14.5.2 Treatment Delivery Quality Assurance.......................................454 14.6 Future Perspective...................................................................................... 455 References.............................................................................................................. 456

14.1  Introduction For static targets one can assume that range uncertainties in the patient geometry, though not known exactly, are consistent over the treatment course, and one can estimate this uncertainty. Setup errors vary from day to day and can also be estimated. These varying setup errors have a doseblurring effect on the tumor. In the worst case they can lead to a geometric 435

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Proton Therapy Physics

miss if the tumor moves too close to, or even outside of, the beam portal. Having an estimate of the magnitude of range and setup uncertainties allows the design of treatment plans that ensure proper target coverage and sparing of organs at risk (OAR) for these static targets. Because the density geometry is possibly inaccurate but consistent, this allows the use of only a single computed tomography (CT) scan for treatment planning. Uncertainties can be taken into account by safety margins in the case of single-field uniform dose (SFUD) treatments (Chapter 10) or, less straightforward, by means of robust planning (Chapter 15) in case of intensity-­ modulated proton therapy (IMPT). Dose delivery to a moving target is influenced by all the uncertainties of static targets (see Chapter 13) and adds considerable complexity to both treatment planning and treatment delivery because of two aspects:



1. Treatment planning is typically performed on a static CT image, whereas the actual density distribution is variable. Even a fourdimensional (4D) CT scan used for treatment planning, which is not yet common in clinical practice, is only a snapshot in time and does not necessarily represent the 4D patient geometry during a treatment fraction. 2. Depending on the mode of treatment delivery, target motion may result in so-called interplay effects when the time structure of treatment delivery is similar to the time structure of intrafractional tumor motion.

A third effect, blurring of the (lateral) dose distribution even in the absence of density variations and interplay effects, is similar to that of multiple setup errors over a large number of fractions. This specific effect can be taken into account by classical safety margins (i.e., target expansion) and will not be discussed in this chapter. As a consequence of density variations and interplay effects, the “classical” approach of treatment planning on a single static CT scan, using safety margins to expand the target volume and evaluating the dose to the target and normal tissues on this CT scan, is clearly insufficient. Following classical forward planning, the dose distribution as observed during treatment planning is not a good representation of what will be delivered to the patient in any treatment fraction (Figure 14.1). This figure also shows that motion affects not only the dose to the target but also the dose to the OAR. This chapter provides an overview of the dosimetric consequences of target motion in proton radiotherapy, discusses strategies to mitigate these consequences, and highlights the prerequisites for safe and accurate treatment of moving tumors.

Precision and Uncertainties in Proton Therapy for Moving Targets

a)

437

b)

FIGURE 14.1 Phantom simulating a unit density tumor (gray circle) in low-density lung tissue (white). The thin black circle indicates a 10-mm 3D geometric expansion of the tumor into the planning target volume (PTV; see Chapters 10 and 11 for the applicability of the PTV for proton therapy). (a) The dashed lines are isodose lines (50%, 80%, 90%, 95%, 100%) for a single passively scattered proton field, incident from the top and designed to cover the PTV. (b) Isodose lines for a 10-mm displacement of the tumor with respect to the treatment beam. The tumor remains within the PTV but is underdosed, whereas the dose to certain parts of the lung is increased.

14.2  Motion from a Clinical Perspective Time-dependent variation in the target location and the patient density distribution can occur on different time scales: over the entire treatment course, between subsequent treatment fractions (interfractional motion), and within a treatment fraction (intrafractional motion). Some examples of density variations are shown in Figure 14.2. All of these will be briefly discussed in this section. In Section 14.4, we will subsequently discuss how to effectively deal with each type of motion. 14.2.1  Over the Course of Treatment The term “motion," in this case, describes gradual, but systematic, variations in the density distribution of the patient that can occur either because of a redistribution of densities within the patient or the addition or disappearance of matter. Examples of such variations are tumor shrinkage and growth (1),  weight gain or loss, increase or decrease in lung density, and systematic variation in bowel and rectal filling. Redistribution of densities includes changes in the motion pattern such as breathing trajectory or changes in the baseline (2). McDermott et al. reported on the use of portal imaging to detect anatomy changes in head and neck, prostate, and lung cancer (3). Barker et  al. reported on the use of an integrated CT/linear accelerator system to track tumor shrinkage, edema, and overall weight loss (4).

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FIGURE 14.2 (See color insert.) Motion and density variation as a function of time. (a) Two CT slices acquired a few weeks apart as an example of density variation over the course of the treatment, as indicated by the white arrow. (Courtesy of Francesca Albertini, Paul Scherrer Institute.) (b) Two CT slices for a prostate cancer patient on different treatment days as an example of interfractional variation. The variation in femoral head rotation affects the dose delivered by the typically applied lateral beam directions. (Courtesy of Lei Dong, MD Anderson Cancer Treatment Center, Dallas, TX.) (c) Two breathing phases for a lung cancer as an example of intrafractional variation. The red contours indicate the target position when in the exhale phase.

14.2.2  Interfractional Motion Interfractional density variations can be as large as the gradual variations over the entire treatment course, but they have a more random character. Examples are variations in the amplitude of breathing, in the average tumor position over the breathing cycle, and daily variation in rectal, bowel, and bladder filling. For prostate tumors, daily variation in the rotation of the femoral heads and corresponding variation in the patient exterior surface may affect the proton range within the patient. Langen et al. provide an extensive overview of interfractional position variation (5). 14.2.3  Intrafractional Motion Much data has been published on the extent of intrafractional motion. Langen et al. provide an overview of many of these studies (5). Without attempting to be complete, we will discuss motion parameters for a few tumor sites. For lung tumors, motion is typically largest for those tumors close to the diaphragm and typically largest in the superior-inferior direction. Although peak-to-peak motion of 30 mm can be observed, the typical motion is less than 10 mm (e.g., 65% of patients in the study of Sonke et al.) (2). Hysteresis in the motion trajectory can be observed (6) as well as a baseline drift over the duration of the treatment fraction (7). Intrafractional variations in proton

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beam penetration can be especially large for tumors near the diaphragm or heart. As the liver is relatively close to the diaphragm, peak-to-peak motion with an average of 17 mm has been observed for these tumors under normal breathing conditions (8). For cardiac sarcomas, the heartbeat causes both tumor excursion and, depending on the choice of beam angles, a large variation (up to several centimeters) in water equivalent depth of the tumor. Intrafractional motion of the prostate is mainly a consequence of moving gas and feces and is typically less than a few millimeter (1 standard deviation) (9), but the effects on proton penetration can be quite severe.

14.3  Magnitude of the Dosimetric Effect of Target Motion In photon radiotherapy great effort is made, by means of image-guided adaptive radiotherapy (10), to ensure translational and rotational alignment of the target with the treatment fields. Density variations are a lesser concern. They have only a minor effect on the dose distribution in the patient, as the photon depth–dose distribution is rather shallow and insensitive to density variations. Figure 14.3 shows the effect of a density variation along the beam path for both a photon and a proton beam. For a proton beam, such (motion-induced) density variations have a large dosimetric effect because it can mean the difference, for example, between 100% and 0% of the prescribed dose for the distal target edge. For the photon beam the variation in the dose behind the density variation is limited to only a few percent. 160

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Interplay effects in intensity-modulated radiation therapy (IMRT) have limited dosimetric consequences if a sufficient number of treatment fractions are delivered (11). In photon therapy, one can therefore estimate the additional safety margin needed for treating moving tumors by a rather straightforward blurring of the dose distribution inside the patient (12–14). In proton therapy the finite range and steep dose gradients make it much more complex to deliver an accurate treatment for moving tumors (15, 16). Because of the finite range, density variations over time as well as the interplay effect can have severe dosimetric consequences. The next two sections describe these consequences and their magnitude. 14.3.1  Density Variations In case of single-field uniform dose (SFUD) proton therapy, density variations (without interplay effect) affect the dose near the proximal and distal edge of the target. For IMPT these density variations may furthermore have dosimetric consequences within the target volume because of mismatches of the possibly very steep dose gradients of the individual fields. Engelsman et al. used a simplified phantom geometry and beam setup to analyze the effect of setup errors and intrafractional lung tumor motion (17). They found that the minimum dose in the target could drop from 95% down to 40% and 65% for a 5-mm setup error and 10-mm breathing motion, respectively, if density variations are not proactively taken into account in the design of the treatment plan. Kang et al. analyzed a variety of forward planning approaches for lung tumors in real patient geometries under intrafractional motion (18). None of the planning approaches accurately predicted the dose distribution in the target (PTV), when comparing the dose as accumulated over all phases of the breathing cycle to the dose distribution as predicted by the plan created on the single treatment-planning CT scan. Although the dose to critical structures was only marginally affected, dose reductions in the PTV of up to 5% were observed. Mori et al. analyzed the variation in water equivalent path length over the breathing cycle for a set of 11 lung cancer patients (15). As a function of beam angle and breathing phase, the average range variation observed was a few millimeters, but maximum local range variations between 10 and 35 mm were observed. Obviously these range variations affect the dose distribution, necessitating the use of larger safety margins to ensure target coverage at the cost of more dose to the OAR. Figure 14.4 shows an example of range variation for a single-beam direction aimed at a lung tumor. Hui et al. analyzed the effect of interfractional motion and anatomic changes for lung cancer patients by means of weekly 4D CT scans and dose recalculation at the end-inhale and end-exhale phases (19). Although the typical patient showed only little variation in target coverage, they conclude that adaptive replanning may be indicated in selected patients, mainly to mitigate dose variation in the surrounding OAR.

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FIGURE 14.4 (See color insert.) Range fluctuation for a posterior to anterior beam direction aimed at a tumor moving in lung. The range variation is expressed in water equivalent length (WEL) and superimposed on 4D CT images. (From Mori et al., Int J Radiat Oncol Biol Phys., 70(1), 253, 2008. With permission.)

In current clinical practice the changing density distribution is taken into consideration at the time of treatment plan design, based on the experience of the dosimetrist or medical physicist. This approach leads to acceptable dose distributions, but several studies showed that 4D treatment plan assessment and/or adaptive planning approaches could further improve dose coverage of the target volume and reduce dose to OAR. 14.3.2  Interplay Effect The interplay effect describes the detrimental effect on the dose distribution for moving targets if delivering a (dosimetric) fraction of the intended dose distribution is not near-instantaneous, as for example in pencil beam scanning (PBS). These interplay effects can occur due to any motion not mitigated by motion reduction (e.g., gating, breath-hold) and for any remaining motion within a gating window. SFUD proton therapy, even if delivered by means of fast-spinning range modulator wheels and not by stationary ridge filters, does not suffer from interplay effects because the motion of the beam is much faster (e.g., periods of 100 ms) than target motion. Interplay effects can, however, be substantial in the case of layer stacking (20, 21) and, more generally, in the case of PBS. This section will not discuss layer stacking but will focus on interplay effects for PBS only. Figure 14.5 shows an example of the possible severity of the interplay effect for a single-field irradiation of a moving lung tumor with a scanned carbon beam. A PBS dose distribution is typically delivered (and treatment planned) by grouping the necessary spot positions in range layers (iso-energy layers). Although dose delivery within a range layer can be near instantaneous,

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FIGURE 14.5 (See color insert.) Isodose distributions for a single PBS irradiation of a moving lung tumor showing the interplay effect between dose delivery and tumor motion. The blue, red, and yellow lines indicate the 50%, 95%, and 105% isodose levels, respectively. (a and b) Stationary dose distributions for treatment plans to the CTV and to an internal target volume accounting for respiratory motion only (ITVr; ICRU Report 62, 1999.). (c) Dose distribution for a breathing period of T = 4s with the beam starting at the inhale breathing phase (φ = 0°). The interplay pattern is sensitive to changes in initial breathing phase, (c) versus (d), and to changes in the scan speed, (d) versus (e), simulated in this case by changing the extraction rate from the synchrotron to 90% of the initial value. (f) Corresponding DVHs of the target. (Reprinted from Bert et al., Phys Med Biol., 53(9), 2253, 2008. With permission.)

the time needed to switch between layers can give rise to interplay effects because the target motion phase changes between individual layers. Interplay effects for PBS have long been recognized to be a potential issue for proton radiotherapy (16, 22–28) and are one of the reasons why PBS is currently not, or almost not, used in a clinical setting to treat patients with moving tumors. Interplay affects the dose at the tumor edge and within the tumor (16). Exactly how interplay affects the dose distribution depends on the target motion characteristics as well as the characteristics of the dose delivery system, such as the choice of scan pattern and the scanning speed. Lambert et al. showed that scanning in planes parallel to the beam direction (i.e., parallel to the slowest scan direction) is worse than scanning in planes perpendicular to the beam direction (16). Their computer simulation on a simple homogeneous phantom showed that interplay effects can result in 100% of the target volume receiving a dose outside the recommended limits. Phillips et al. showed that dose inhomogeneity increases most for motion in the direction of the slowest scanning speed (22). They found that dose uniformity in the target varied between 1% in the case of no motion, to 11% in the presence of breathing motion. If scanning a single layer takes 1–2 s, characteristic patterns may occur in the dose distribution (25): diagonal stripes for motion perpendicular to the (major) scanning direction and stripe

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patterns for motion parallel to the scanning direction. Modern scanning systems, however, are able to scan a single layer in less than one-tenth of a second. Typically the slowest scanning direction is the depth direction, that is, from range layer to range layer, with current commercially available systems having range layer alteration times of a single to a few seconds. For actual patient geometries the extent of the effect is shown by, for example, Bert et al (25). They performed a treatment-planning study using a number of 4D patient geometries and a large set of individual motion parameter combinations (e.g., motion amplitude, breathing period). The volume of the clinical target volume (CTV) covered by 95% of the prescribed dose was 71.0 ± 14.2% (mean ± standard deviation) for a single fraction for a single beam direction. They conclude that especially for small fraction numbers (i.e., hypofractionation) treatment of moving targets with scanned particle beams requires motion mitigation strategies such as rescanning, gating, or tracking.

14.4  Dealing with Motion There are a variety of strategies available to mitigate the effects of motion in proton radiotherapy. The best approach to deal with motion may differ for different tumor sites and is likely a combination of some of the strategies described below. Although some of these strategies act only at the time of treatment delivery, all of them already have to be taken into account at the time of treatment plan design. Gating, for example, controls the patient and target position inside the treatment room, but the treatment plan has to be designed to the correct phase(s) of a 4D CT scan. Residual uncertainty in the target position (e.g., within the gating window) also has to be addressed during treatment planning. 14.4.1  The Importance of Motion Monitoring Most of the strategies discussed in the following sections (e.g., beam gating and especially beam tracking) depend heavily on accurate assessment of the time-dependent target position and patient geometry. Although motion monitoring is not unique to proton therapy, it should be clear that the importance of precise motion monitoring, when compared to photon radiotherapy, is much higher because of the strong dosimetric impact. In addition, some motion-monitoring devices are not fully compatible with a proton beam. We will therefore provide a brief overview of the various motion-monitoring strategies. Motion-monitoring can be as simple as observing if the patient indeed holds his breath during beam-on, for example, in deep-inspiration breathhold (29). It can also be as technologically advanced as real-time image-guided

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radiotherapy (IGRT) by means of integrating a magnetic resonance imaging (MRI) scanner into the treatment room (30), although this has not yet been attempted for proton therapy. Other strategies include the 4D tracking of implanted markers (31) and motion phase/amplitude monitoring by means of external markers. The former strategy has questionable usability in proton therapy due to the disturbance of the deposited dose distribution. The latter strategy relies on assuming or measuring a correlation between external markers and internal target position (32). A hybrid solution that does not require ionizing radiation for measuring the position of implanted fiducials as described by Shirato et al. (31), but that can provide comparable accuracy, is model-based prediction of internal target motion. In these approaches a model is trained by parallel observation of internal motion (e.g., based on implanted fiducials) and an external motion surrogate, such as the height of the chest wall. During treatment delivery the model then predicts internal target position based on frequent assessment of the external surrogate position. In case of longer irradiations the model might be updated or checked by additional measurements of the internal motion. Clinically such a model approach is used in the Cyberknife Synchrony (Accuray, Sunnyvale, CA) (33). Accurate motion monitoring is not limited to the treatment room only but obviously should also take place during the treatment preparation phase (e.g., motion assessment during 4D CT scanning). Ideally, the same motionmonitoring system is used both at the treatment preparation phase and during treatment delivery. 14.4.2  General Treatment-Planning Considerations During treatment planning one can (try to) address uncertainties in the actually delivered dose distribution as a consequence of a time-varying geometry. A simple approach is to choose beam directions that minimize the effect of motion. For example, one should choose not to use beam directions that skim the heart or that treat through the diaphragm. The resulting variation in local proton range affects the required distal safety margin as well as the probability to spare OARs distal to the target. In choosing beam directions it may also be valuable to increase the number of fields in the treatment plan/ treatment fraction because this averages out the dose uncertainties of single beams. Knopf et al. investigated the importance of the number and direction of fields in a treatment plan (34) and suggested two strategies: For treatment plans having two fields or less the beam directions should be chosen carefully, and an increased number of rescans is indicated in order to reduce the interplay effects. For multiple-field plans rescanning may not be necessary for small target motion if at least some of the fields have a favorable direction with respect to target motion. With beam directions chosen, it is still a challenge to design a plan that ensures target coverage in the presence of (remaining) motion. Chapter 10 provides a few approaches for the case of SFUD delivered by means of

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passive scattering. Typically, in passively scattered proton therapy (PSPT) one performs forward (or manual) treatment planning and chooses beam parameters (range, modulation width, and range compensator shape) that either ensure target coverage in every separate breathing phase or that will likely ensure target coverage when the dose is accumulated over the motion cycle. SFUD using PBS is similar, but next to providing target coverage under density variation, it furthermore requires analysis of the interplay effect (e.g., by multiple 4D dose calculations with varying motion parameters). Bert et al. suggested, for PBS and limited target motion, optimizing the spot size and the distance between spots laterally, and Bragg peak shape and distance between energy layers longitudinally for a reduction of the dosimetric effect on motion (27). They show that increasing the overlap between pencil beams provides a sort of “intrinsic” rescanning. As more pencil beams contribute to the dose at each position in the target, no additional rescanning may be needed. Within the range layer, decreasing the distance between spots or increasing the spot size increases the pencil beam overlap. In the latter case, the lateral beam penumbra may, however, be negatively affected. In the direction parallel to the beam one can decrease the distance between range layers and potentially also the shape of the Bragg peak by, for example, incorporating a small ripple filter to broaden the peak. The effectiveness of the strategy of increasing the overlap of spots is, however, reduced at very high dose gradients where some spots will deliver no or very little dose. IMPT, by definition, adds the ability to optimize the dose distribution over multiple beams all at once. In case of static tumors and no uncertainties the automatic optimization of IMPT plans allows the use of pencil beams that are most beneficial in geometrically sparing OAR. With range and setup uncertainties and, more important for this section, a variable-density geometry, robust optimization (Chapter 15) will furthermore allow the use of those pencil beams that suffer least from density variations. Regardless the use of SFUD or IMPT, one should not expect the treatment plan on the static CT scan to appear perfectly conformal to the target. Target motion and other density variations add to the necessary distal overshoot and proximal undershoot already needed to ensure target coverage for range uncertainties and setup errors. Choosing the number and direction of beams wisely, maybe in combination with robust optimization, can help mitigate the effects of both (remaining) intrafractional motion (e.g., for lung cancer) and interfractional density variations (e.g., for prostate cancer). Increasing pencil beam overlap reduces the effect of intrafractional motion. 14.4.3  Motion Reduction A logical method to prevent unwanted effects of motion is to reduce the motion itself. Reduction of tumor motion is not unique to proton therapy,

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but the potential gain is larger than in photon radiotherapy because it may improve reproducibility in both the target position and the patient density distribution. What follows is a brief description of a number of motion-­ mitigation strategies. When applied during CT scan acquisition they help reduce CT artifacts. When applied during treatment delivery they may prevent variation in the day-to-day delivered dose to the target and healthy tissues. Use of an abdominal press reduces residual tumor motion (35), but may limit the possible incident beam directions. Two other approaches to reduce residual tumor motion are beam gating (36, 37) and breath-hold (38). In both cases, treatment planning should ideally be based on a 4D CT scan  (39), choosing a specific phase of the 4D CT scan for treatment planning. If 4D CT acquisition is not available, gated CT or CT acquisition in breath-hold can be used if the extend of motion is checked by other means (e.g., in a fluoroscopy study). The quasi-stationary geometry represented by the CT phase can then be reproduced at the moment of treatment delivery as part of patient positioning. In case of gating, the patient breathes freely with radiation delivery inhibited if the target is not within the defined parts of the breathing cycle, the gating window. The treatment beam is triggered on and off automatically by a motion-monitoring system. Residual motion within the gating window requires mitigation for interplay effects in case of PBS as described above (increased spot overlap) or by combination with other mitigation schemes such as rescanning (24). In case of breath-hold it is the patient who is triggered, by audio or visual feedback, to maintain the correct target position for a prolonged time period of up to 20 s or as long as the patient can comfortably manage. Again, radiation is only delivered with the target close enough to the intended location. Both gating and breath-hold increase the overall time to deliver a treatment fraction, which may be a challenge for a sick patient. Perhaps the most advanced method of minimizing breathing motion is the use of apnea during controlled short anesthesia (“General intubation anesthesia under oxygen insufflations in apnea”) as utilized at the Rinecker Proton Therapy Center (Munich, Germany) (40). As a more general approach, prescribing a diet can reduce inter- and intrafractional position and density variation (9). It can also help control the patient’s weight over the treatment course. Furthermore, it may reduce the passing of gas that otherwise could affect the accuracy of, for example, proton therapy for prostate cancer. Abdominal press, gating, breath-hold, and apnea reduce (the effect of) intrafractional motion. These techniques may, however, reduce intrafractional motion at the cost of increasing interfractional variations, that is, variation in the daily “frozen” target position. Rietzel et al. stated that the reproducibility of the target position between beam-on periods should be in the order of 3–5 mm to allow accurate delivery of (intensity-modulated) particle therapy (41).

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14.4.4  Rescanning Rescanning, also called repainting, is a strategy to mitigate interplay effects by controlling the timing of beam delivery with respect to the motion cycle. Rather than delivering all dose continuously in one pass, dose delivery to an appropriately sized internal target volume is broken up into several cycles, thereby smoothing the delivered dose distribution. This decreases the risk of large localized dose discrepancies at the cost of accepting smaller dose discrepancies to a larger volume. To first order, multiple rescans within a treatment fraction has the same dose averaging effect as described by Bortfeld et al. (11) for interplay effects in multiple-fraction IMRT treatments (i.e., the standard deviation in dose to a point in the target is expected to reduce by the square root of the number of rescans). Figure 14.6, however, shows that more rescans are not automatically better. The effectiveness of the chosen rescanning strategy depends as much on the target motion characteristics as on the timing and dosimetric characteristics of treatment delivery. The Paul Scherrer Institute (PSI), for example, is developing a PBS gantry that can change the energy in about 80 ms per 5-mm range step. They can treat a 10 × 10 × 10-cm3 target within 8 s, which is fast enough to allow dose delivery within a single breath-hold, thereby circumventing interplay effects completely. There are many variables to be adjusted as part of a rescanning strategy (see below), and the optimal rescanning solution is best determined at the time of treatment planning (41). The only parameter that is typically fixed is that the direction of slowest rescanning is the depth direction. Anything else (e.g., the scan path or the scanning speed within a layer) can be subject of optimization, and many of these variables have not yet been extensively researched in clinically realistic density geometries. Where possible, in this section we will follow the scanning/rescanning nomenclature as used by Zenklusen et al. (28). Within a range layer the dose can be delivered by means of discrete spot scanning, continuous scanning or continuous line scanning (see Chapters 6 1 rescan

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FIGURE 14.6 (See color insert.) 4D treatment-planning study of a tumor moving in a unit-density phantom (gray). The thin dashed line indicates the target outline. The solid white line indicates a protonrange adjusted internal target volume. The figures show the calculated dose distributions versus the number of rescans, assuming the dosimetric and dose delivery timing characteristics of Gantry 2 of the Paul Scherrer Institute. (a–e) Dose distribution for no motion and one, four, six, and eight rescans, respectively. (Courtesy of Dirk Boye, Paul Scherrer Institute.)

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and 11). The choice of which method to use affects the time structure of dose delivery within a layer and thereby the interplay effect. For example, indirectly, if the intention is to limit the total treatment time, this can also affect the number of rescans that can be performed. There are two approaches for rescanning within a range layer. In isolayered rescanning there is a maximum to the dose delivered per spot that is small in absolute dose (particle numbers). This means that spots with a higher weight will be rescanned more often than lower-weighted spots and that the beam path varies for each rescan because the number of remaining beam positions within a layer changes. In scaled-rescanning each spot is rescanned equally often. This can lead to arbitrarily low spot weights, the application of which may be limited by technical constraints of the treatment delivery system. There are also several possibilities for rescanning the dose distribution to the entire target volume. In volumetric rescanning the three-dimensional (3D) dose distribution for a single field is delivered one after another, with the absolute dose delivered per scan reduced proportionally to the number of rescans. As in scaled rescanning, this may lead to too low spot weights. In nonvolumetric rescanning (also known as slice-by-slice rescanning) all dose is delivered within an energy layer by means of rescanning, before switching to the next energy layer and repeating this process. It is also feasible to only rescan the deepest layers, which typically have the highest spot weights. Because of the proton depth–dose distribution this will result in intrinsic rescanning of the more proximal layers as well (41). The time structure of rescanning is the final parameter that can be varied. Furukawa et al. suggest the use of phase-controlled rescanning (PCR) (24). PCR aims at temporally adjusting the number of rescans to the periodical breathing cycle. In their case, PCR is used in combination with gating, and thus the extraction from the synchrotron is adjusted such that the number of rescans in an energy layer is synchronized to the length of a gating window. This approach reduces the standard deviation in the target dose by roughly a factor of 2 compared to when PCR is not used. For a cutoff of 2% target dose inhomogeneity it allows a reduction in number of rescans from 20 to 6. Whether or not this translates into a decrease in treatment delivery time will, however, depend on the gating efficiency. A similar approach was proposed by Seco et al. who investigated five different rescanning strategies by means of a simulation study on a homogeneous phantom aiming to deliver a homogeneous dose over 30 fractions (26). The most effective method was breathsampled rescanning in which the layer-scan start times of each ­rescan are distributed evenly throughout the breathing cycle. When rescanning 6–10 times, dose delivery errors were below 5% at the cost of only a minimal increase in treatment time. Zenklusen et al. analyzed various rescanning strategies (28). Their extensive simulations showed that rescanning needs to achieve a dose inhomogeneity of less than 1.5% (root mean square) in order to comply with the International Commission on Radiation Units and Measurements (ICRU)

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recommendations of a target dose between 95% and 107%. For motion up to 5-mm amplitude their simulations indicated that, when using spot scanning, it is best to have the number of rescans of a spot be proportional with the spot weight (i.e., “isolayered rescanning”). Large tumor sizes benefit from continuous line scanning as it allows more rescans per time period, thereby substantially reducing the overall treatment time. For full benefit of continuous line scanning it has to be combined with fast energy switching. They furthermore concluded that for motion amplitudes above 5-mm rescanning has to be combined with a strategy to control the motion amplitude, such as breath-hold or beam gating. This reduces both dose inhomogeneity in the target and the required safety margins. For limited motion, rescanning is an effective method to reduce interplay effects in PBS. There are, however, a number of downsides. Rescanning inevitably increases the treatment time of each treatment fraction, but this increase may be inconsequential with the development of faster scanning and layer switching. More research is needed to determine the optimal beam scanning parameters for specific tumor sites and motion characteristics. For rescanning to be most effectively applied to patient treatments, commercial treatmentplanning systems need to be able to allow optimization of all parameters, taking into account the limitations of the various treatment delivery systems and the patient motion characteristics (i.e., 4D treatment planning). It is important to realize that rescanning addresses the consequences of the interplay effect only (i.e., only one of the effects of intrafractional motion). The amplitude of target motion and the corresponding density variation, either intra- or interfractional, still has to be addressed in the treatment-­ planning phase, by using safety margins and any of the approaches mentioned in Section 14.4.2. 14.4.5  Tracking Arguably at the moment the most sophisticated and technically challenging approach is so-called beam tracking. In beam tracking the aim is to adjust the position of the beam to the time-varying position of the target, in three dimensions. Figure 14.7 shows a possible implementation of beam tracking for carbon beam scanning and some dosimetric results obtained with this system (42). The idea was originally proposed for photon therapy (43) and has been clinically applied in, for example, Cyberknife treatments (44). Tracking in photon therapy is a two-dimensional (2D) problem; one needs to adjust the beam (or segments thereof) to the time-varying lateral 2D position of the target with respect to the central beam axis. In proton therapy, lateral target alignment is only half a solution, and one also has to adjust for the third dimension: the water-equivalent radiological depth of each point in the target as a function of time. We stress that the essence of tracking differs from that of rescanning in that it is not a mitigation technique but rather addresses the problem, motion, directly.

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FIGURE 14.7 (a) Experimental motion tracking system as designed at the GSI Helmholtzzentrum für Schwerionen­forschung (GSI) facility in Darmstadt, Germany. The scanner magnets allow fast variation of the pencil beam in the direction perpendicular to the central beam axis (Δx, Δy). Required range adaptation is performed by a fast wedge system (Δz). (b) Results of ionization chamber measurements positioned in the target volume normalized to measurements with a stationary target. (c) Radiographic film responses and corresponding dose profiles along the line indicated by the arrow in the panel labeled “stationary.” (From Bert et al., Radiat Oncol., 5, 61, 2010 and Bert et al., Med Phys., 34(12), 4768, 2007. With permission.)

There are three prerequisites to successful application of beam tracking in proton radiotherapy. The first is a highly accurate treatment delivery system that allows fast position and energy switching. Saito et al. estimate that the scanning system should be able to adapt to an updated target position within a time-scale comparable or even shorter than the irradiation time of a single spot (45). Updating the spot position in the depth direction on such a short time scale is a challenge. PSI Gantry 2 allows a 5-mm shift in proton range in about 80 ms, whereas Saito et al. developed a custom wedge-system that allows 5-mm depth correction within 16 ms (45). Even higher energy modulation speeds should be possible with electromagnetic solutions rather than using the mechanical modulation methods of both PSI and Saito et al. Chaudhri et al. proposed an energy modulation system that facilitates a pair of dipole magnets to pass the beam through a stationary wedge-shaped absorber within the beam line (46). The initial tests in “slow-motion” focusing on beam parameters were promising. Implementation at full speed will require further research (e.g., with respect to updating the settings of the beam line). The second prerequisite is accurate real-time monitoring of the target position. Van de Water et al. found that the positioning error (root mean square) should be less than 1 mm to ensure a sufficiently homogeneous target dose

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(D5 –D95 < 5%) (47). This is in agreement with the report of Rietzel and Bert who expressed that the millimeter precision that is achievable with stateof-the-art fluoroscopic motion-monitoring systems should be sufficient for beam tracking (41). The third prerequisite is near-instantaneous range correction estimates. As this third dimension, the target depth, can not (yet) be measured on-line in real time; the current approach to account for time-dependent range variations is precalculation of the range correction for each motion phase and scan position (48). Currently this is performed during the treatment planning phase. Based on 4D CT data and nonrigid registration maps, look-up tables of compensation parameters are created. The motion phase at the time of delivery of every single spot determines what compensation parameters are applied. The technical feasibility of on-line motion compensation has been shown by means of computer simulation studies (47–51) and by means of phantom irradiations (45, 52). Tumor tracking may have to be combined with rescanning (“retracking”). Li et al. suggested retracking as a measure to deal with target rotations (49). Van de Water et al. suggested retracking as a means to reduce the sensitivity to positional errors, that is, allowing target position errors up to 3 mm (47). They also stressed that, on top of the 3D pencil beam position, the weights of pencil beams may have to be adjusted because timevarying density gradients can affect the dose deposition of a pencil beam. Lüchtenborg et al. have achieved real-time change of the weight of individual pencil beams based on a database provided as part of the treatment plan (53). These changes are used to compensate for target rotations and deformations. The third prerequisite, accurate range correction estimates, is arguably the weakest link, limiting the clinical application of beam tracking. Unless adaptive schemes are used (see the next section), the accuracy of precalculated range corrections is limited by the representativeness of the 4D CT scan used for treatment planning with respect to the actual time-dependent density geometry at the moment of treatment delivery. Beam tracking is presumably most successful at controlling the effect of intrafractional motion if both interfractional motion and gradual density changes over the entire treatment course are controlled as well. 14.4.6  Adaptive Radiotherapy Gradual density variations that occur over the course of a fractionated treatment may not have a clinically relevant dosimetric effect on a timescale of one treatment fraction to the next, but over the course of a few fractions they can have just as devastating an effect on the dose to the tumor as, for example, a sizable setup error. The practice of repeated imaging is at the moment not routine in the proton therapy community, perhaps justifiably so, because good clinical results have been obtained with proton therapy without taking this into account. On the other hand, proton therapy has historically mainly

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been applied for tumor locations that suffer minimally from density variations (e.g., eye and brain tumors), and long-term follow-up and data for other tumor sites (e.g., pancreas, prostate, lung) may not yet be sufficient to show an effect. Simply tracking the patient weight, or the more sophisticated use of patient localization images (either portal images or cone beam CT, [3]) can serve as the basis for a decision protocol to indicate a need for replanning, or at least to assess continued adequacy of the existing treatment by recalculating the dose distribution on the new patient geometry. Variation in patient geometry over the course of treatment is best addressed by adaptive radiotherapy. With the current state of proton therapy technology, however (i.e., with passive-scattering still the dominant mode of proton therapy), gradual density variations can not efficiently be addressed by replanning. Design and then fabrication of updated field-specific hardware (aperture, range compensator) is a time consuming and expensive process. PBS allows for adaptive radiotherapy or even on-line changes of the treatment plan because no patient-specific hardware has to be built. Adaptive schemes that take into account patient-specific changes of the target region are thus applicable and have the potential to increase the precision of proton beam therapy by minimizing margins. Adaptive treatment schemes might also be the method of choice to overcome the main limitation of tracking, which is the uncertainty associated with the 4D CT scan that is used for range assessment. If this scan is repeated over the duration of the fractionated treatment schedule, variations in the moving geometry can be assessed and incorporated into the treatment plan’s database that result in the compensation vectors at time of treatment delivery.

14.5  Quality Assurance for Moving Tumors Proton therapy in general, and IMPT specifically, provides benefits for many patients, but the clinical staff (i.e., radiation oncologists and clinical physicists) have to be intricately aware of the uncertainties mentioned in this and the previous chapter. The tighter we try to control and conform the dose by means of new and evolving technology and treatment modalities, the more susceptible we may be to “misses” due to remaining uncertainties that have not been properly taken into account in the treatment plan design. It is difficult to draw a single conclusion as to the best strategy to deal with time-­varying density variations. There are many treatment delivery para­meters that can be optimized (see the Section 14.4), and one can combine approaches such as gating and rescanning. The best strategy may also depend on beam-line performance, something that is gradually improving over time. In any case, it is important not to simply apply proton therapy to

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any tumor site without at least performing a rudimentary sensitivity analysis to density variations, motion, and interplay effects. 14.5.1  Treatment-Planning Quality Assurance The effectiveness of any proton therapy delivery technique in dealing with target motion is, judging by the available literature, typically validated in silico using homogeneous or highly stylized phantoms. This simplification helps in assessing the merits of the various techniques but does not exclude the possibility of severe unexpected dose variations for any actual patient characteristics. It is impossible to overemphasize the need for a priori assessment of the accuracy of a proton therapy treatment plan, especially for moving tumors, by means of using a 4D treatment-planning simulation platform that incorporates 4D CT, the patient’s breathing trace, and the time-resolved dose delivery characteristics of the beam line, and that takes any techniquespecific parameters into account (41, 48, 54). In general, an estimate of target dose and normal tissue dose can be obtained by recalculating the 3D dose distribution for a variety of possible treatment scenarios (12). In photon therapy, the shape of the dose distribution to first order can be considered invariant under density variations and setup errors. This makes a probabilistic approach towards the likelihood of “a good treatment plan” as suggested by, e.g., van Herk et al. quite feasible (12). Rather than recalculating the dose distribution for every possible setup error and density variation, one only has to shift it. Interplay effects are proven to be small given a sufficient number of treatment fractions and/or beam portals (11). But even in photon radiotherapy, clinical use of such doseerror simulation platforms is very limited. Typically the appropriateness of a treatment plan (and of a treatment) is judged, by the radiation oncologist and the clinical physicist, based on dose-volume histograms (DVHs) and axial dose distributions for a single static patient geometry: the treatmentplanning CT scan. The application of proton therapy to tumor sites with a variable density geometry (e.g., lung and liver instead of intracranial treatments) in combination with the advance of IMPT is a recent development and warrants caution. Interestingly, the development and application of dose-error simulation platforms in proton therapy has not kept up with these new developments. A similar probabilistic approach as described above (12) may be feasible for proton therapy. Many variables can, however, have a significant degrading effect on the cumulative dose, for example, Hounsfield unit-to-proton stopping power conversion, setup errors, intrafractional and interfractional density variation, variation in the motion characteristics, and timing of treatment delivery with respect to this motion. A probabilistic plan evaluation approach may therefore require a nearly prohibitive number of recalculations of the dose distribution making a priori plan evaluation an immense numerical challenge. Some of the variables mentioned may have only

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a limited effect on the cumulative dose to the tumor, but this needs to be proven comprehensively. Chapter 15 provides a framework for taking (some of these uncertainties) into account intrinsically in the treatment plan design by means of robust optimization. Furthermore, Mori et al. describe a tool that allows a priori selection of beam directions with reduced sensitivity to range variations over the motion cycle, thereby increasing the confidence that what is treatment planned will also be delivered to the patient (55). 14.5.2  Treatment Delivery Quality Assurance Proton radiotherapy, like any other means of radiation therapy, requires a quality management program that assesses and ensures the continued accuracy of treatment delivery. This means system-wide quality assurance (QA) as well as patient-specific QA. Aside from the general dosimetric QA (see Chapter 8), system-wide QA for moving tumors also has to validate the motion-effect mitigation technique applied. General testing of the system under reference conditions provides a great amount of confidence, and such tests can be quite elaborate. The minimal solution typically involves dosimetric measurements in a (solid) water phantom positioned on a motion platform using a known motion trajectory. As discussed below, however, more elaborate motion phantoms should be developed to mimic the clinical situation more closely. Validation of each step in the radiation therapy chain individually may not be able to anticipate all circumstances that may occur during clinical operation. For completeness, an end-to-end test should be designed and executed, simulating an actual treatment as closely as possible. Several authors have therefore recommended the development and use of a dedicated 4D motion phantom (41, 54). Ideally such a phantom closely mimics a realistic patient density geometry, has programmable motion characteristics, and has the possibility to measure the (4D) dose distribution in several points and/or planes. Such a phantom allows end-to-end testing from 4D CT scanning, to deformable registration, to (robust) plan optimization, to in-room patient positioning, and to dose delivery. True a priori patient-specific verification is very difficult (if not impossible) because the time-varying density geometry cannot be mimicked exactly. The next best approach is to limit the duration of undesired dose delivery. In vivo dosimetry (see Chapter 16), for example, can provide an early warning as to the inadequateness of a delivered treatment fraction and allows the clinical team to take corrective action. Another approach, that also only allows correction after delivery of at least some dose, may be to perform closedloop dose accumulation. Using the treatment fraction–specific 3D/4D patient information, the on-line measured motion characteristics, and a detailed log of all machine parameters as a function of time, one may be able to recalculate a best estimate of the actually delivered dose. Patient-specific QA and adaptive therapy are thus closely interrelated.

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14.6  Future Perspective The finite range of protons allows for substantial sparing of OAR, but also requires great caution in mitigating the detrimental dosimetric effects of time-varying position and density variations. Figure 14.8 attempts to visualize the susceptibility of a number of proton and photon treatment modalities to these variations. Photon radiotherapy dose distributions suffer relatively little from these uncertainties, or they can often be taken into account adequately by means of a straightforward margining approach. The term “density variations” in this graph denotes range and setup uncertainties, as well as density variations over time (intrafractional, interfractional, and gradual changes over the entire treatment course). For the proton modalities, PSPT is the only modality that does not suffer from interplay effects. IMPT is the most sensitive treatment modality as, by definition, multiple inhomogeneous dose distributions have to be matched accurately (in 3D) to ensure the intended, and typically homogeneous, target dose coverage. At the moment, motion in proton radiotherapy is a problem that has not yet been completely solved. For PSPT one may be able to choose a practical solution, realizing that the approach used may not ensure target coverage for all possible patients and motion characteristics (see Chapter 10), but, for now, perhaps the best strategy is to play it safe, for example, by performing “selection at the gate.” This means assessing motion at patient intake and choosing the treatment modality, in the range from photon beam therapy to beam tracking with IMPT, dependent on the observed motion characteristics.

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FIGURE 14.8 Sensitivity of the proton modalities, and some photon modalities, to density variations and interplay effect. The bottom left corner indicates the least sensitivity and the top right corner the most sensitivity. 3D CRT, three-dimensional conformal (photon) radiotherapy.

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Of the strategies defined in Section 14.4, general treatment planning considerations, gating, and apnea have been clinically applied for actual patient treatments, and mostly for PSPT only. The proton radiotherapy community is, however, longing to transfer the promises of PBS for static tumors (increased dose conformity and OAR sparing, biology-guided adaptive radiotherapy) to moving tumors as well. In the next two to five years, according to Rietzel & Bert (41), gating and rescanning will be applied in a clinical treatment environment for PBS. Beam tracking is currently technically feasible but needs more development and validation. It will likely not be clinically applied within the next five years. In the long run, perhaps the field of proton therapy will (have to) evolve toward in-room 4D imaging and on-line reoptimization of the dose distribution, in combination with beam tracking or near-instantaneous dose delivery because then the high accuracy that is provided by the biophysical properties of the beam can be ideally applied to the patient.

References







1. Britton KR, Starkschall G, Tucker SL, Pan T, Nelson C, Chang JY, et al. Assessment of gross tumor volume regression and motion changes during radiotherapy for non-small-cell lung cancer as measured by four-dimensional computed tomography. Int J Radiat Oncol Biol Phys. 2007 Jul 15;68(4):1036–46. 2. Sonke JJ, Lebesque J, van Herk M. Variability of four-dimensional computed tomography patient models. Int J Radiat Oncol Biol Phys. 2008 Feb 1;70(2):590–98. 3. McDermott LN, Wendling M, Sonke JJ, van Herk M, Mijnheer BJ. Anatomy changes in radiotherapy detected using portal imaging. Radiother Oncol. 2006 May;79(2):211–17. 4. Barker JL Jr, Garden AS, Ang KK, O’Daniel JC, Wang H, Court LE, et al. Quantification of volumetric and geometric changes occurring during fractionated radiotherapy for head-and-neck cancer using an integrated CT/linear accelerator system. Int J Radiat Oncol Biol Phys. 2004 Jul 15;59(4):960–70. 5. Langen KM, Jones DT. Organ motion and its management. Int J Radiat Oncol Biol Phys. 2001 May 1;50(1):265–78. 6. Seppenwoolde Y, Shirato H, Kitamura K, Shimizu S, van Herk M, Lebesque JV, et al. Precise and real-time measurement of 3D tumor motion in lung due to breathing and heartbeat, measured during radiotherapy. Int J Radiat Oncol Biol Phys. 2002 Jul 15;53(4):822–34. 7. Sonke JJ, Rossi M, Wolthaus J, van Herk M, Damen E, Belderbos J. Frameless stereotactic body radiotherapy for lung cancer using four-dimensional cone beam CT guidance. Int J Radiat Oncol Biol Phys. 2009 Jun 1;74(2):567–74. 8. Balter JM, Ten Haken RK, Lawrence TS, Lam KL, Robertson JM. Uncertainties in CT-based radiation therapy treatment planning associated with patient ­breathing. Int J Radiat Oncol Biol Phys. 1996 Aug 1;36(1):167–74. 9. Smitsmans MH, Pos FJ, de Bois J, Heemsbergen WD, Sonke JJ, Lebesque JV, et al. The influence of a dietary protocol on cone beam CT-guided radiotherapy for prostate cancer patients. Int J Radiat Oncol Biol Phys. 2008 Jul 15;71(4):1279–86.

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10. Dawson LA, Jaffray DA. Advances in image-guided radiation therapy. J Clin Oncol. 2007 Mar 10;25(8):938–46. 11. Bortfeld T, Jokivarsi K, Goitein M, Kung J, Jiang SB. Effects of intra-fraction motion on IMRT dose delivery: statistical analysis and simulation. Phys Med Biol. 2002 Jul 7;47(13):2203–20. 12. van Herk M, Remeijer P, Rasch C, Lebesque JV. The probability of correct target dosage: dose-population histograms for deriving treatment margins in radiotherapy. Int J Radiat Oncol Biol Phys. 2000 Jul 1;47(4):1121–35. 13. Killoran JH, Kooy HM, Gladstone DJ, Welte FJ, Beard CJ. A numerical simulation of organ motion and daily setup uncertainties: implications for radiation therapy. Int J Radiat Oncol Biol Phys. 1997 Jan 1;37(1):213–21. 14. Engelsman M, Sharp GC, Bortfeld T, Onimaru R, Shirato H. How much margin reduction is possible through gating or breath hold? Phys Med Biol. 2005 Feb 7;50(3):477–90. 15. Mori S, Wolfgang J, Lu HM, Schneider R, Choi NC, Chen GT. Quantitative assessment of range fluctuations in charged particle lung irradiation. Int J Radiat Oncol Biol Phys. 2008 Jan 1;70(1):253–61. 16. Lambert J, Suchowerska N, McKenzie DR, Jackson M. Intrafractional motion during proton beam scanning. Phys Med Biol. 2005 Oct 21;50(20):4853–62. 17. Engelsman M, Kooy HM. Target volume dose considerations in proton beam treatment planning for lung tumors. Med Phys. 2005 Dec;32(12):3549–57. 18. Kang Y, Zhang X, Chang JY, Wang H, Wei X, Liao Z, et al. 4D proton treatment planning strategy for mobile lung tumors. Int J Radiat Oncol Biol Phys. 2007 Mar 1;67(3):906–14. 19. Hui Z, Zhang X, Starkschall G, Li Y, Mohan R, Komaki R, et al. Effects of interfractional motion and anatomic changes on proton therapy dose distribution in lung cancer. Int J Radiat Oncol Biol Phys. 2008 Dec 1;72(5):1385–95. 20. Farr JB, Mascia AE, Hsi WC, Allgower CE, Jesseph F, Schreuder AN, et al. Clinical characterization of a proton beam continuous uniform scanning system with dose layer stacking. Med Phys. 2008 Nov;35(11):4945–54. 21. Fujitaka S, Takayanagi T, Fujimoto R, Fujii Y, Nishiuchi H, Ebina F, et al. Reduction of the number of stacking layers in proton uniform scanning. Phys Med Biol. 2009 May 21;54(10):3101–11. 22. Phillips MH, Pedroni E, Blattmann H, Boehringer T, Coray A, Scheib S. Effects of respiratory motion on dose uniformity with a charged particle scanning method. Phys Med Biol. 1992 Jan;37(1):223–34. 23. Seiler PG, Blattmann H, Kirsch S, Muench RK, Schilling C. A novel tracking technique for the continuous precise measurement of tumour positions in conformal radiotherapy. Phys Med Biol. 2000 Sep;45(9):N103–10. 24. Furukawa T, Inaniwa T, Sato S, Tomitani T, Minohara S, Noda K, et al. Design study of a raster scanning system for moving target irradiation in heavy-ion radiotherapy. Med Phys. 2007 Mar;34(3):1085–97. 25. Bert C, Grözinger SO, Rietzel E. Quantification of interplay effects of scanned particle beams and moving targets. Phys Med Biol. 2008 May 7;53(9):2253–65. 26. Seco J, Robertson D, Trofimov A, Paganetti H. Breathing interplay effects during proton beam scanning: simulation and statistical analysis. Phys Med Biol. 2009 Jul 21;54(14):N283–94. 27. Bert C, Gemmel A, Saito N, Rietzel E. Gated irradiation with scanned particle beams. Int J Radiat Oncol Biol Phys. 2009 Mar 15;73(4):1270–75.

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28. Zenklusen SM, Pedroni E, Meer D. A study on repainting strategies for treating moderately moving targets with proton pencil beam scanning at the new Gantry 2 at PSI. Phys Med Biol. 2010 Sep 7;55(17):5103–21. 29. Mageras GS, Yorke E. Deep inspiration breath hold and respiratory gating strategies for reducing organ motion in radiation treatment. Semin Radiat Oncol. 2004 Jan;14(1):65–75. 30. Lagendijk JJ, Raaymakers BW, Raaijmakers AJ, Overweg J, Brown KJ, Kerkhof EM, et al. MRI/linac integration. Radiother Oncol. 2008 Jan;86(1):25–29. 31. Shirato H, Shimizu S, Shimizu T, Nishioka T, Miyasaka K. Real-time tumourtracking radiotherapy. Lancet. 1999 Apr 17;353(9161):1331–32. 32. Berbeco RI, Nishioka S, Shirato H, Chen GT, Jiang SB. Residual motion of lung tumours in gated radiotherapy with external respiratory surrogates. Phys Med Biol. 2005 Aug 21;50(16):3655–67. 33. Nioutsikou E, Seppenwoolde Y, Symonds-Tayler JR, Heijmen B, Evans P, Webb S. Dosimetric investigation of lung tumor motion compensation with a robotic respiratory tracking system: an experimental study. Med Phys. 2008 Apr;35(4):1232–40. 34. Knopf A, Hug EB, Lomax AJ. Scanned proton radiotherapy for mobile ­targets— which plan characteristics require rescanning, which maybe not? In: Proceedings of the XVIth Conference on the Use of Computers in Radiotherapy; 2010 May 30–Jun 3; Amsterdam, the Netherlands. 35. Negoro Y, Nagata Y, Aoki T, Mizowaki T, Araki N, Takayama K, et al. The effectiveness of an immobilization device in conformal radiotherapy for lung tumor: reduction of respiratory tumor movement and evaluation of the daily setup accuracy. Int J Radiat Oncol Biol Phys. 2001 Jul 15;50(4):889–98. 36. Lu HM, Brett R, Sharp G, Safai S, Jiang S, Flanz J, et al. A respiratory-gated treatment system for proton therapy. Med Phys. 2007 Aug;34(8):3273–78. 37. Minohara S, Kanai T, Endo M, Noda K, Kanazawa M. Respiratory gated irradiation system for heavy-ion radiotherapy. Int J Radiat Oncol Biol Phys. 2000 Jul 1;47(4):1097–103. 38. Wong JW, Sharpe MB, Jaffray DA, Kini VR, Robertson JM, Stromberg JS, et al. The use of active breathing control (ABC) to reduce margin for breathing motion. Int J Radiat Oncol Biol Phys. 1999 Jul 1;44(4):911–19. 39. Ford EC, Mageras GS, Yorke E, Ling CC. Respiration-correlated spiral CT: a method of measuring respiratory-induced anatomic motion for radiation treatment planning. Med Phys. 2003 Jan;30(1):88–97. 40. Eckermann M, Hillbrand M, Herbst M, Rinecker H. Scanning proton beam radiotherapy under functional apnea. In: Proceedings of the 50th Conference of the Particle Therapy Co-Operative Group (PTCOG); 2011 May 8–14; Philadelphia, PA. 41. Rietzel E, Bert C. Respiratory motion management in particle therapy. Med Phys. 2010 Feb;37(2):449–60. 42. Bert C, Gemmel A, Saito N, Chaudhri N, Schardt D, Durante M, et al. Dosimetric precision of an ion beam tracking system. Radiat Oncol. 2010;5:61. 43. Keall PJ, Kini VR, Vedam SS, Mohan R. Motion adaptive x-ray therapy: a feasibility study. Phys Med Biol. 2001 Jan;46(1):1–10. 44. van Klaveren RJ, Pattynama P, Nuyttens JJ. Stereotactic radiotherapy with realtime tumor tracking for non-small cell lung cancer: clinical outcome. Radiother Oncol. 2009 Jun;91(3):296–300.

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45. Saito N, Bert C, Chaudhri N, Gemmel A, Schardt D, Durante M, et al. Speed and accuracy of a beam tracking system for treatment of moving targets with scanned ion beams. Phys Med Biol. 2009 Aug 21;54(16):4849–62. 46. Chaudhri N, Saito N, Bert C, Franczak B, Steidl P, Durante M, et al. Ion-optical studies for a range adaptation method in ion beam therapy using a static wedge degrader combined with magnetic beam deflection. Phys Med Biol. 2010 Jun 21;55(12):3499–513. 47. van de Water S, Kreuger R, Zenklusen S, Hug E, Lomax AJ. Tumour tracking with scanned proton beams: assessing the accuracy and practicalities. Phys Med Biol. 2009 Nov 7;54(21):6549–63. 48. Bert C, Rietzel E. 4D treatment planning for scanned ion beams. Radiat Oncol. 2007 Jul 3;2:24. 49. Li Q, Groezinger SO, Haberer T, Rietzel E, Kraft G. Online compensation for target motion with scanned particle beams: simulation environment. Phys Med Biol. 2004 Jul 21;49(14):3029–46. 50. Grözinger SO, Rietzel E, Li Q, Bert C, Haberer T, Kraft G. Simulations to design an online motion compensation system for scanned particle beams. Phys Med Biol. 2006 Jul 21;51(14):3517–31. 51. Bert C, Saito N, Schmidt A, Chaudhri N, Schardt D, Rietzel E. Target motion tracking with a scanned particle beam. Med Phys. 2007 Dec;34(12):4768–71. 52. Grözinger SO, Bert C, Haberer T, Kraft G, Rietzel E. Motion compensation with a scanned ion beam: a technical feasibility study. Radiat Oncol. 2008 Oct 14;3:34. 53. Lüchtenborg R, Saito N, Chaudhri N, Durante M, Rietzel E, Bert C. On-line compensation of dose changes introduced by tumor motion during scanned particle therapy. In: Proceedings of the 11th World Congress of Medical Physics and Biomedical Engineering; 2010 September 7–12; Munich, Germany. 54. Knopf A, Bert C, Heath E, Simeon N, Kraus K, Richter D, et al. Special report: Workshop on 4D-treatment planning in actively scanned particle therapy—­ recommendations, technical challenges, and future research directions. Med Phys. 2010 Sep;37(9):4608–14. 55. Mori S, Chen GT. Quantification and visualization of charged particle range variations. Int J Radiat Oncol Biol Phys. 2008 Sep 1;72(1):268–77. 56. ICRU Report 62. Prescribing, recording and reporting photon beam therapy. International Commission on Radiation Units and Measurements; 1999.

15 Treatment-Planning Optimization Alexei V. Trofimov, Jan H. Unkelbach, and David Craft CONTENTS 15.1 Optimization of SOBP Fields.................................................................... 462 15.1.1 Optimization of Field Flatness...................................................... 462 15.1.2 Forward Planning with SOBP Fields...........................................464 15.2 IMPT as an Optimization Problem.......................................................... 465 15.2.1 Setup of the IMPT Optimization Problem.................................. 466 15.2.2 Solving the Optimization Problem.............................................. 469 15.3 Multicriteria Optimization........................................................................ 470 15.3.1 Prioritized Optimization............................................................... 471 15.3.2 PS Approach.................................................................................... 471 15.3.3 Navigation of the PS....................................................................... 472 15.3.4 Comparing Prioritized Optimization and PS-Based MCO...... 474 15.4 Robust Optimization Methods for IMPT................................................ 475 15.4.1 IMPT Dose in the Presence of Uncertainties.............................. 475 15.4.2 Robust Optimization Strategies.................................................... 476 15.4.2.1 The Probabilistic Approach............................................ 477 15.4.2.2 The Robust Approach...................................................... 478 15.4.2.3 Optimization of the Worst-Case Dose Distribution..... 478 15.4.3 Examples of Robust Optimization............................................... 478 15.5 Temporospatial (4D) Optimization.......................................................... 480 15.5.1 Plan Optimization Based on a Known Motion Probability Density Function............................................................................. 482 15.5.2 Plan Optimization for an Uncertain Motion PDF...................... 483 15.5.3 Optimizing a Different Fluence Map for Every Phase..............483 15.6 Accounting for Biological Effects in IMPT Optimization.....................483 15.7 Other Applications of Mathematical Optimization in Proton Therapy.........................................................................................................484 15.7.1 Scan Path Optimization.................................................................484 15.7.2 Beam Current Optimization for Continuous Scanning............484 References..............................................................................................................484

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This chapter describes various applications of mathematical optimization techniques in treatment planning for proton therapy. The most prominent example is the optimization of beam weights for intensity-modulated proton therapy (IMPT). The conceptual and practical aspects of IMPT have been introduced in previous chapters (see primarily Chapter 11). Here, we focus on the mathematical aspects of treatment planning. First, in Section 15.1, we briefly recapitulate the basics of three-dimensional (3D) conformal therapy, including the design of spread-out Bragg peaks (SOBPs), and forward planning. In Section 15.2, we illustrate how IMPT inverse planning is formulated as a mathematical optimization problem and comment on methods to solve this problem. Then, we discuss advanced optimization techniques for proton therapy: multicriteria optimization (Section 15.3), robust optimization methods for handling range and setup uncertainty (Section 15.4), incorporation of intrafractional motion in treatment planning (Section 15.5), and consideration of radiobiological effects in IMPT optimization (Section 15.6). Finally, in Section 15.7, we review other applications of mathematical optimization in proton therapy, such as the optimization of beam current modulation and scan path for continuous scanning.

15.1  Optimization of SOBP Fields An SOBP is the foundation of forward treatment planning for 3D-conformal proton therapy. It is used to achieve a longitudinal conformality of the required dose to the target. In his seminal paper on therapeutic use of protons, Dr. Robert Wilson recognized the need for optimization of proton dose distribution for clinical treatments, by pointing out that Bragg peaks need to spread out to uniformly cover large tumor volumes. In his assessment this could be “easily accomplished by interposing a rotating wheel of various thickness” in the beam path (1), the method of modulation that is now widely used for proton therapy (see Chapter 5). By using the word “easily,” Dr. Wilson, perhaps, anticipated the fact that the problem of optimization of modulation of SOBP would be relatively easy compared to the optimization problems yet to arise in proton therapy. 15.1.1  Optimization of Field Flatness To create a clinically relevant SOBP of the desired flatness in a passive beam scattering system, a variety of components must operate in conjunction to produce the desired beam parameters. Koehler et al. (2) described one of the earliest examples of design of flat SOBPs using computer-based optimization. Based on the input values of range and modulation width, the

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FIGURE 15.1 Depth–dose profile of a spread-out Bragg peak (SOBP), and constituent pristine peaks: optimization of pristine peak weights leads to (A) uniform SOBP dose, while variation in the pristine peak dose profile may introduce a (B) raising or (C) falling slope in SOBP. In principle, arbitrary profiles of the peak dose can be achieved by optimization, for example, (D) a profile with the integrated dose boost of 10% to the middle part of the SOBP.

code written in Fortran IV iteratively searched for the set of amplitudes of shifted pristine peaks, and spacings between them (in other words, relative width, and thickness of the wheel steps), which realized the desired SOBP (see Figure 15.1A). Notably, because the shape of the Bragg peak curve varies with the beam energy, the weights of individual peaks in the SOBP need to be optimized separately for different ranges in tissue, to avoid sloping in the SOBP, as shown in Figure 15.1B and C. In the early days of proton therapy, the wide variety of clinically required combinations of range and SOBP modulation required a large number of premanufactured wheels, with separate wheels required for shallow and deep tumors, one wheel for a close set of modulation width (the smallest steps of the propeller could be added or removed to allow for some variation in the total modulation width). A more flexible modern solution uses a beam current modulation system, with a limited number of wheel tracks (see Chapter 5). The pulled-back Bragg peaks can be individually controlled to produce uniform dose plateaus for a large range of treatment depths using only a small number of modulator wheels (3–5).

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In principle, by temporally optimizing the beam current during the modulation cycle, one can create SOBPs with arbitrary depth–dose profiles. This includes “intensity-modulated” fields according to the common definition, namely, dose distributions, that are inhomogeneous by design. Notably, the beam current modulation literally constitutes intensity modulation of the beam, regardless of whether the resulting distribution is inhomogeneous or not. An example of inhomogeneous dose achievable with range modulation is the SOBP including a simultaneous integrated dose boost delivered to a subsection of the target, as in Figure 15.1D. It should be noted though that this technique allows for intensity modulation only in depth, whereas the beam intensity is homogeneous laterally. 15.1.2  Forward Planning with SOBP Fields Procedures of forward planning for 3D-conformal proton therapy have been well described by Bussière and Adams (6), as well as in Chapter 10 of this book. Figure 15.2 illustrates how a “manual optimization” of a treatment plan might be undertaken. The search for a satisfactory solution does A

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FIGURE 15.2 (See color insert.) Forward planning and manual optimization for a case of retroperitoneal tumor. Dose distributions from three beam directions are shown in (A–C). These can be combined with various weights leading to a variety of clinically acceptable dose distributions, for example, with doses shown in (D–F), and the DVH in (G–I), respectively.

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involve iterative adjustment; however, it is rather subjective (e.g., depends on the planner’s training, habit, and judgment) and is not systematic (e.g., iterations do not always lead toward a more preferable solution). Thus the process cannot be termed optimization in the strictly mathematical sense. First, the irradiation directions are selected as well as the range and SOBP modulation width necessary to cover the target. Range compensators are designed to conform the dose to the distal aspect of the target, and accommodations are made to prevent underdosing of the target in case of misalignment of treatment field and tissue heterogeneities, for example, using the technique of compensator expansion, or “smearing” (7) (also see Chapter 10). Once these steps are completed, a forward calculation is performed to determine the dose from the given field, based on the assumed beam fluence. The task of the planner is then to iteratively adjust the fluences, or “weights,” of multiple beams and to combine their doses so that the resulting distribution suits a particular set of requirements. For example, in the case illustrated in Figure 15.2, irradiating the spinal cord up to the tolerance (Figure 15.2, D and G) may be considered acceptable in a certain situation, because this configuration minimizes the integral dose and the main irradiation direction is least affected by internal motion (e.g., of liver with respiration for the rightanterior beam) or variations in the stomach and bowel filling (for the left beam lateral). In other situations, such as repeat treatments, cord tolerance may be reduced, and other directions have to be used. In those cases, the clinically optimal balance, between irradiation of various structures, needs to be selected (compare, e.g., Figure 15.2, H vs. I).

15.2  IMPT as an Optimization Problem Intensity-modulation methods allow one to achieve highest conformality of proton dose distributions to the target volume and best sparing of healthy tissue. Unlike 3D-conformal treatments, in which each SOBP field delivers a uniform (within a few percent) dose to the whole target volume, individual IMPT fields typically deliver nonuniform dose distributions (e.g., see Figure 15.3). Similar to IMRT with photons, these nonuniform field contributions combine to produce the desired therapeutic dose distribution, which may be shaped to conform to the clinical prescription. An important difference from photon intensity-modulated radiation therapy (IMRT) is that the Bragg peak of the proton depth dose distribution introduces an additional degree of freedom in modulation of the dose in depth along the beam axis, in addition to the modulation in the transverse plane, which is available in both IMRT and IMPT. Despite this difference, IMRT and IMPT are very similar regarding the mathematical formulation of the treatmentplanning problem.

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A

C

B

D

E

FIGURE 15.3 (See color insert.) IMPT plan for a paraspinal tumor. (A) CT scan showing outlines of the tumor and the spinal cord, (B) dose distribution from a 3D IMPT treatment plan, using three beam directions. Dose contributions from individual beams are shown for (C) right-posterior oblique, (D) posterior, and (E) left-posterior oblique fields. (The conventional IMPT plan did not include any consideration of delivery uncertainties.)

To take full advantage of the possibility to sculpt the dose in depth, IMPT treatments use narrow proton pencil beams, which can be scanned across the transverse plane while changing energy and intensity to control the dose to a point. The most common and versatile IMPT technique is the 3D-modulation method, in which individually weighted Bragg peak “spots” are placed throughout the target volume (8). The examples in this chapter use 3D-modulation; however, most optimization methods described below are equally applicable to other techniques, such as single-field uniform dose (SFUD) treatments or the distal edge tracking (DET). SFUD treatments also use weighted pencil beams distributed in three dimensions, but aim at delivering a homogeneous dose to the target from every individual field direction. In the DET method, Bragg peaks are placed only at the distal surface of the tumor (9). 15.2.1  Setup of the IMPT Optimization Problem To apply general optimization methods to radiation therapy planning, technical limitations and treatment goals need to be formulated mathematically

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as objectives and constraints. For that purpose, the patient image data are partitioned into volumes of interest (VOI), which could include targets, critical organs at risk of undesired side effects (organs at risk [OAR]), and other tissue volumes. VOI are further divided into basic geometric elements called voxels. The total dose distribution from an IMPT field delivered with a scanned beam can be calculated as the sum of contributions from “static” pencil beams fixed at various positions along the scan path. The dose from individual pencil beams to various voxels of interest can be represented in the form of the dose influence matrix Dij , where i is the voxel index, and j is the beam index. The total dose to any voxel is then calculated as follows: di = ∑ x j ⋅ Dij



j

(15.1)



where xj is the relative “weight” of the beam j, which is proportional to the total number of protons delivered at the given spot, that is the position of Bragg peak. The weights xj are the optimization variables that need to be determined in treatment planning. Because of the large number (thousands or tens of thousands) of such pencil beams involved, IMPT treatment planning requires mathematical optimization methods (10, 11). The output of the plan optimization is a set of beam weight distributions, often called intensity or fluence maps. Unlike in IMRT, where a single two-dimensional (2D) fluence map characterizes a field, in IMPT, many beam energies may be used to irradiate the target from the same direction, and optimization will yield separate maps for every energy setting. Dosimetric or other planning objectives may be defined for volumes or individual voxels. The planning objectives and their priorities can be expressed in the objective function (OF). The term optimization, in the context of treatment planning, typically signifies the search for a set of plan parameters that minimize the value of the OF, subject to a set of constraints that have to be fulfilled. A widely used objective function that aims at minimizing the volume, within a given OAR n, that exceeds the maximum tolerance dose Dmax is given by the quadratic penalty function:

On ( d ) =

∑

i∈OARn

H ( di − Dmax ) ( di − Dmax )

2

(15.2)

where H(d) is the Heavyside step function. Similarly, one can define a quadratic function that aims to reduce volumes of the tumor, which receive less than the minimum dose Dmin. Objective functions may also include the generalized equivalent uniform dose (12):



 1 On ( d ) =   Nn 

∑ (d )

i∈OARn

i

p

  

1/p

(15.3)

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where Nn is the number of voxels in the VOI n, and p is an organ-specific parameter. In addition, there may be constraints on the dose in a VOI that have to be fulfilled in order to make the treatment plan acceptable. For example, one can request that the dose in every voxel belonging to the tumor should be between a minimum dose Dmin and a maximum dose Dmax. This would result in the hard constraint

Dmin ≤ di ≤ Dmax

∀i ∈ VOI .

(15.4)

In clinical situations, treatment objectives often directly conflict each other: for example, a target may not be completely irradiated to the prescribed level if a dose-sensitive critical structure is immediately adjacent to it. In this case, hard dosimetric constraints have to be used with care, and it is often necessary to reformulate a constraint as an objective. For example, it may be necessary to minimize the dose to an OAR that exceeds the tolerance dose through a quadratic objective, rather than enforcing the dose to be below the maximum dose in every voxel through a constraint. Such an objective is often referred to as a “soft constraint” in the medical physics literature. Multicriteria optimization methods, discussed in Section 15.3, address such inherent treatment-planning contradictions. Thus, one can formulate the general IMPT optimization problem as follows: minimize  (with respect to the beam weights x):

∑α



n

n

⋅ On (d)

subject to the constraints:

di = ∑ x j ⋅ Dij j





lm ≤ Cm ( d ) ≤ um



x j ≥ 0.

(15.5)

In the above formulation the different objectives On are multiplied by respective weighting factors αn and are added together to form a single composite objective. By selecting and adjusting the weighting factors, the treatment planner can prioritize different objectives and control the trade-off between them. The approach of a weighted sum of objectives is pursued in most current treatmentplanning systems. (An alternative to this standard approach is multicriteria optimization.) The functions Cm denote a general constraint function, and lm and um are upper and lower bounds. An example of a simple constraint function is the minimum or maximum dose constraint mentioned above. Alternatively, constraints on equivalent uniform dose (EUD) can be imposed (12).

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A number of additional parameters often need to be specified before optimization of beam weights is performed. These include, for example, the choice of the algorithm for placement of Bragg peaks (8), as well as the volume used for placement (which may be larger than the target), the spacing of peaks and layers in depth (13), and the size of the pencil beam used for delivery of therapy (14). These additional treatment parameters, or hyperparameters, affect the outcome of optimization; however, they are not determined through an optimization algorithm in the mathematical sense. Instead they are chosen based on experience, planning studies, and physical or theoretical considerations. 15.2.2  Solving the Optimization Problem IMPT represents a textbook example of a large-scale optimization problem, especially if convex objectives and constraints are used. The variables, the beam weights x, are continuous, that is, can take any nonnegative value (although these are often discretized, when sequenced for delivery). The objectives can typically be formulated in closed form as a function of the optimization variables, and also the gradient of the objective can be calculated analytically. Therefore a large variety of algorithms can be applied. Those can be categorized into constrained and unconstrained methods. In the case of unconstrained methods, no dosimetric hard constraints are applied, that is, all treatment goals are formulated as objectives. The only constraints that always need to be fulfilled to yield a physically meaningful plan are the variable bound constraints xj ≥ 0. However, those can be treated through relatively simple methods such as gradient projection methods. Most current treatment-planning systems use unconstrained optimization methods. In this case, improved gradient methods are used such as quasi-Newton methods or the diagonalized Newton method. Constrained optimization for IMPT is still challenging because of the large number of variables (103 to 105) and the large number of voxels (105 to 107). If only linear objectives and constraints are used, the linear programming framework can be applied. In the nonlinear case, sequential quadratic programming methods have been used (RayStation; Raysearch Laboratories, Stockholm, Sweden) as well as barrier-penalty methods (Monaco; Elekta, Stockholm, Sweden). Optimization problems may further be classified as convex or nonconvex. In a convex optimization problem, all of the constraints as well as the minimized objective function are convex functions. For example, linear functions, and therefore, linear programming problems are convex. The feasible region (i.e., all sets of spot weights x that fulfill the constraints) is then also convex, being the intersection of convex constraint functions. With convex objectives and a convex feasible region a local optimal solution is also a global optimal solution. Thus, optimization would either yield the globally

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optimal solution or demonstrate that there is no feasible solution. All the objectives and constraints described above (e.g., quadratic function, EUD) are convex. Conversely, a nonconvex optimization problem is any problem where the objective is nonconvex or nonconvex constraint functions give rise to a nonconvex feasible region. In this setting, multiple local optimal solutions are possible and, in practice, considering the large number of variables in IMPT, it is typically not possible to guarantee that an algorithm used to solve the optimization problem indeed converges to the globally optimal solution. Nonconvex constraints are becoming increasingly common in optimization. Examples of nonconvex objectives include typical radiobiological models of tumor control and normal tissue complication probabilities. Another example is the dose-volume constraints, which can be conveniently defined to specify the desired shape of the dose-volume histogram (DVH) directly (15); for example, “the fraction of the volume of a specific OAR irradiated to 40 Gy is not to exceed 30%.”

15.3  Multicriteria Optimization Optimization theory is built up around the single criterion optimization problem, where there is one objective and other problem considerations are included as constraints. In radiotherapy, the main objective—to cover the target with the prescription dose—is in direct conflict with the other objectives of keeping the dose to the healthy organs to a minimum. If biological response models such as tumor control probability (TCP) and normal tissue complication probability (NTCP) were reliable, one might be able to solve radiotherapy optimization well in a single criterion mode: maximize TCP subject to the NTCPs of the relevant organs at risk being below acceptable levels. However, even in this setting, depending on the patientspecific trade-off (for the treatment plan under consideration, how much gain in TCP is there if you allow NTCP for some organ to increase by some amount), were there a tool to easily explore other options, a physician might choose a different plan than the plan returned from the single-criterion optimization. Presently, the standard commercial systems available for treatment optimization still attempt to solve the radiotherapy optimization problem with a single-criterion approach, and this leads to a lengthy optimization iteration cycle, where treatment planners try to find the set of weights and function parameters that give a plan that best matches the physician’s goals for treatment. The problem is, it is very difficult to guess those weights and function parameters to get a good plan, and as the number of organs to consider

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increases, this task becomes increasingly more difficult. Several groups are at work to bring multicriteria optimization (MCO) into routine clinical usage (16–22). There are two main approaches to MCO for radiotherapy treatment planning: prioritized optimization and the Pareto surface (PS) approach. Below, we describe the two approaches, show how they are related, and discuss their pros and cons. 15.3.1  Prioritized Optimization Prioritized optimization, or lexicographic ordering, as it is sometimes called in the literature, is a natural approach for dealing with multiple objectives when the objectives can be ranked in terms of importance (23, 24). Letting O1 denote the highest priority objective, O2 the second highest, etc., prioritized optimization solves the following sequent of optimization problems for k priority levels: (1) minimize  O1(x) subject to x ∈ X ; (2) minimize  O2(x) subject to x ∈ X , and O1(x) ≤ O1* · (1 + ε); … (k) minimize  Ok(x) subject to x ∈ X, and, for all i < k, Oi(x) ≤ Oi* · (1 + ε), (15.6) where x is a set of the decision variables, X is a constraint set that represents constraints on the beamlet fluences (upper and lower bounds) and is also used to denote hard dosimetric constraints, such as voxel dose, organ mean dose, or EUD that must be met by every considered solution. O1* is the optimal objective value from the first optimization (i.e., the fluence values in the case of IMPT), and ε is a small positive slip factor. Multiplication by (1 + ε) allows a small degradation in the value of the first optimization, thus hopefully permitting the second priority objective to achieve a good value, and so forth. The result of the final optimization is the single result of the prioritized optimization approach. The choice of ε (and whether it is the same for each step) and the priority ordering of the objectives will influence the final result. 15.3.2  PS Approach The PS approach does not prioritize the objectives, but instead treats every objective equally. Unlike prioritized optimization, the PS approach yields not a single plan, but a set of optimal plans that trade off the objectives in a variety of ways. Given a set of objectives and constraints, a plan is considered Pareto-optimal if it is feasible and if there does not exist another feasible

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plan that is strictly better with respect to one or more objectives and that is at least as good for the rest. Assuming that the objectives are chosen correctly, Pareto-optimal plans are the plans of interest to planners and doctors. The set of all Pareto-optimal plans comprises the PS. The PS-based MCO problem can be formulated as follows:

minimize  [O1(x), O2(x), … , ON(x)] subject to x ∈ X

(15.7)

where X is used, as before, to represent all beamlet and dose constraints, and N is the number of objective functions. The algorithmic decisions to be made for this approach are as follows: (1) how to compute a reasonable set of diverse Pareto-optimal plans and (2) how to present the resulting information to the decision makers. Radiotherapy seems to be one of the first fields, if not the first, to fully address the question of populating PSs for N ≥ 3. Two main types of strategies populating the PS have been put forward for the radiotherapy problem: weighted sum methods and constraint methods. Weighted sum methods are based on combining all the objectives into a weighted sum and solving the resulting scalar optimization problem. By solving the problem for a variety of weights, a variety of different Paretooptimal plans are found. If the underlying objectives and constraint set are convex, every Pareto-optimal point can be found by some weighted sum. Several publications describe methods to choose the weights appropriately, to produce a small set of plans that covers the PS sufficiently well (18, 21, 25). These methods intrinsically take into account convex combinations of calculated PS points when evaluating the goodness of a set of Pareto plans. All of these methods get bogged down when the number of objectives is large (e.g., >8). Fortunately, on a practical level, even as few as N + 1 PS plans are often sufficient to determine good treatment plans (26, 27). Constraint methods use the objective functions as constraints (as in prioritized optimization), and by varying the constraint levels, different Pareto-optimal solutions are found. The state-of-the-art of constraint-based method is the improved normalized normal constraint (NNC) method (28). The main deficit of constraint-based methods is that error measures, which give the quality of the PS approximation, are not a natural part of the algorithm or output, as they are in the methods of Craft et al. (18) and Rennen et al. (25). Weighted sum and constraint methods are graphically depicted for 2D PSs in Figure 15.4. 15.3.3  Navigation of the PS The final task in a PS-based approach to treatment planning is to allow the user to select a plan from the PS. Because the PS is represented by a finite set

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A)

Weighted sum method

O2

B) e-Constraint method

C)

Normalized normal constraint method

O2

O2 w = (.6,.4) w = (.2,.8)

O1

O1

O1

FIGURE 15.4 Methods to compute a database of Pareto surface points. (A) Weighted sum, (B) e-constraint, and (C) normalized normal constraint method.

of Pareto-optimal treatment plans, there are two natural approaches to plan selection. The easiest way is simply to allow the treatment planner to select one of the computed Pareto-optimal treatment plans. In the case of IMPT, where treatment plans can be weighted and combined to form other valid treatment plans, it makes sense to allow users to smoothly transition between the computed solutions. When navigating across convex combinations of the database plans, either forcing Pareto optimality or not, the standard method is to present N sliders, one for each objective, and the underlying algorithmic task is to determine how to move in the objective space in response to a slider movement (21, 29). An alternative to presenting the users with N sliders is to allow them to select two of the N objectives and then display a 2D trade-off for those two objectives. For the other N – 2 objectives, the user can impose upper bounds, influencing the 2D tradeoff surface being evaluated. The benefit of this method is that it allows the user to visualize a 2D slice of PS, which may yield intuition into the problem at hand. Figure 15.5 shows what this might look like for examining the trade-off between sparing the lung and controlling hot spots within a target. Target dose homogeneity

OAR Sparing FIGURE 15.5 (See color insert.) Illustration of two Pareto-optimal plans, showing trade-offs in OAR sparing vs. target dose homogeneity.

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A) O2

Prioritized optimization method 1

ε

B) O2

Pareto surface method Actual pareto surface Approximated pareto surface

2

O1

O1

FIGURE 15.6 Illustration of approaches to multicriteria optimization. (A) Prioritized optimization, and (B) Pareto surface method.

15.3.4  Comparing Prioritized Optimization and PS-Based MCO Prioritized optimization and PS MCO are compared graphically in Figure 15.6. It is important to note that both methods rely on optimization with hard constraints. In the prioritized approach, this is obvious because objectives move into the constraint section. In the PS method, constraints are important in the problem formulation, to restrict the domain of the PS to a useful one. For example, it makes sense to put an absolute lower bound on target doses normally, even if a user is interested in exploring some underdosing of the tumor to improve OAR sparing (otherwise, anchor plans for OAR will be “all 0” dose plans, which are not helpful for planning). Similarly, a hard upper maximum dose on all voxels is useful. Therefore, MCO methods in general are best used when a constrained solver is at hand. Solvers implemented in RayStation (RaySearch Laboratories), Pinnacle (Philips Healthcare, Andover, MA), Monaco (Electa), UMPlan/UMOpt (University of Michigan, Ann Arbor, MI), and Astroid (Massachusetts General Hospital, Boston, MA) are examples of solvers that allow true hard constraints (as opposed to those that handle constraints approximately by using a penalty function with a high weight). The advantage of the prioritized approach is that it is a programmable procedure that results in a single Pareto-optimal plan, but the disadvantage is there is only one plan presented to the user at the end of the process. PS methods on the other hand present all optimal options to the user, but might be considered overwhelming for routine planning because the user has to decide on selecting a single plan manually from the large number of options on PS. However, plan selection in standard cases may be fast, even with many options, because sliding with navigation sliders is much more efficient than the reoptimization iteration loop. Notably, because the navigation process is user-driven, it is not as reproducible as the prioritized approach.

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15.4  Robust Optimization Methods for IMPT Uncertainties in proton therapy have been addressed in detail in Chapters 13, and 14, and, for example, in publications by Lomax (30, 31). From the delivery point of view, an optimal plan needs also to be “robust,” that is, designed in such a way that slight deviations from the plan due to various uncertainties during treatment delivery will not affect the quality of treatment outcome. In other words, a robust treatment plan will deliver a clinically acceptable dose distribution as long as the deviations from the planned do not exceed the assumed levels. Heuristics to mitigate the effects of uncertainty in patient setup and proton range have been developed for different treatment modalities. These methods include compensator smearing in passively scattered proton therapy or selection of favorable beam angles (see Chapter 10). Here, we discuss robust optimization strategies specifically for intensity-modulated proton therapy (IMPT).

15.4.1  IMPT Dose in the Presence of Uncertainties Doses delivered from different directions in IMPT are typically inhomogeneous and require the use of a number of proton energies. For this reason, variations in the target setup and penetration depth during delivery can lead to misalignment and mismatch of doses from individual fields, and, consequently, alter the combined dose distribution. To satisfy the requirement of dose conformity to the target, steep dose gradients are often delivered at the target border. Such steep dose gradients in the dose contributions of individual beams make IMPT plans yet more sensitive to both range and setup errors. In particular, dose gradients in the beam direction make the treatment plan vulnerable to range errors, because an error in the range of the proton beams corresponds to a relative shift of these dose contributions longitudinally inside the patient. As a consequence, the dose within the target may not add up to a homogeneous dose as desired. Hot and cold spots may arise. Moreover, dose may be shifted into critical organs. Generally, the more conformal the combined IMPT dose is, the more complex the fluence maps per field are and the more sensitive the plans are to the delivery uncertainties. As an illustration, consider a conventional IMPT plan for a case of paraspinal tumor, shown in Figure 15.3. The target entirely surrounds the spinal cord, which is to be spared. Total IMPT dose distribution was optimized using a quadratic objective function, thus aiming at a homogeneous target dose. As is characteristic of IMPT, the homogeneous dose distribution in the target is achieved through a superposition of highly inhomogeneous contributions delivered from three beam directions.

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A

B

FIGURE 15.7 (See color insert.) Estimated dose distribution from the plan in Figure 16.3, assuming (A) a 5-mm range overshoot of all pencil beams, and (B) a systematic 3.5-mm setup error (posterior shift).

The dose distribution that results from a range overshoot of all pencil beams in this plan (i.e., protons penetrate further into the patient than anticipated during planning) would lead to a higher dose to the spinal cord, as shown in Figure 15.7A. Sensitivity of the same plan to setup errors is illustrated in Figure 15.7B, which shows the dose distribution resulting from a 3.5-mm setup error posteriorly (upwards in the picture). This shift has no impact on the dose contribution of the posterior beam. However, the oblique beams hit the patient surface at a different point. For a posterior shift, the dose contributions of the oblique beams are effectively shifted apart, which results in the cold spots around the spinal cord. From this illustration, it is evident that, unlike in conventional x-ray therapy, plan degradation in the presence of range and setup uncertainties in IMPT cannot be prevented, to a satisfying degree, with safety margins. Expanding the irradiated area around the target with margins could potentially reduce underdosage at the edge of the target in the presence of an error. However, the general problem of misaligning the dose contributions of different fields, which leads to dose uncertainties in all of the target volume, cannot be solved through margins. This problem instead relates to steep dose gradient in the dose contributions of individual fields. 15.4.2  Robust Optimization Strategies The methods presented in this section have been described largely in three publications (32–34) that deal specifically with range and setup uncertainty in IMPT. In addition, a number of earlier publications investigate the handling of uncertainty and motion in IMRT with x-rays. Some of that work could also be applied to IMPT. For a review of developments in handling of motion and uncertainty in IMRT, see Orton et al. (35). Although this section illustrates robust optimization techniques in the context of range and setup errors, the methodology is also applicable to other types of uncertainty, for example, irregular breathing motion or uncertainty in the biological effectiveness of radiation (36).

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Several approaches that apply either the concepts of stochastic programming or robust optimization have been suggested for incorporating uncertainty into IMPT optimization. The common feature of these approaches is that the delivered dose distribution depends on a set of uncertain parameters. In the case of a rigid setup error without rotation, the set of uncertain parameters would be a 3D vector describing the patient shift in space. A simple model of range uncertainty, where it is assumed that all pencil beams simultaneously overshoot or undershoot, would have one uncertain variable that describes the range error of all beams. A more complicated model of range uncertainty could allow for different range errors for different pencil beams. Below, we denote the set of uncertain parameters by a vector λ. The dose distribution d(x, λ) delivered to the patient depends on the beam spot weights x to be optimized, and the values of the uncertain parameters λ. The objective function used for treatment planning O(d(x, λ)) is a function of the dose distribution. 15.4.2.1  The Probabilistic Approach In the probabilistic or stochastic programming approach (34), a probability distribution P(λ), reflecting the probability for a given error to occur, is assigned to the set of uncertain parameters. Treatment plan optimization is performed by optimizing the expected value of the objective function:

minimize

E [O ] = ∫ O(d( x, λ))P(λ)dλ.

(15.8)

This composite objective function can be interpreted in a multicriteria view: The composite objective is a sum of objectives for every possible error scenario weighted with the probability of that error to occur. The general goal is to find a treatment plan that is good for all possible errors, but larger weights are assigned to those scenarios that are likely to occur, and lower weights to large errors that are less likely to happen. 2 For a pure quadratic objective function, O = ∑ i ( di − Dipres ) , the expected value of the objective function is

(

)

2 2 E [O] = ∑ ( E [ di ] − Dipres ) + E ( di − E [ di ])    i

(15.9)

which is the sum of two terms: the first term is the quadratic difference of the expected dose E[d] and the prescribed dose, and the second term is the variance of the dose. Hence, minimizing the expected value of the quadratic objective function aims at bringing the expected dose close to the prescribed dose in every voxel and simultaneously minimizes the variance of the dose in every voxel such that the expected dose is approximately realized even if an error occurs.

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15.4.2.2  The Robust Approach In robust optimization (32), the values of uncertain parameters are assumed to be within some interval called the uncertainty set. Treatment planning is performed by solving the robust counterpart of the conventional IMPT optimization problem. For an introduction to robust optimization, see Ben-Tal and Nemirovski (37). Typically, this means that the constraints of the optimization problem have to be satisfied for every realization of the uncertain parameters. For example, if the original problem constrained that the maximum dose to the spinal cord be less than 50 Gray (Gy), the robust counterpart would demand that the maximum spinal cord dose is less than 50 Gy for every possible range and setup error within the uncertainty set. For objectives, this formulation of the robust counterpart results in a worst-case optimization problem: that is, if the objective was to minimize the maximum dose to the spinal cord, then the robust counterpart would minimize the maximum spinal cord dose that can happen for any possible range or setup error. Hence, the aim is to find a treatment plan, which is as good as possible for the worst case that can occur. 15.4.2.3  Optimization of the Worst-Case Dose Distribution Yet another approach to robust IMPT planning utilizes the concept of a worst-case dose distribution (33). This hypothetical dose distribution is defined voxel by voxel as the worst dose value that can be realized for any error anticipated in the uncertainty model. For every target voxel, the worst dose value is the minimum dose, whereas for nontarget voxels it is the maximum dose. The worst-case dose distribution is unphysical because every voxel is considered independently. Whereas in one voxel the worst case may correspond to a patient shift anteriorly, the worst case in another voxel may correspond to a patient shift posteriorly. Hence the worst-case dose distribution cannot be realized. However, it can be considered as a lower bound for the quality of a treatment plan. The method optimizes the weighted sum of the objective function evaluated for the nominal case dnom (no errors) and the objective function evaluated for the worst-case dose distribution dwc. If O is the primary objective function, then the composite objective to be optimized is given by O comp = O(d nom ) + wO(d wc ). 15.4.3  Examples of Robust Optimization Incorporating uncertainty in IMPT optimization yields increasingly robust treatment plans. Consider two treatment plans: a conventional plan optimized without accounting for uncertainty, and a plan optimized for range and setup uncertainty using the probabilistic approach (i.e., the setup and range uncertainties modeled with a Gaussian distribution). Figure 15.8 shows the DVHs corresponding to dose distributions calculated for range

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100 Conventional Robust

80 60 40 20 0

0

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FIGURE 15.8 DVH comparison between a conventional and a robust IMPT plan. DVHs for the CTV and the spinal cord are shown for randomly sampled range and setup errors.

and setup errors randomly sampled from these Gaussian distributions. For the conventional plan, target coverage is strongly degraded in many cases, and the dose to the spinal cord can be very high for some scenarios. The variation in the DVHs of the robust plan is greatly reduced, ensuring better target coverage and lower spinal cord doses. To gain some insight into how this robustness is achieved, let us consider the dose contributions of individual beams. Figure 15.9 compares four treatment plans: the conventional plan, a plan optimized for range uncertainty only, a plan optimized for setup uncertainty only, and a plan incorporating both types of errors. The conventional plan is characterized by steep dose

A

B

C

D

FIGURE 15.9 For the case illustrated in Figure 15.3, dose contributions from the posterior beam from four differently optimized plans. (A) Conventional IMPT, robust IMPT incorporating (B) range uncertainty only, (C) setup uncertainty only, and (D) considering both range and setup uncertainty.

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gradients both in beam direction and laterally, especially around the spinal cord. The plan optimized for range uncertainty shows reduced dose gradients in beam direction and avoids placing a steep distal falloff of a Bragg peak in front of the spinal cord. The lateral falloff is used instead of the distal falloff to shape the dose distribution around the spinal cord. The plan optimized for setup errors only shows reduced dose gradients in the lateral direction, but it does not avoid placing a distal Bragg peak falloff in front of the critical structure and therefore does not provide robustness against range errors per se. The plan optimized for both range and setup errors shows reduced dose gradients both longitudinally, in the beam direction, and laterally. In summary, robustness is achieved through a redistribution of dose contributions among the beam directions and through avoiding unfavorable dose gradients. For our sample paraspinal case, the price of robustness is a higher dose to the spinal cord for the nominal case. In a conventional plan, the steep distal Bragg peak falloff is utilized, which allows for optimal sparing of the spinal cord. If range errors are to be accounted for, the shallower lateral falloff is used, leading to a more shallow dose gradient between tumor and spinal cord for the nominal case. Publications by Pflugfelder et al. (33) and Unkelbach et al. (34) provide a more detailed analysis. In the experience of the authors, all of the methods to account for uncertainty, described above, lead to similar treatment plans and may be equally suited to account for systematic uncertainties.

15.5  Temporospatial (4D) Optimization Precision of therapy delivery can be affected not only by the changes in setup and patient anatomy between treatment fractions, but also by the intrafractional motion of the target, which could be due to respiration, peristalsis, or organ settling due to gravity (see Chapter 14 for more details). If no action is taken, there is always a risk that parts of the target may move outside of the treatment field, resulting in a loss of dose coverage. Even in cases where treatment-planning margins are generous enough to cover the full amplitude of motion, intrafractional motion would degrade dose gradients and increase irradiation of surrounding healthy tissues. An important difference from x-ray therapy is that, in particle therapy, because of the limited range, the use of margin expansions, such as internal target volumes, requires explicit consideration of possible changes in radiological depth to target, because these are often affected by organ motion (38). Additionally, as with x-rays, in dynamically delivered intensity-modulated therapy, certain patterns of superposition of motion of the target and the scanned beam, or so-called “motion interplay,” can have a severe impact on the delivered dose (e.g., 39).

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Numerous ideas have been put forward that aim to mitigate the impact of intrafractional motion: these include recommendations for selection of planning image set, compensator expansion, internal margins (40, 41), delivery methods using beam gating (42), field rescanning (43), and target tracking (44). In this section, we review approaches to incorporate intrafractional motion into the optimization of beam weights in IMPT. Those methods have been investigated primarily in the context of IMRT with photons. Although the methodology can be transferred to IMPT, those approaches have not been validated in detail regarding the specific challenges mentioned above, that is, interplay effects and sensitivity to changes in radiological path length. Methods to incorporate intrafractional motion in plan optimization require a characterization of the geometrical variation of the patient’s anatomy. For respiratory motion, this can be obtained from respiratory-correlated computed tomography (CT) (often called 4D CT), which provides the geometry of the patient in several phases of the breathing cycle (45). The task of evaluating the actual dose distribution delivered to a moving target requires first calculating instantaneous dose to all phases of the 4D CT. Figure 15.10 illustrates variation in the proton dose distribution delivered to a changing anatomy, throughout the respiratory cycle. Such instantaneous doses can then be mapped onto a reference anatomical set, by using the correspondence established between the voxels of different CT sets, obtained through elastic image registration. The mapped dose can be subsequently added along with contributions from all instances of variable anatomy, to yield the dose accumulated throughout the respiratory cycle (46, 47). Instantaneous dose on phase-specific CT

B

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A Full inhalation Full

exhalation

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Mid-ventilation E

Instantaneous dose mapped to exhalation CT FIGURE 15.10 Dosimetric evaluation of a treatment plan for a tumor in the liver, using respiratory-correlated CT. Estimated instantaneous dose delivered during (A) the full exhalation, (B) full inhalation, and (C) mid-ventilation phases of the respiratory cycle. To estimate the total dose, contributions from various instances of the anatomy have to be mapped onto the reference CT set, for example, for (D) full inhalation dose (dose “B” mapped onto the full exhalation CT “A”), and (E) mid-ventilation (dose “C” mapped onto CT “A”). (CT images courtesy of Dr. S. Mori (NIRS). With permission.)

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15.5.1 Plan Optimization Based on a Known Motion Probability Density Function In a simple approach to include motion, it is assumed that motion is sufficiently well described by the reconstructed phases of a 4D CT and that the dose delivered to a voxel i is obtained by summation of the dose contributions from all phases:

di = ∑ p ( r ) di( r ) = ∑ p ( r ) ∑ x j ⋅ Dij( r ) . r r j

(15.10)

Here, r is an index to the instance of geometry, and the voxel index i refers to an anatomical voxel defined in the reference phase. Dij(r) is the dose influence matrix for phase r. Its calculation requires elastic registration of the CT of phase r with the reference phase. The parameters p(r) are probabilities that the patient is in phase r and are referred to as the motion probability density function (PDF), which can be estimated from a recorded breathing signal. Treatment planning can be performed by optimizing the beam weights xj based on objectives and constraints evaluated with the cumulative dose from Equation 15.10 above (48). The general idea is that, rather than passively letting the motion deteriorate the original plan, one should anticipate it, and, in fact, actively engage it in shaping the desired dose distribution. The resulting treatment plan would deliver an inhomogeneous dose distribution to a static geometry. However, the inhomogeneities are designed such that, after accumulating dose over the whole breathing cycle, the desired dose distribution is obtained. Because one of the most manifest effects of motion on the dose is the smoothing or washout of gradients both within the target and at its borders, the logical way to counter this effect is dose boosting at the edges of the target, in what is termed “edge-enhancement” (49). The exact pattern of optimum inhomogeneity enhancement is determined by the form of motion PDF. Generally, the effect of motion on the dose may be approximated as convolution of the dose with the PDF; thus, the desired motion-compensated plan can be roughly approximated with the inverse process: deconvolution. However, this is constrained by the requirement that the fluences delivered at all pencil beam spots are physical; thus, if negative values arise from deconvolution or during optimization, those need to be reset to zero (or the minimum should be allowed, if the beam cannot be completely turned off, e.g., in a continuous scan). Because the PDF does not depend on time, the use of probabilistic planning does not require complex technical delivery modifications to ensure synchronization of the beam with the motion cycle, and thus delivery of such fields can be relatively easily implemented in practice. However, PDF-based optimization methods rely on the reproducibility of target motion patterns during delivery, and sufficient sampling of the motion PDF. When motion deviates from the expectation, a significant dosimetric deviation may occur.

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15.5.2  Plan Optimization for an Uncertain Motion PDF Through the use of robust planning techniques, the dosimetric outcome of a treatment plan based on a known motion PDF can be made less vulnerable to variations in the breathing pattern. This approach thus aims at finding a treatment plan that yields an acceptable cumulative dose distribution even if the actual breathing pattern during treatment differs from the estimated motion PDF assumed for treatment plan optimization. Chan et al. (50, 51) investigated robust optimization for respiratory motion by modeling the variability in the breathing motion via uncertainties in the motion PDF parameters p(r). 15.5.3  Optimizing a Different Fluence Map for Every Phase Instead of optimizing a single fluence map that is delivered irrespective of the breathing phase the patient is currently in, one can also optimize a separate fluence map xj(r) for every phase. The objectives and constraints for treatment plan optimization are formulated in terms of the cumulative dose, with the distinction that the fluence map is different in every phase (48). The delivery of such treatment plans would however require a synchronization of the dose delivery with the breathing motion.

15.6 Accounting for Biological Effects in IMPT Optimization Treatment planning for proton therapy usually uses a constant relative biological effectiveness (RBE) factor of 1.1 for the conversion of physical dose di to “biological” dose (see Chapter 19). The biological effective dose is defined as the photon dose from a 60Co source that would produce the same cell-kill in the tumor. Under the assumption of a constant RBE, treatment plan optimization can be performed based on the physical dose alone as described in the preceding sections of this chapter. In other words, the physical dose is the only measure that is needed to characterize the radiation field and to assess the quality of the treatment plan. However, this may be an oversimplification and a second quantity may be needed to characterize the radiation field and its radiobiological effectiveness. This second measure is the linear energy transfer (LET) (see Chapters 2 and 19). Radiobiological experiments suggest that the amount of radiation-induced cell-kill increases with higher LET, and consequently at the end of range of the proton beams. To directly incorporate effects of varying RBE in IMPT planning, the objective function needs to be formulated in terms of physical dose and LET, instead of dose alone. One approach has been suggested by Wilkens and Oelfke (52), who formulate their objective function based on the linear-quadratic cell survival model, where the α-parameter depends

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linearly on LET. Recently, Grassberger et al. (53) have demonstrated that it is feasible in IMPT optimization to influence the distribution of LET without significantly altering the physical dose distribution.

15.7 Other Applications of Mathematical Optimization in Proton Therapy 15.7.1  Scan Path Optimization In 3D spot scanning, beam spots are typically placed on a regular grid over the tumor region. In practice though, a large number of beam spots will be assigned zero weight in the optimization of the treatment plan. Nevertheless, in a naïve implementation of spot scanning, the beam would be steered in a zigzag pattern over the entire grid, including the spot positions that correspond to zero weight. Kang et al. (54) investigated the optimization of the scan path of the beam in order to avoid regions with zero weight spots. The problem corresponds to a “traveling salesman” problem and simulated annealing has been applied to solve the problem. 15.7.2  Beam Current Optimization for Continuous Scanning There are different ways to perform pencil beam scanning. In spot scanning, the proton beam is steered to one desired position on the grid, delivers dose according to the optimized spot weight, is switched off, and is moved to the next grid point. In continuous scanning, the beam is constantly moving according to a predefined pattern. The intensity-modulated field is delivered by modulating the beam current in time while the beam is repeatedly scanned over the tumor volume. In this case, an additional computational step is needed that converts the optimized spot weights defined at discrete positions to the beam-current modulation that approximately delivers the same fluence. For this step, optimization methods have been applied (14); however, this optimization can be performed in fluence space. It does not require dose calculation in the patient and is therefore easier to solve than the optimization of spot weights.

References

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3. Lu HM, Kooy H. Optimization of current modulation function for proton spread-out Bragg peak fields. Med Phys 2006; 33:1281–87. 4. Lu HM, Brett R, Engelsman M, Slopsema R, Kooy H, Flanz J. Sensitivities in the production of spread-out Bragg peak dose distributions by passive scattering with beam current modulation. Med Phys 2007; 34:3844–53. 5. Engelsman M, Lu HM, Herrup D, Bussiere M, Kooy HM. Commissioning a passive-scattering proton therapy nozzle for accurate SOBP delivery. Med Phys 2009; 36:2172–80. 6. Bussière MR, Adams AA. Treatment planning for conformal proton radiation therapy. Technol Cancer Res Treat 2003; 2:389–99. 7. Urie M, Goitein M, Wagner M. Compensating for heterogeneities in proton radiation therapy. Phys Med Biol 1984; 29:553–66. 8. Lomax A. Intensity modulation methods for proton radiotherapy. Phys Med Biol 1999; 44:185–205. 9. Deasy JO, Shepard DM, Mackie TR. 1997. Distal edge tracking: A proposed delivery method for conformal proton therapy using intensity modulation. In Proceedings of XIIth ICCR, eds. D.D. Leavitt, and G. Starkshall, 406–409. Salt Lake City: Medical Physics Publishing. 10. Oelfke U, Bortfeld T. Inverse planning for photon and proton beams. Med Dosim 2001; 26:113–24. 11. Nill S, Bortfeld T, Oelfke U. Inverse planning of intensity modulated proton therapy. Z Med Phys 2004; 14:35–40. 12. Thieke C, Bortfeld T, Niemierko A, Nill S. From physical dose constraints to equivalent uniform dose constraints in inverse radiotherapy planning. Med Phys. 2003; 30:2332–39. 13. Kang JH, Wilkens JJ, Oelfke U. Non-uniform depth scanning for proton therapy systems employing active energy variation. Phys Med Biol. 2008; 53:N149–55. 14. Trofimov A, Bortfeld T. Optimization of beam parameters and treatment planning for intensity modulated proton therapy. Technol Cancer Res Treat 2003; 2:437–44. 15. Bortfeld T. Optimized planning using physical objectives and constraints. Semin Radiat Oncol. 1999; 9:20–34. 16. Lahanas M, Schreibmann E, Baltas D. Multiobjective inverse planning for intensity modulated radiotherapy with constraint-free gradient-based optimization algorithms. Phys Med Biol 2003; 48:2843–71. 17. Romeijn E, Dempsey J, Li J. A unifying framework for multi-criteria fluence map optimization models. Phys Med Biol 2004; 49:1991–2013. 18. Craft D, Halabi T, Bortfeld T. Exploration of tradeoffs in intensity-modulated radiotherapy. Phys Med Biol 2005; 50:5857–68. 19. Hong TS, Craft DL, Carlsson F, Bortfeld TR. Multicriteria optimization in ­intensity-modulated radiation therapy treatment planning for locally advanced cancer of the pancreatic head. Int J Radiat Oncol Biol Phys 2008; 72:1208–14. 20. Thieke C, Küfer KH, Monz M, Scherrer A, Alonso F, Oelfke U, et al. A new concept for interactive radiotherapy planning with multicriteria optimization: first clinical evaluation. Radiother Oncol. 2007; 85:292–98. 21. Monz M, Küfer KH, Bortfeld TR, Thieke C. Pareto navigation: algorithmic foundation of interactive multi-criteria IMRT planning. Phys Med Biol 2008; 53:985–98.

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22. Clark VH, Chen Y, Wilkens J, Alaly JR, Zakaryan K, Deasy JO. IMRT treatment planning for prostate cancer using prioritized prescription optimization and mean-tail-dose functions. Linear Algebra Appl 2008; 428:1345–64. 23. Ehrgott M. Multicriteria Optimization. Berlin: Springer. 2005. 24. Jee KW, McShan DL, Fraass BA. Lexicographic ordering: intuitive multicriteria optimization for IMRT. Phys Med Biol 2007; 52:1845–61. 25. Rennen G, van Dam ER, den Hertog D. 2009. Enhancement of Sandwich Algorithms for Approximating Higher Dimensional Convex Pareto Sets. Discussion Paper 2009-52, Tilburg University, Center for Economic Research. 26. Craft D, Bortfeld T. How many plans are needed in an IMRT multi-objective plan database? Phys Med Biol 2008; 53:2785–96. 27. Craft D. Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization. Phys Med 2010; 26: 184–91. 28. Messac A, Mattson CA. Normal constraint method with guarantee of even representation of complete Pareto frontier. AIAA J 2004; 42:2101–11. 29. Craft D, Monz M. Simultaneous navigation of multiple Pareto surfaces, with an application to multicriteria IMRT planning with multiple beam angle configurations. Med Phys 2010; 37:736–41. 30. Lomax AJ. Intensity modulated proton therapy and its sensitivity to treatment uncertainties 1: the potential effects of calculational uncertainties. Phys Med Biol 2008; 53:1027–42. 31. Lomax AJ. Intensity modulated proton therapy and its sensitivity to treatment uncertainties 2: the potential effects of inter-fraction and inter-field motions. Phys Med Biol 2008; 53:1043–56. 32. Unkelbach J, Chan TC, Bortfeld T. Accounting for range uncertainties in the optimization of intensity modulated proton therapy. Phys Med Biol 2007; 52:2755–73. 33. Pflugfelder D, Wilkens JJ, Oelfke U. Worst case optimization: a method to account for uncertainties in the optimization of intensity modulated proton therapy. Phys Med Biol 2008; 53:1689–700. 34. Unkelbach J, Martin BC, Soukup M, Bortfeld T. Reducing the sensitivity of IMPT treatment plans to setup errors and range uncertainties via probabilistic treatment planning. Med Phys 2009; 36:149–63. 35. Orton C, Bortfeld T, Niemierko A, Unkelbach J. The role of medical physicists and the AAPM in the development of treatment planning and optimization. Med Phys 2008; 35: 4911–23. 36. Kroupal F, Frese M, Heath E, Oelfke U. Robust radiobiological optimization for proton therapy treatment planning. Proc. of the World Congress on Medical Physics and Biomedical Engineering 2009; 1:433–36. 37. Ben-Tal A, Nemirovski A. Robust solutions of uncertain linear programs. Operations Res Lett 1999; 25:1–13. 38. Mori S, Chen GT. Quantification and visualization of charged particle range variations. Int J Radiat Oncol Biol Phys 2008; 72:268–77. 39. Rietzel E, Bert C. Respiratory motion management in particle therapy. Med Phys 2010; 37:449–60. 40. Engelsman M, Rietzel E, Kooy HM. Four-dimensional proton treatment planning for lung tumors. Int J Radiat Oncol Biol Phys 2006; 64:1589–95. 41. Kang Y, Zhang X, Chang JY, Wang H, Wei X, Liao Z, et al. 4D Proton treatment planning strategy for mobile lung tumors. Int J Radiat Oncol Biol Phys. 2007; 67:906–14.

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42. Lu HM, Brett R, Sharp G, Safai S, Jiang S, Flanz J, et al. A respiratory-gated treatment system for proton therapy. Med Phys. 2007; 34:3273–78. 43. Seco J, Robertson D, Trofimov A, Paganetti H. Breathing interplay effects during proton beam scanning: simulation and statistical analysis. Phys Med Biol. 2009; 54:N283–94. 44. Bert C, Gemmel A, Saito N, Chaudhri N, Schardt D, Durante M, et al. Dosimetric precision of an ion beam tracking system. Radiat Oncol. 2010; 5:61. 45. Keall P. 4-dimensional computed tomography imaging and treatment planning. Semin Radiat Oncol 2004; 14:81–90. 46. Bert C, Rietzel E. 4D treatment planning for scanned ion beams. Radiat Oncol 2007; 2:24. 47. Zhang X, Zhao KL, Guerrero TM, McGuire SE, Yaremko B, Komaki R, et al. Four-dimensional computed tomography-based treatment planning for ­intensity-modulated radiation therapy and proton therapy for distal esophageal cancer. Int J Radiat Oncol Biol Phys 2008; 72:278–87. 48. Trofimov A, Rietzel E, Lu HM, Martin B, Jiang S, Chen GT, et al. Temporo-spatial IMRT optimization: concepts, implementation and initial results. Phys Med Biol 2005; 50:2779–98. 49. Chan TC, Tsitsiklis JN, Bortfeld T. Optimal margin and edge-enhanced intensity maps in the presence of motion and uncertainty. Phys Med Biol. 2010; 55:515–33. 50. Chan TC, Bortfeld T, Tsitsiklis JN. A robust approach to IMRT optimization. Phys Med Biol. 2006; 51:2567–83. 51. Bortfeld T, Chan TCY, Trofimov A, Tsitsiklis JN. Robust management of motion uncertainty in intensity-modulated radiation therapy. Operat Res 2008; 56:1461–730. 52. Wilkens JJ, Oelfke U. Optimization of radiobiological effects in intensity modulated proton therapy. Med Phys 2005; 32:455–65. 53. Grassberger C, Trofimov A, Lomax A, Paganetti H. Variations in linear energy transfer within clinical proton therapy fields and the potential for biological treatment planning. Int J Radiat Oncol Biol Phys 2011; 80:1559–66. 54. Kang JH, Wilkens JJ, Oelfke U. Demonstration of scan path optimization in proton therapy. Med Phys 2007; 34:3457–64.

16 In Vivo Dose Verification Katia Parodi CONTENTS 16.1 Introduction................................................................................................. 489 16.2 In Vivo Treatment Verification and DGRT in Photon and Proton Therapy......................................................................................................... 491 16.3 PET Imaging................................................................................................ 493 16.3.1 The Production of Irradiation-Induced β+-Activity................... 494 16.3.2 The Imaging Process...................................................................... 497 16.3.3 The Clinical Implementation........................................................500 16.3.4 Worldwide Installations and Clinical Experience..................... 506 16.3.5 On-Going Developments and Outlook.......................................509 16.4 Prompt Gamma Imaging........................................................................... 512 16.4.1 The Production of Irradiation-Induced Prompt Gamma.......... 512 16.4.2 The Imaging Process...................................................................... 512 16.4.3 Worldwide Preclinical Investigations.......................................... 514 16.4.4 The Foreseen Clinical Implementation........................................ 515 16.5 Magnetic Resonance Imaging................................................................... 516 16.6 Conclusion and Outlook............................................................................ 519 References.............................................................................................................. 520

16.1  Introduction The favorable physical and radiobiological properties of light ion beams (i.e., protons and heavier ions up to charge Z ≈ 10) offer the possibility of a highly precise and biologically efficient radiation therapy, which promises improved clinical outcome for various tumor sites in comparison to conventional radiotherapy with photons and electrons. However, because of the increased physical selectivity, ion beam therapy is also more sensitive than conventional radiation modalities to changes of the actual treatment situation with respect to the planned one. In particular, the finite “beam range” in tissue is strongly influenced by the radiological path length, which determines the position of the Bragg peak in the tumor and thus the precise localization 489

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of the intended dose delivery. Therefore, uncertainties in the knowledge of the in vivo beam range in the patient is one of the major concerns in ion therapy, hampering full clinical exploitation of the dosimetric advantages of ion beams in clinical practice. Major sources of random range (and thus dose delivery) errors during the fractionated course of radiation therapy include patient positioning, anatomical and physiological changes (Chapter 13), and, for certain tumor locations, organ motion (Chapter 14). Additional sources of systematic range uncertainties in the treatment-planning process may include the usage of semiempirical calibration of the planning x-ray computed tomography (CT) into ion range, the presence of CT artifacts and the particle scattering in complex anatomy or in the presence of metallic implants. To account for all the possible sources of random and systematic errors in clinical practice, cautious safety margins are added to the tumor volume when designing the treatment plan. Moreover, treatment strategies tend to rely on the more controllable but less conformal lateral penumbra of the beam, rather than placing the sharper distal dose falloff in front of radiosensitive structures (Chapters 10 and 11). However, reduction of margins and safe application of doses tightly sculpted to the tumor target is a major goal of modern radiotherapy to avoid excess toxicity and promote dose escalation for increased tumor control. Therefore, the advances in the achievable selectivity of the dose delivery with external beam treatment modalities have been accompanied by an increasing role of imaging in the whole radiotherapy process (1). The various efforts span from precise identification of the target volume at the planning stage to the evaluation of the patient geometry directly at the treatment site and, eventually, quantification of the actual dose delivery in comparison to the planned one as well as treatment response assessment for adaptive strategies. Nowadays, conventional and novel methods of image-guided radiotherapy (IGRT) are increasingly well established in photon therapy for evaluation of the patient geometry and tumor position directly at the treatment site. Typical implementations include the usage of in-room radiographic (twodimensional, 2D) and volumetric (three-dimensional, 3D) x-ray kilovoltage or megavoltage imaging for assessment of internal anatomy, as well as nonionizing monitoring sensors of external motion surrogates. Corresponding IGRT solutions of 2D and/or 3D x-ray kilovoltage imaging also have been adopted at most ion beam therapy centers. Even dedicated solutions tailored to ion beam therapy have been developed, such as vertical CT systems for volumetric in-room imaging of patients treated in the seated position (2) or x-rays shining through a hole in the last bending magnet of a novel beam gantry for beam’s eye view (BEV) portal imaging simultaneous with the proton beam (3). In some implementations, time-resolved operation is supported for 4D capabilities (e.g. for fluoroscopic imaging of internal motion to complement external surrogates during irradiation).

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Indeed, IGRT techniques offer essential information not only for helping reducing positional errors at the treatment site for the individual patients, but also for obtaining population-based estimation of geometrical uncertainties to optimize the choice of clinical safety margins in treatment planning (1). However, they cannot provide the ultimate solution to the more stringent issue of reduction of range uncertainties and in vivo treatment verification in ion beam therapy, because they do not bear information on the interaction of the ions with the penetrated tissue. Therefore, availability of additional imaging techniques capable of assessing the beam range and the delivered dose in vivo and noninvasively would be highly beneficial. For optimal quality of patient care, the in vivo treatment verification methods should enable an independent validation of the complete therapy chain from treatment planning to beam delivery. On the one hand, these ­methods should provide in vivo confirmation of the successful tumor-conformal dose delivery, in order to improve treatment confidence and thus promote safe dose escalation studies for full clinical exploitation of the dosimetric advantages of ion beams. This also promises to play an important role in the increasingly considered high-dose hypofractionated therapy, where less or even no subsequent fractions are available for compensation of errors. On the other hand, in vivo treatment verification methods should also enable prompt identification and quantification of unexpected deviations between planned and actual dose delivery for promoting adaptive treatment strategies toward dose-guided radiation therapy (DGRT) and, ideally, for inhibiting improper dose delivery during treatment (“real-time” monitoring). This chapter will address the specific demands and challenges of in vivo treatment verification and DGRT of proton therapy in comparison to photon therapy, reviewing techniques already being investigated clinically or still at the stage of research and development.

16.2 In Vivo Treatment Verification and DGRT in Photon and Proton Therapy The physical properties of the penetrating megavoltage photon beams enable detection of the radiation traversing the patient simultaneously to the therapeutic treatment. This is typically achieved by using planar detectors such as electronic portal imaging devices (EPIDs) (4) integrated into the linear accelerator treatment head, opposite to the radiation source beyond the patient. Historically, EPIDs were initially developed and used for pretreatment confirmation of the lateral field position via analysis of 2D projections of the transmitted irradiation with respect to visible landmarks such as implanted markers or bony structures. However, latest research has shown that the portal images can also be converted into portal dose measurements; compare, for

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example, Nijsten et al. (5). Therefore, EPID data are now being acquired during irradiation for a quantitative dosimetric comparison with the corresponding expectation based on the planned treatment. This can be done not only at the detector level (2D transit dosimetry) but also within the patient (in vivo 3D dosimetry) by a proper backprojection approach (6). An implementation independent from the therapy chain can be obtained when combining a dose calculation engine different from the treatment-planning system (e.g., Monte Carlo) with anatomical information of the patient in the treatment position as acquired by a megavoltage cone beam CT shortly before irradiation (7). The promising clinical results reported so far clearly indicate that the advances in portal imaging and EPID dosimetry have opened new avenues in the quality of adaptive radiation therapy (ART) based not only on detection of anatomical changes (IGRT), but also of dose delivery differences (DGRT) in modern photon therapy. Unfortunately, the different properties of charged particles with respect to neutral photon radiation prohibit the usage of EPID dosimetry for in vivo quality assurance and DGRT of ion beam therapy. In fact, the primary therapeutic ions are completely stopped in the patient in order to place the Bragg peak in the tumor. Therefore, in vivo noninvasive verification of the actually delivered treatment and, in particular, of the primary ion beam range has to rely on some kind of surrogate signal induced by the therapeutic irradiation. The more straightforward approach for verification of the treatment simultaneously to or shortly after ion beam delivery is based on the detection of irradiation-induced secondary radiation emerging from the patient. This radiation is produced as the result of nuclear fragmentation reactions between the incoming ions and the target nuclei of the penetrated tissue. Because of the intrinsic physical differences between the nuclear and electromagnetic interactions underlying nuclear fragmentation and dose deposition, the surrogate emission signal can only be correlated but not directly matched to the delivered dose. Nevertheless, valuable information can be inferred from the comparison of the measured signal with a corresponding expectation (e.g., based on the planned treatment, the time course of the beam delivery and the chosen imaging strategy). Section 16.3 will address the already clinically investigated unconventional usage of positron emission tomography (PET), aiming to exploit the transient pattern of β+-activation generated as a byproduct of the therapeutic irradiation. Section 16.4 will present the very encouraging investigations on prompt-gamma imaging, which promises several advantages over PET imaging but is still hampered by the main challenge of the realization of an efficient detector solution. In addition to irradiation-induced secondary radiation emitted as the result of nuclear reaction processes, other imaging possibilities are being explored that may enable in vivo range verification on a different time scale before treatment or even days up to weeks after completed fractionated therapy. The latest novel method being clinically evaluated is magnetic resonance imaging (MRI). This intriguing technique addressed in Section 16.5 aims to

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∆T

Irradiation

Time Sum Long after therapy (∆T days - weeks) Magnetic Resonance Imaging (MRI) of Fxs

Long after treatment (∆T ~ 10 – 20 min) Selected Fx Offline PET (/CT) Post treatment (∆T ~ 0 – 10 min) In-room or nearby PET(/CT) In-beam “delayed” (∆T ms – min) PET In-beam “real-time” (∆T < ms) Prompt gamma, emitted particles Pre-treatmnt (-∆T ~ min) Radioactive ion (RI) beams Ion radiography / tomography

Each or selected Fx Each Fx Each Fx

First or each fraction (Fx)

FIGURE 16.1 Schematic representation of the different imaging approaches for in vivo dose or range verification on different time scales and delays ΔT with respect to the time of irradiation (upper axis). White characters refer to methods only mentioned but not further addressed in the text because either limited to heavy ion applications (RI imaging, emitted particles) or not induced by the therapeutic irradiation (ion radiography/tomography). The right arrow suggests possible clinical implementations for monitoring first, individual, or selected fractions (FXs), up to the integral fractionated treatment course (cf. text).

exploit irradiation-induced physiological processes such as bone marrow replacement, which is found to become manifest in follow-up MRI scans after completion of the entire fractionated therapy course. Finally, when available, ion beams at higher energies than for therapy could be used for transmission imaging of the residual ion range beyond the patient before or even in-between treatments (e.g., when range variation due to organ motion is of concern). Radiographic and tomographic implementations could enable indirect validation and even substitution of the semi-empirical x-ray CT-range calibration curve, besides low-dose image guidance of the patient position at the treatment site (8, 9). However, this method cannot provide in vivo treatment verification and DGRT because it does not rely on a signal induced by the interaction of the therapeutic beam with the patient. Hence, it will not be addressed further. A schematic representation of the different time scales of the available techniques, with emphasis on those reviewed in this chapter, is summarized in Figure 16.1.

16.3  PET Imaging PET currently offers the only technically feasible method for a volumetric, in vivo, and noninvasive verification of the actual treatment delivery and, in

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particular, of the ion beam range in the patient during or shortly after irradiation. This unconventional application of a well-established nuclear medicine technique exploits the coincident detection of the annihilation photon pairs resulting from the β+-decay of positron-emitting isotopes formed as a byproduct of the therapeutic irradiation. The mechanism of activity production, the image formation process, the data acquisition strategies, the clinical implementation, and the worldwide installation and experiences are reviewed in the following sections. 16.3.1  The Production of Irradiation-Induced β+ -Activity Nuclear interactions between the impinging ion beam and the target nuclei of the traversed tissue are typically regarded as a major drawback for therapeutical applications. In fact, they are responsible for modifying the composition and energy spectrum of the radiation field, preventing primary ions to reach the Bragg peak for localized dose deposition in the tumor via inelastic Coulomb collisions. However, this drawback is somewhat compensated by the fact that fragmentation reactions may yield with a considerable probability positron-emitting nuclei (cf. typical cross sections of relevance for proton therapy in Figure 16.2), thus opening the possibility of PET-based in vivo treatment verification. Nuclear fragmentation is a complex two-stage process resulting in the fast (within ca. 10−22 s) production of excited prefragments, which eventually approach the final state via nucleon evaporation and photon emission in about 10−21 to 10−16 s (11). A schematic illustration is given in Figure 16.3. Among the possible reaction yields, neutron-deficient nuclei are produced that are likely to undergo β+-decay. Depending on the primary ion beam species, the mechanism of β+-activation includes either target fragmentation only or the formation of both target and projectile positron-emitting fragments. Although the focus of this contribution is on proton therapy only, 120

12C(p,p+n)11C

Cross section/mb

100

16O(p,p+n)15O

80 60 40 20 0 0

100

300 200 Energy/MeV

400

FIGURE 16.2 Compilation of available experimental cross sections for the main (p, pn) [including (p, d)] reaction channels on carbon and oxygen yielding positron emitting 11C and 15O, respectively. (After Parodi, PhD thesis, Dresden University of Technology, 2004.)

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ion

Projectile fragment

Projectile

evap. νf ≈ νp

νp

Target Abrasion

Target fragment νf ≈ 0

p,d,t n -emission Ablation

Proton Projectile

Target Abrasion

Projectile p,d,t n Target fragment -emission Ablation

FIGURE 16.3 Schematic representation of peripheral nuclear collisions with special emphasis on the different fragmentation mechanisms undergone by carbon ions (projectile and target fragments with related velocities v) and protons (target fragments only). Different reaction products are also illustrated, including evaporation of nucleons and light fragments as well as γ-emission. (Adapted from Schardt et al., Rev Mod Phys, 82, 383, 2010.)

all the possible mechanisms of irradiation-induced β+-activity will be briefly reviewed. This is because of their relevance in the historical developments of PET monitoring (cf. subsections 16.3.3 and 16.3.4). Protons and light ions up to beryllium can only contribute to the β+-activation of the target nuclei of the irradiated medium. This is because they either do not fragment at all (protons Z = 1), or they cannot produce positron-emitting projectile fragments (Z ≤ 4). Typical reaction products in living tissue include light isotopes such as 11C, 15O, and 13N, with half-lives T1/2 of about 20, 2, and 10 min, respectively. These β+-active target fragments are formed all along the ion beam path as long as the energy is above the threshold for nuclear interaction. The latter is mostly located at 10–20 MeV/u, corresponding to about 1–4 mm residual ion range in tissue. Because of the interaction kinematics, the activated target recoils remain approximately at the place of production. Therefore, according to the typically weak energy dependence of the reaction cross sections for most of the therapeutically relevant ion beam energies in the most abundant tissue constituents (cf. Figure 16.2), the characteristic track of activation in homogeneous media exhibits a rather constant

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or slowly rising slope, dropping to zero few millimetres in front of the Bragg peak (Figure 16.4). For primary proton beams, the contribution of secondary radiation other than protons (e.g., neutrons) to the activation of the traversed tissue can be assumed to be negligible (13). Differently, for heavier primary ions (1 < Z ≤ 4), the longer ranging non-positron-emitting projectile fragments yield an additional tail of β+-emitting target fragments beyond the Bragg peak, as experimentally observed for 3He and 7Li ions in Fiedler et al. (14) and Priegnitz et al. (15). In addition to the formation of β+-active target fragments, heavier ions (Z  ≥  5) can also yield positron-emitting projectile fragments. This is also called “auto-activation” of the beam (17, 18), for distinction to the direct external implantation of primary β+-radioactive ions (19). Because the stopping in matter is a faster process than the radioactive decay, the activity contribution from β+-emitting projectile fragments is formed at their end of range. This can be particularly advantageous for beam range verification, as β+-active isotopes of the primary ion beam are typically formed in abundance and tend to accumulate shortly before the range of the primary stable ions due to the kinematics of the nuclear reaction (20). Therefore, the auto-activation (e.g., of a 12C ion beam) results in a marked activity maximum shortly before the Bragg peak due to the major contribution of the long-lived 11C and, to a lesser extent, of the short-lived 10C (T1/2 ≈ 20 s), superimposed onto the pedestal of β+-active target fragments (Figure 16.4). Nevertheless, the weaker spatial correlation between the depth distributions of dose and positron emitters for proton in comparison to carbon ion irradiation (cf. Figure 16.4) is somewhat outweighted by the approximately three times higher activity yield at the same range and delivered dose, as experimentally shown by Parodi, Enghardt, and Haberer (21). This is mainly Activity Dose

Arbitrary units

1.2 1.0 0.8 0.6 0.4 0.2 0.0

–20

0

1H

20 40 60 80 100 120 –20

Activity Dose

0

3He

20 40 60 80 100 120 –20

Penetration depth (mm)

Activity Dose

0

12C

20 40 60 80 100 120

FIGURE 16.4 Depth distributions of calculated dose (dashed line) and measured β+-activity (solid line) for 1H (left), 3He (middle), and 12C (right) ions impinging in homogeneous targets of polymethyl methacrylate (PMMA, C5H8O2). As a consequence of the different fragmentation mechanisms (cf. Figure 16.3 and text), projectile fragments of 12C ions yield a pronounced activity maximum shortly before the Bragg peak (right panel). For the lighter ion beams (left and middle), activation is only due to the target fragments produced along the beam penetration depth, including a tail beyond the Bragg peak from lower charge projectile fragments of the primary 3He beam (middle). (Adapted from Parodi, PhD thesis, Dresden University of Technology, 2004; Fiedler et al., IEEE Trans Med Sci, 53, 2252, 2006; and Pawelke et al., Proc. IBIBAM meeting, 2007.)

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due to the higher fluence of protons required to compensate their lower energy loss rate in the delivery of the same dose. 16.3.2  The Imaging Process Regardless of the formation mechanism, the transient pattern of β+-activation induced as a byproduct of the irradiation can be imaged via PET techniques. The first step in the image formation process is the β+-decay of the irradiation-induced positron emitter A(Z, N), with mass number A and neutron number N at a random time, depending on the isotope half-life:

A(Z, N) → A(Z – 1, N + 1) + e+ + νe.

(16.1)

In this radioactive transformation, one proton is transformed into one neutron, and a positron and a neutrino are emitted with a continuous energy spectrum. While the neutrino escapes without interaction, the positron is slowed down typically within a few millimeters path in the medium, losing its energy in Coulomb inelastic collisions with the atomic electrons and suffering several angular deflections. Once almost at rest, the positron either annihilates as a free particle with an electron of the medium into two photons, or it captures an electron to form an unstable bound state e− e+, so called positronium. Although the two different atomic states of the positronium can lead to different annihilation processes into two (para-positronium) or three (ortho-positronium) photons, the three γ-emission is in practice negligible. Thus, all the detectable radiation can be attributed to the two annihilation γ-quanta that, according to the momentum and energy conservation law, are emitted in opposite directions and carry an energy of 511 keV each, equal to the positron and electron rest mass. Deviations from perfect co-linearity can occur because of the residual energy of the electron-positron system, resulting in emission angles that approximately follow a Gaussian distribution centred at 180° with ca. 0.3° full-width at half-maximum (FWHM) for typical residual energy values of about 10 eV. The 511-keV photon pairs are energetic enough to penetrate the tissue surrounding the place of annihilation and eventually escape from the patient. Therefore, the PET signal can be acquired by opposite detector pairs surrounding the patient and operated in coincidence (Figure 16.5). Because of the relatively high photon energy, dense high-Z inorganic scintillators are usually used for stopping the penetrating photon radiation and, at the same time, for enabling fast timing performances of coincident detection typically within a few nanoseconds time window. Commonly used PET detectors are based on bismuth germanate (BGO), gadolinium orthosilicate (GSO), or lutetium oxyorthosilicate (LSO) scintillator crystals, though other promising materials such as lanthanum bromide (LaBr3) now are being investigated (22). The detected coincidences can be attributed to radiation either emerging from a single annihilation event (“true” or “scattered”), or belonging

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Detector hit 2 γ +

β -emitter e+

e-

Coincidence processor

Image reconstruction

180° γ Eγ = 511 keV

Detector hit 1 FIGURE 16.5 Schematic representation of the PET imaging process in the case of a full-ring detector surrounding the activity source. All the depicted steps of β+-decay, positron emission and moderation in the medium, annihilation and concident detection of the resulting γ-pairs for subsequent image reconstruction are explained in the text.

to independent emissions accidentally occurring close in time (“random”). Under the assumption of perfect co-linearity of the annihilation photon pairs, true coincidences refer to emission events originating along the line of response (LOR) connecting the two opposed crystals fired in coincidence. Differently, scattered coincidences are generated by events where at least one photon has experienced a scattering process and thus a change with respect to the initial direction. This results in a mismatch between the detected LOR and the original annihilation place. A similar mismatch obviously applies to random coincidences due to the different origins of the independent annihilation events accidentally detected in the same coincidence window (see Figure 16.6). For a reliable reconstruction of the β+-activity distribution underlying the measured signal, the amount of true coincidences has to be recovered from the whole collected data. This can be achieved via proper corrections for random (23) and scattered (24) coincidences. In this process, the properties of the used detector system can be critical. In particular, energy resolution is helpful for discrimination of scattered events, whereas short decay constants are essential for good coincidence timing and related random suppression. The latter has also been the main argument for the rapid establishment of latest True coincidence

Random coincidence

Scattered coincidence

FIGURE 16.6 Schematic illustration of true (left), random (middle), and scattered (right) coincidence events in PET acquisitions. The solid lines indicate the real photon paths, whereas the dashed lines depict the assigned lines of response to the detected coincident γ-ray pairs. Obviously, solid and dashed lines coincide only in the case of true coincidence (left). (After Parodi, PhD thesis, Dresden University of Technology, 2004.)

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generation lutetium-based scintillators like LSO, whose timing properties (and light output) outperform the more traditional detector systems based on BGO. This is at the expense of a minor amount of intrinsic radioactivity that is responsible for a small background (especially of random coincidences) in the measurable signal. This detector radioactivity is of no concern in standard nuclear medicine imaging, but it may become more relevant at the typical low activity levels of ion therapy monitoring, as discussed below. The quantitative amount of decays from the activity source can be then recovered from the estimated number of true coincidences by taking into account the total photon attenuation along each LOR as well as the quantum detection efficiency of the hit crystal pairs. The 3D distribution of the β+-activity map can be finally recovered from the measured projections using tomographic reconstruction algorithms, typically approximating the position of the β+-decay with the annihilation emission place and including a normalization for the space-dependent geometrical probability of detection from each emission position. The most reliable solutions are in general provided by iterative methods using the maximum-likelihood expectation maximization (MLEM, 25) or the ordered subsets expectation maximization (OSEM, 26) algorithms. Because of the typical detector granularity of 4–6 mm as well as the intrinsic limitations coming from the nonperfect colinearity of the annihilation photons and the finite positron range, spatial resolutions of approximately 4–5 mm FWHM are generally attainable in the center of the scanner field-of-view. It should be noticed that this coarse resolution introduces a blurring of the imaged map of activation, but it does not alter the center of gravity of the distributions. Thus, it does not prevent millimeter accuracy for localization of the distal activation falloff, which is correlated with the primary proton beam range (cf. Section 16.3.1 and Figure 16.4), as experimentally demonstrated in phantom studies (Figure 16.7) as long as sufficient counting statistics are detected (27). When available, additional information on the arrival time difference (time-of-flight, TOF) of the photons on the crystals fired in coincidence can be used to reduce the uncertainty of the reconstructed spatial position of the emission along the LOR. According to the 3 · 1010 cm/s speed of light and the time resolutions of 500 ps achievable with the latest generation PET scanners, the uncertainty in the localization of the emission event can be reduced to ±7.5 cm. Thus, TOF information cannot dramatically improve spatial resolution, but it can offer increased signal-to-noise ratio in the reconstructed images. In comparison to conventional tracer imaging in diagnostic nuclear medicine, a major challenge for the unconventional application of PET imaging to the verification of ion treatment is the extremely low counting statistics. The irradiation-induced activity signal amounts to approximately 0.2– 10  kBq/Gy/cm3 depending on the ion type, the time course of irradiation, and the involved anatomical site (15, 28–30). For typical fraction doses of 0.5–2 Gy this corresponds to activity densities that can be far below those of ≈10–100 kBq/cm3 reached in standard PET imaging. Moreover, once positron

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Arbitary units

1.2

Activity Dose

1.0 0.8 0.6 0.4 0.2 0.0

0

200

156.06 - 171.62 MeV 156.60 - 171.13 MeV 157.13 - 172.63 MeV 157.66 - 173.13 MeV

1.2 Arbitary units

50 100 150 Penetration depth/mm

1.0 0.8 0.6 0.4 0.2 0.0

0

50 100 150 Penetration depth/mm

200

FIGURE 16.7 Experimental validation of the range resolving power of in-beam PET for proton irradiation of thick PMMA targets. Top: the planned spread-out-Bragg peak dose (dashed line, built by 11 mono-energetic beams in the 156.06–171.62-MeV interval) and the corresponding measured activity (solid line) depth profiles. Bottom: the panel additionally depicts the activity depth distributions measured when changing the nominal SOBP plan in energy steps corresponding to incremental variations of less than 1 mm in depth. (After Parodi, PhD thesis, Dresden University of Technology, 2004.)

emitters are formed in living body by external irradiation, they undergo a complex hot chemistry and can be partly spread out by diffusion or even carried away (washed out) from the location of activity production by different physiological processes (e.g., perfusion) occurring at different time scales. As a result, the irradiation-induced activity tends to disappear more quickly in living tissues than in inorganic matter, thus following not only a physical but also a so-called biological decay with varying half-lives from 2 up to 10,000 s, according to pioneering investigations in dead and living animals (31, 32). 16.3.3  The Clinical Implementation Different imaging strategies can be implemented clinically for acquisition of the irradiation-induced activity signal, exploiting different portions of the characteristic time curve of the activity build-up and decay during and after therapeutic beam application (Figure 16.8). In situ detection of the transient activation of the patient directly in the treatment position can be performed during (“in-beam”) or immediately after (“in-room on-board”) end of irradiation by means of customized systems fully integrated in the dose

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Count rate/cps

8000 6000 4000 2000

Count rate/cps

0 a) 0

b) c) 500

5000 a) 4000

1000 Time / s b) c)

d) 1500 15 O 11

C C

d)

10

3000 2000 1000 0 0

500

1000 Time/s

1500

FIGURE 16.8 Illustration of the different time windows for detection of the β+-activity build-up and decay during and after irradiation. Top: (a–d) The measured (solid line) coincidence rate detected for an approximately 10-min proton irradiation of a PMMA target. The dashed line refers to the calculation using the estimated contributions of the different isotopes separately shown in the bottom panel (a–d). The corresponding different strategies of in-beam (a), in-room on-board (b), in-room (c), and off-line (d) PET imaging are discussed in the text. (Adapted from Parodi, PhD thesis, Dresden University of Technology, 2004; and Parodi et al., Trans Nucl Sci, 52, 778, 2005.)

delivery environment (28, 33). Alternatively, the patient can be moved to a remote installation for imaging starting from 2 up to 20 min after therapeutic beam application using conventional nuclear medicine PET scanners located inside (“in-room”) or outside (“off-line”) the treatment room (30). Indeed, the on-line implementations (in-beam and in-room on-board) are the most appealing solutions, which better preserve the correlation between the measurable signal and the delivered dose by detecting the major activiity contribution from short-lived emitters such as 15O and by minimizing the signal degradation from positioning uncertainties and biological washout. However, they are also the most demanding approaches, which require the development of dedicated detector instrumentation with typical dual-head geometrical configuration in order to avoid interference with the beam as well as to enable flexible patient positioning. In-beam implementations additionally offer the possibility to measure the time-resolved formation of the activity during irradiation. However, they also require customization of the data acquisition system for synchronization with the beam delivery and for rejection of the undesired background, for example, due to prompt-gamma emission, during the “beam-on” time (34). In fact, unless novel dedicated

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solutions are implemented (35), the prompt radiation background during beam extraction currently limits meaningful in-beam PET detection only to the pauses of pulsed beam delivery, thus reducing the amount of measurable decays from the produced isotopes in dependence of the accelerator duty cycle and dose rate. This is especially crucial for conventional in-beam PET data acquisition at efficient accelerator systems such as continuous-wave cyclotrons and dedicated clinical synchrotrons (36). Therefore, although inbeam solutions ideally offer the optimal workflow for exploitation of the activity signal already during beam delivery, they may still require prolongation of the measurement for a few minutes after the end of the irradiation for sufficient counting statistics, similar to the in-room on-board solutions. This is obviously at the expenses of patient throughput in the treatment room. In terms of imaging performances, for both on-line implementations the space-variant detector response of dual-head configurations in combination with the generally low counting statistics of irradiation-induced activation pose challenging issues for trustful image reconstruction, thus requiring careful design of the detector geometry (37) and cautious interpretation of the reconstructed activity distributions. In particular, existent limited angle installations are either restricted to central planar imaging (33) or suffer from severe degradation of the imaging performances far from the central plans of the field-of-view in the tomographic reconstruction (28, 37). In this respect, theoretical investigations have indicated the promise of future ultra-fast TOF techniques with timing resolution less than 200 ps, which would enable almost artefact-free, real-time images for the next-generation in-beam ­installations currently being under investigation (38), as addressed in Section 16.3.5. Postradiation in-room and off-line imaging can rely on commercially available full-ring tomographs, but requires accurate replication and fixation of the treatment position. Especially for in-room instrumentation, this can be achieved using modern robotic positioning systems with minimal perturbation of the patient fixation. Availability of CT imaging in combined PET/CT scanners can considerably help coregistration at the expenses of additional radiation exposure of the patient, which can be however justified in the context of IGRT. For in-room instrumentation, moderate efforts are required for integration of the scanner in the treatment environment and for optimization of the workflow in order to minimize the occupation of the treatment room after irradiation. Off-line imaging outside of the treatment room is less demanding in terms of integration efforts, but requires longer measuring times for accumulation of sufficient counting statistics as in the in-beam or in-room acquisition during or shortly after treatment (cf. Figure 16.8). Moreover, off-line imaging can only enable detection of the integral fraction dose delivery, without the capability to resolve the contribution of the first applied treatment field. This restricts verification of the in vivo beam range to non-opposing-beam portals for multifield irradiation. Individual monitoring of the first-delivered treatment field is instead possible with in-room

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instrumentation, provided that modification of the patient position for transportation into the scanner is accepted by the clinical staff when additional fields are to be delivered after the PET imaging. Obviously, minimization of the time elapsed between irradiation and in-room or off-line imaging is crucial to keep the degradation of the measurable signal at an acceptable level, taking into account the typical half-lives of 2 and 20 min for the main  15O and  11C products, respectively, as well as the typical time scale of 2 up to 10,000 s for the different components of biological washout (32). This would ideally require delays of a couple of minutes at most, which seem to be feasible for in-room installations. Larger delays may be unavoidable for off-line implementations, depending on the vicinity of the installation and the automation of the workflow. The loss of activity in the time elapsed between irradiation and imaging consequently affects the choice of the acquisition time window, which has to be selected as a reasonable compromise between counting statics, patient throughput in the treatment room (in-room imaging), and patient comfort in prolonged acquisitions (off-line imaging). This typically translates into measuring times of approximately 5 min for in-room imaging and maximum 30 min for off-line imaging. In terms of tomographic imaging, full-ring scanners typically provide improved performances compared with limited angle in situ installations, but may suffer from the shortcomings of the postradiation application in terms of reduced counting statistics and increased washout in dependence of the imaging delay and the acquisition time window. Furthermore, reconstruction algorithms of commercial scanners are typically optimized for imaging high level, localized activity concentrations as typically administered in standard tracer imaging and may thus suffer limitations in the imaging of low level, extended activity distributions as induced by therapeutic irradiation. Additional issues can be due to the minor amount of intrinsic radioactivity of the PET detector components (e.g., LSO-based) that may generate a background noise comparable with the signal to be imaged (29). Regardless of the chosen imaging strategy, the irradiation-induced activity within the patient represents only a “surrogate” signal that is correlated but not directly matching the delivered dose (cf. Figure 16.4). The distinction is clearly due to the different nuclear and electromagnetic processes underlying the mechanisms of β+-activation and energy deposition, respectively. The ideal clinical exploitation of PET imaging would require a solution to the challenging ill-posed inverse problem directly relating the measured activity to the actual dose delivery. Despite promising attempts to establish this relationship for phantom studies (39, 40), a straightforward solution is not yet available for application to low statistics and washout-affected patient data. Nevertheless, useful clinical information on the correct delivery of the intended treatment field and beam range can be obtained from the comparison of the measured PET images with an expected pattern of β+-activation. This can be either the reference activity measured at the first day of treatment (41) or a detailed calculation taking into account the patient-specific

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treatment plan and the fraction-specific time course of irradiation and PET acquisition, as well as the detector-dependent imaging performances (28). The former approach only enables a consistency check over the course of fractionated therapy, whereas the latter may allow a direct in vivo validation of the planned beam range in the patient when the PET calculation shares similar physical beam models as the treatment-planning system and, in particular, the same CT-range calibration curve (42). Indeed, the possibility of in vivo validation of the beam range in the patient is of utmost importance when starting the operation of a new ion beam therapy facility or when introducing new ion species into clinical practice, as demonstrated by the clinical experience of in-beam PET monitoring of 12C ion treatments at Gesellschaft für Schwerionenforschung (GSI), Darmstadt, Germany (28). However, the computational approach implemented in Pönisch et al. (42), tailored to application at the GSI pilot therapy project, could exploit the reduced sensitivity of carbon ion–induced activation to the patient tissue stoichiometry because of the relevance of projectile-fragmentation processes (cf. Section 16.3.1 and Figure 16.4). For proton therapy, the computational model must carefully take into account both the elemental composition of the medium and the different reaction channels leading to the production of the positron emitters whose decay can be measured in the considered acquisition time window. Preclinical studies in homogeneous materials of known compositions highlighted the benefit of directly using available experimental cross sections folded with the energy-dependent proton fluence rather than relying on the predictions of general-purpose nuclear models (21, 27). Moreover, they highlighted changes of the distal activity falloff up to a couple of millimeters, depending on the acquisition time window, due to the signal contribution from different isotopes such as 11C, 10C, and  15O, as well as the different energy dependence and threshold of the reaction cross sections (27). First computations of proton-induced activation in clinical cases were implemented using either full-blown Monte Carlo simulation methods (13, 43) or analytical convolution of the planned dose distribution with proper reaction-dependent filter functions (43, 44). Clearly, the accuracy of the computational methods strongly depends on the used cross sections for the involved activation channels, as well as on the extraction of information on the tissue elemental composition from the available CT images. In this respect, a recent Monte Carlo study quantified the uncertainties of the CT conversion scheme already to account for a 1-mm limitation in the accuracy of range verification from PET images (45). Moreover, the computational modeling cannot be ­limited to the description of the physical production and decay of positron emitters, but must also include the complex effect of biological washout, which can considerably affect the magnitude and spatial pattern of the measurable activity especially in postradiation imaging. For this purpose, a first solution has been proposed in Parodi et al. (43) on the basis of literature data for implanted radioactive ions in animal tissue (32), as well as time-decay analysis of activity curves in regions of interest set in

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different tissue for clinical PET acquisitions after proton therapy. The basic idea is the model suggested in Mizuno et al. (32), which decomposes the biological processes (Cbio) into fast (f), medium (m), and slow (s) components affecting the physical activity (Aphys) decay in the final measurement (Ameas) as follows:

Ameas(t) = Cbio(t) Aphys(t) Cbio(t) = [Mf exp(–λbio ft) + Mm exp(–λbio mt) + Ms exp(–λbio st)];  ∑M = 1.  (16.2)

A patient-independent segmentation of the patient CT was then proposed to identify different tissues (e.g., brain, muscle, fat) for assignment of the biological M and λ coefficients selected on the basis of the above-mentioned literature (32) and clinical data (36, 43). This modeling already provided very encouraging results with quantitative agreement between calculation and predictions from 5% to 30%, especially for head-and-neck tumor locations  (43). However, other investigations reported more severe deviations in extracranial anatomical sites, especially in the pelvic region (46), thus demanding further model refinements. In addition to range verification, PET imaging can also confirm the lateral position of the irradiation field as well as detect unpredictable deviations between planned and actual treatment caused by minor misalignments or local anatomical and/or physiological changes of the patient, which introduce density modifications in the beam path (10, 41). Although the latter modifications of the patient position and/or morphology can also be deduced from in-room radiographic or tomographic kilovoltage x-ray imaging, the PET method has the advantage of not delivering any additional radiation exposure to the patient (when using the planning CT for attenuation correction and anatomical coregistration). Furthermore, the in-beam implementation may detect transient modifications occurring during treatment, which could be missed by pre- or posttreatment imaging. When discrepancies between measurement and expectation are detected, a PET-guided quantification of the most likely applied dose corresponding to the experimental observation can be performed. This requires careful inspection of the PET images possibly supported by computer-aided tools for interactive or ideally automatized assessment of the underlying reason of mismatch (e.g., mispositioning or anatomical change), in combination with the access to the treatment-planning system for the recalculation of the dose delivery. This indirect approach of PET-based dose reconstruction was proposed and clinically implemented for carbon ion therapy (10). Eventually, improvement of the PET imaging performances and better understanding of the current uncertainties in the knowledge of the tissue stoichiometry, reaction cross sections, and washout parameters might enable direct dose reconstruction based on the promising preclinical approaches proposed in Parodi and Bortfield (39) and Fourkal, Fan, and Veltchev (40).

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16.3.4  Worldwide Installations and Clinical Experience The original proposition of using the (at that time newly developed) PET technology for the monitoring of ion irradiation dates back to the 1970s in connection with the pioneering heavy ion therapy program at the Lawrence Berkeley National Laboratory (LBL), Berkeley, CA. Here, a dedicated in-beam planar positron camera was installed directly at the treatment site in order to verify the range of low-dose β+-radioactive beams (e.g., 19Ne) injected into the patient prior to the therapeutic treatment with the stable isotope (e.g., 20Ne) (17, 19). Unfortunately, the prototype system never reached clinical routine use, mostly because of activation of the BGO detector itself and the premature end of the therapy project due to the BEVALAC accelerator shutdown in 1993. Nevertheless, after the encouraging first results demonstrated at LBL, the PET method was further pursued for heavy ions at the new carbon ion therapy facilities established at the Heavy Ion Medical Accelerator at Chiba (HIMAC), Japan (18), and GSI (28). In particular, at the experimental carbon ion therapy facility at GSI the first in-beam tomographic PET installation has been realized by the Research Centre of Dresden-Rossendorf, in order to measure the autoactivation of the primary stable 12C ion beam during irradiation (28). The dedicated tomograph was assembled from commercial BGO-detector components and optimized with respect to geometrical configuration and data acquisition for complete integration into the treatment environment (47). In the recently concluded 11 years of clinical operation, each individual therapeutic fraction of more than 400 patients mainly treated for head-and-neck and pelvic tumors has been monitored with the system, demonstrating clinical feasibility as well as valuable clinical feedback (48). PET played an essential role at the beginning of the clinical pilot project back in 1997 to spot inaccuracies of the initially used CT-range calibration curve, especially in the soft tissue region, triggering its improvement (49). Over the several years of operation, PET also proved to be a very useful tool for detecting and quantifying deviations between planned and delivered treatment due to small positioning inaccuracies or anatomical modifications in the time course of fractionated therapy (10, 48). Moreover, a recent in silico study based on the collected clinical data indicated the capability of achieving a sensitivity of ca. 92% and a specificity of ca. 96% for detection of ±6-mm range modifications for the considered anatomical indications (50). Finally, the installation has been used for the first promising phantom experiments addressing the feasibility of time-resolved 4D PET imaging for confirmation of motion-compensated carbon ion beam tracking delivery to moving targets (51). For protons, detectability and usability of the irradiation-induced β+-target activation was first investigated at the Brookhaven National Laboratory (BNL), Upton, NY, in the late 1970s, using an in-beam pair of position-­ sensitive BGO detectors for irradiation of tissue-equivalent plastics and frozen animal samples (31). Later on in the 1990s, feasibility phantom studies

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were carried out using commercial off-line PET scanners by different groups in the Netherlands and Canada (52, 53). Thorough investigations of the activity detection during and after proton irradiation of homogeneous and inhomogeneous targets have been performed with an in-beam limited-resolution BGO-based prototype at the Michigan State University, East Lansing, MI (54), and with the dedicated in-beam PET installation at GSI Darmstadt (21, 27). In particular, the latter phantom experiments indicated that the proton-induced activation is about three times larger than that produced by 12C ion beams of the same range at the same physical dose delivery, hence further renewing the interest in PET monitoring for the more widely used proton therapy. For clinical application with passively scattered proton beams, the first trials have been performed with commercial full-ring PET scanners a few minutes after treatment, thus suffering from major coregistration issues between the treatment and imaging positions and lacking a calculation modeling for comparison with the measured images (30, 55). Confirmation of the irradiated area from measured off-line PET scans has been performed on a regular basis at the combined proton and carbon ion therapy facility of Hyogo, Japan, since 2002 (56). However, this implementation is limited to a qualitative ­comparison between the measured PET images and the planned dose distribution or available PET scans from previous treatment fractions. The first attempt to overcome the coregistration issues of off-line imaging via the usage of a combined PET/CT scanner together with the establishment of a detailed modeling of the expected pattern of activation, including biological washout, has been realized at Massachusetts General Hospital (MGH), Boston, MA. The pilot clinical study reported in Parodi et al. (43) included nine patients with tumors in the cranial base, spine, orbit, and eye. Postradiation imaging was done for a duration of 30 min starting up to 20 min after a single treatment fraction was delivered in one or two fields for a total dose of 1.8–3 GyE up to 10 GyE (ocular melanoma). This study highlighted the importance of using the same treatment immobilization device at the imaging site despite the availability of the additional CT used for coregistration to the planning CT. Moreover, it indicated the possibility to achieve good spatial correlation and quantitative agreement between the measured and calculated activity distributions when taking metabolic processes into account according to Equation 16.2. In particular, for head-and-neck patients the beam range could be verified within 1–2 mm in favorable locations of well-coregistered, low-perfused bony structures. However, low spine and eye sites indicated the need for better fixation and coregistration methods, thus calling for further technological and methodological improvements. Following these promising results, a successive study extended the population of patients to a total (including the pilot trial) of 23 subjects receiving at least one postradiation PET/CT acquisition after proton treatment (57). For quantitative data analysis different strategies were implemented and compared to address the agreement between measured and calculated depth activity distributions in terms of range verification. This work helped

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identifying and characterizing the limitations and promises of the PET verification method for different tumor entities in different anatomical locations (cranial base, spine, orbit, eye, sacrum, and prostate), overall supporting the initial findings of the pilot investigation. In fact, both the clinical studies confirmed the potential of the technique for millimeter range verification in favorable locations such as well coregistered and low-perfused bony structures for lesions in the head and cervical spine. However, they also identified challenges especially for extracranial tumor sites, due to major limitations from biological washout, breathing motion, coregistration issues, and lack of Hounsfield unit tissue correlativity for reliable extraction of elemental composition to be used in the activation modelling (43, 46). Most of these drawbacks were however ascribed to the suboptimal implementation relying on a remote PET/CT installation within ca. 10-min walking distance from the proton therapy center, resulting in up to 20 min of time elapsed between irradiation and imaging. Moreover, off-line acquisition could only measure the global activation produced by the fraction dose, without the possibility to resolve the activity contribution of the individual treatment fields applied to the patient. This made the method of range verification only feasible for the considered cases of single- or multiple-angulated treatment fields, while presenting major shortcomings in the case of opposed beams. After the MGH experience, other proton therapy facilities have started addressing the capability of off-line PET/CT not only for in vivo verification of the beam range and confirmation of the treated volume (58), but also for assessment of patient-specific information on prostate motion and patient position variability during daily proton beam delivery to help establish patient-specific planning target volume margins (59). In these clinical studies approximately 30 patients with tumors of the brain, head and neck, liver, lung, sacrum (58), and prostate (59) have been imaged at commercial off-line PET/CT installations for 5 or 30 min starting 7 or 15 min after the end of irradiation, respectively. Nowadays, on-going efforts in the clinical environment are mainly devoted to optimal implementation and evaluation of imaging strategies relying either on conventional commercial instrumentation installed nearby the treatment site (off-line) or on new industrial prototypes tailored to inroom PET imaging. In particular, a novel dedicated BGO-based dual-head planar camera has been integrated into the proton beam gantry at the National Cancer Center of Kashiwa, Japan (41), for routine verification of the delivered treatment with respect to the reference activation at the first day of irradiation. In this ­in-room on-board implementation, the 200-s-long measurement can be started immediately after the end of irradiation without changing the patient position. Despite the limitations to central planar imaging, the first relevant clinical results from the investigation of 48 patients with tumors of the head and neck, liver, lungs, prostate, and brain included early detection of beam range variations due to anatomical modifications with respect to the planning CT, similar to the findings reported in (10, 48) for tomographic in-beam

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PET monitoring of 12C ion therapy. A very recent study also suggested the applicability of the on-board PET installation to verify patient positioning via radioactive markers (called molecular image-guided radiation therapy [m-IGRT]), alternatively to x-ray radiographic IGRT (60). At MGH, a prototype of a mobile full-ring neuro-PET scanner based on cesium iodide (CsI)-scintillators is being characterized and clinically investigated for in-room detection of the β+-activation shortly after the end of irradiation (61). In this concept, the PET scanner can be rolled into the treatment room where it is needed, and the robotic table is then used for positioning the immobilized patient in the field-of-view of the detector a few minutes after the therapeutic beam delivery is completed. The considerable reduction of the time elapsed between irradiation and imaging enables only a few minutes of acquisition time, promising to overcome the major drawbacks of the off-line implementation at a remote PET/CT scanner. This is however at the expense of the missing additional CT imaging for attenuation correction, for coregistration to the planning CT, and/or for assessment of anatomical modifications. Moreover, the applicability of this instrumentation is limited to cranial or pediatric indications because of the small-bore opening. Finally, at the newly operational Heidelberg Ion-Beam Therapy Center in Germany, a commercial, latest generation PET/CT scanner has been recently installed outside of the treatment rooms and is currently being characterized in view of forthcoming clinical application after scanned proton and carbon ion therapy. Before this dedicated installation, a proof-of-principle first-time measurement after actively shaped proton treatment has been realized at a remote PET/CT scanner in the nearby Heidelberg University Hospital starting more than 20 min after the irradiation (62). Examples of installations and results for different implementations are shown in Figures 16.9 and 16.10. 16.3.5  On-Going Developments and Outlook In addition to the on-going clinical studies using conventional or prototype instrumentation tailored to off-line and in-room PET imaging, several research institutions are working on technological advances toward the development of next-generation, dedicated in-beam PET detectors. In particular, major efforts are being invested to advance the performances of fast scintillators such as LSO, LYSO (cerium-doped lutetium yttrium orthosilicate), and LaBr3 or to investigate alternative detection concepts such as resistive plate channels (RPC, 64) for realization of dedicated dual-head TOF-PET scanners. The final goal is to enable direct, event-by-event reconstruction of the activity measured during patient irradiation, with minimal degradation of the image quality despite the limited-angle geometry (38). However, the applicability of PET techniques to detection during proton beam delivery strongly depends on the accelerator and, in particular, the time structure of the extracted beam. In fact, the time structure of a synchrotron easily enables

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Proton

Rotating Detector head Moving

Gamma ray Detector head

Moving

Rotating

FIGURE 16.9 Example of installations being investigated for clinical in vivo PET verification of proton therapy. (Adapted from Nishio et al., Int J Radiat Oncol Biol Phys, 76(1), 277, 2005; and Parodi et al., Nucl Instrum Methods A, 591, 282, 2008.) Top left and bottom: off-line PET/CT and movable inroom PET scanner, respectively, at Massachusetts General Hospital in Boston, MA. (Adapted from Parodi et al., Int J Radiat Oncol Biol Phys 68, 920, 2007; Knopf et al., Phys Med Biol, 54, 4477, 2009; and España et al., Med Phys, 37, 3180, 2010.) Top right: dual-head in-room on-board camera integrated into the beam gantry at the National Cancer Center of Kashiwa, Japan. (Adapted from Nishio et al., Int J Radiat Oncol Biol Phys, 76(1), 277, 2005.)

detection in the pauses of the pulsed irradiation. Differently, a continuous wave cyclotron poses issues related to the considerable background radiation, making true in-beam detection impossible unless novel data acquisition strategies are implemented as proposed in Enghardt et al. (35). Thus, careful workflow considerations are required for those facilities where a prolongation of the in-beam PET detection after the end of irradiation is needed for counting statistics, in order to maintain an acceptable compromise between imaging performances and patient throughput. Overall, despite the already demonstrated clinical value in selected anatomical locations (e.g., head and neck) as well as the promise of the on-going

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FIGURE 16.10 (See color insert.) Examples of different clinical implementations of in vivo PET-based verification of proton therapy. The top row refers to off-line PET/CT imaging long after irradiation at MGH, Boston (cf. Figure 16.9). In particular, the mismatch of the PET/CT measurement (PET/CT Meas) with the planned dose is evident. Instead, a good agreement is obtained for the PET MC modeling when taking biological washout into account (MC PET + washout), in contrast to the physical activation alone (Physical MC PET). The rainbow colorbars give absolute dose or activity values, and the gray scale refers to arbitrary rescaled CT values. The bottom row refers to inroom on-board imaging immediately after irradiation at the National Cancer Center, Kashiwa, Japan (cf. Figure 16.9). For this patient, the planar activity measurements taken at different days (cf. quoted accumulated dose on top) revealed inconsistency, with a clear trend to activation at larger penetration depth (cf. activity profiles in right inset). This finding prompted the detection of a serious anatomical modification of the patient (more than 100-cm3 tumor shrinkage on a new CT image), thus calling for plan adaptation. (Adapted from Nishio et al., Int J Radiat Oncol Biol Phys, 76(1), 277, 2005; and Parodi et al., Int J Radiat Oncol Biol Phys 68, 920, 2007.)

methodological and technological developments, the PET method intrinsically suffers from the major drawbacks of low counting statistics and biological washout. Indeed, both issues could be mitigated in the near future by the likely changes of current fractionation schemes toward hypofractionation treatments with higher dose delivery, as well as by improved imaging detection during or shortly after ion irradiation. In particular, the planned future generation of ultra-fast, in-beam TOF scanners promises quantitative and artifact-free imaging to be achieved almost simultaneously to the data acquisition. Nevertheless, the PET signal is intrinsically “delayed” with respect to the time of beam interaction with the tissue according to the 2–20-min halflife time of the most abundant β+-emitter products. This makes IGRT and

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DGRT difficult to achieve in real-time, thus stimulating research on other viable approaches of in vivo imaging.

16.4  Prompt Gamma Imaging To overcome the intrinsic limitations of PET imaging, different research groups have recently started investigating complementary or maybe even alternative imaging techniques still based on the detection of the emerging secondary radiation induced by nuclear interactions. The proposed most promising approach exploits the challenging detection of prompt gammas. 16.4.1  The Production of Irradiation-Induced Prompt Gamma Gamma emission from excited nuclear states is a typical process occurring in the final de-excitation phase of prefragments formed in nuclear interactions between the therapeutic ion beam and the irradiated tissue (Figure 16.2). Indeed, this is also the process responsible for the major component of the undesired radiation background, which complicates in-beam PET detection during real beam-on time, as experimentally addressed in Parodi et al. (34). According to the typical energy dependence of the reaction cross sections, the prompt-gamma yield increases toward the end of the beam path until the energy of the primary ions and of the secondary hadronic radiation drops below the reaction threshold, resulting in a distal falloff correlated with the primary beam range (Figure 16.11). After the nuclear fragmentation reaction has occurred, the de-excitation prompt gammas are typically emitted in a very short time (<1 ns) and isotropically in space. The energy spectrum can be very broad, extending up to several, or even tens, of megaelectronvolts. The shape exhibits an almost exponentially decreasing continuum superimposed onto several emission lines corresponding to the transitions between the discrete energy levels of the excited nuclei. Because de-excitation emission can also occur in-flight, the width of the spectral lines can be affected by Doppler broadening. 16.4.2  The Imaging Process The energetic prompt gammas are able to escape from the patient after production, with a reduced attenuation in comparison to the 511-keV annihilation photon pairs. Therefore, detection of this penetrating radiation preserving spatial information on the place of emission may be exploited for a real-time verification of the treated area and, in particular of the beam range (66). In addition, spectroscopic identification of the characteristic emission lines can be used as a means to determine tissue composition (65, 67).

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FIGURE 16.11 Left: relative gamma-ray production as a function of energy for proton interaction on carbon ( ), nitrogen ( ), oxygen ( ), and calcium ( ). (Adapted from Polf et al., Phys Med Biol, 54, 731, 2009.) Right: promising correlation between the depth–dose profiles measured with an ionization chamber (IC) and the corresponding prompt-gamma scans (PGS) along the proton beam penetration in water. (From Min et al., Appl Phys Lett, 89, 1063, 2011. With permission.) The pioneering detection of right-angled prompt gammas was achieved with a collimated and neutronshielded CsI scintillator at the National Cancer Center, Seoul, Korea, as described in the text.

The main principle of the imaging process is similar to standard singlephoton emission imaging. This requires a photon detector and a collimation system for selecting a particular angular direction from the isotropic gamma emission, differently from the intrinsic collimation of the PET signal. However, the following considerations rule out the applicability of conventional photon detection systems that are well established in diagnostic nuclear medicine imaging. First, the emission energy of the radiation to be detected is not known a priori, in opposition to the known emission energy of radioactive tracers in nuclear medicine. Moreover, the high spectral energies in the megaelectronvolts regions make the collimation process quite challenging. Mechanical approaches similar to the gamma (or Anger) camera solutions indeed require much more bulky material for efficient collimation of the penetrating radiation. Alternative solutions under investigation aim to achieve electronic collimation via exploitation of the known kinematics of Compton scattering. However, the applicability of conventional Compton camera setups is complicated by the fact that the scattered photon is typically not completely stopped in the subsequent absorber. Therefore, alternative designs are being explored that exploit multiple scattering processes until the final interaction (ideally complete absorption) of the energy-degraded prompt gamma occurs in the last component of the multistage detector assembly (68). Directional information can be recovered from the intersection of the characteristic Compton cones (in which scattering at a certain angle take place) with the plane of emission. This is particularly appealing in the case of scanned ionbeam irradiation, where the prompt-gamma signal can be resolved along the impinging direction of each individual pencil beam. Finally, the signal of

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interest is typically embedded in a large radiation background due to neutrons, in addition to scattered photons. This requires either dedicated shielding techniques for neutron absorption or data acquisition strategies such as pulse-shape-discrimination or time-of-flight (69), capable of separating the signal induced by the different radiation components. Therefore, although several proof-of-principle measurements have been recently accomplished by different investigators with nonoptimal detector setups in order to address the promise of this technique, a viable imaging solution is not yet existent and is still the subject of on-going research. 16.4.3  Worldwide Preclinical Investigations The initial experimental investigations have been limited to the detection of collimated (mostly right-angled) prompt gammas, scanned along the proton beam penetration depth in homogeneous targets for 1D assessment of spatial correlation with the dose delivery and the ion beam range. The first pioneering study has been performed with a CsI(Tl) scintillator and a collimator system consisting of lead, paraffin, and B4C powder to suppress the considerable background from scattered photons and neutrons, respectively  (66). The prompt-gamma scans (PGSs) along the beam penetration in water were successfully compared to ionization chamber (IC) measurements of depth dose to illustrate the promising correlation with the Bragg peak location (Figure 16.11). In addition to further efforts of the research team at the Korean National Cancer Center, Seoul, for testing alternative detector concepts such as pinhole or Compton cameras (70), recent Monte Carlo and experimental investigations were reported by Polf et al. (65, 67) with the innovative goal to provide spectroscopic insight on the tissue composition from the acquired prompt-gamma energy spectra. For this challenging purpose, promising results could be demonstrated at the Cyclotron Institute at Texas A&M University in Houston, Texas, with a dedicated experimental setup consisting of a high-purity germanium (HPGe) detector shielded either with lead or a Compton suppression system. In addition to the results for proton beams, a similar correlation between prompt-gamma profiles and ion range could be experimentally demonstrated also for carbon ions (71). Therefore, several groups are currently concentrating their research on the optimization of the detector layouts aiming to develop novel prototype solutions for an efficient, at least 1D detection of prompt gammas emitted during proton or carbon ion irradiation. Although currently proposed concepts are limited to estimated detection efficiencies ranging in the order of 10−6 to 10−5 for gamma energies in the few megaelectronvolt range, on-going developments hold the promise to eventually make prompt-gamma detection a viable method for real-time in vivo verification of ion beam delivery. A very recent Monte Carlo study has also addressed the first-time comparison of in-room PET imaging versus prompt-gamma emission for real

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clinical indications of passively scattered and pencil beam proton beam delivery (72). Although this theoretical approach was limited to account only for the prompt-gamma production without calculation of detector response, the detailed analysis could anticipate a clear advantage of prompt-gamma imaging, especially for pencil beam scanning. This was mainly attributed to the typically lower energy thresholds resulting in an improved spatial correlation between prompt-gamma and dose–depth profiles, as well as the reduction of intrinsic PET uncertainties, such as physiological washout and delayed detection (Figure 16.12). However, despite the estimated superior (up to a factor of 80) prompt-gamma yield and the reduced (factor of about  5) signal attenuation in the patient with respect to the considered in-room PET implementation (5-min acquisition starting 2 min after a 30-s-long irradiation), the signal-to-noise realistically available in prompt-gamma measurements will ultimately depend on the achievable detection efficiency for clinical applicability. 16.4.4  The Foreseen Clinical Implementation Similar to the β+-activation, the irradiation-induced prompt-gamma production only represents a “surrogate” signal correlated but not directly matching the delivered dose (cf. Figure 16.12). Therefore, unless a straightforward relationship between prompt-gamma emission yield and dose deposition can be established, this promising technique will have to rely on the comparison of the measured signal with an expectation (e.g., deduced from detailed MC calculations). Because of the manifold reaction channels leading to nuclear excitation and subsequent gamma emission, direct usage of experimental cross sections folded with proton fluence does not seem to be a viable solution. This is a major restriction having to entirely rely on the accuracy of 5961.3

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FIGURE 16.12 (See color insert.) Theoretical MC comparison between total prompt gamma emissions (PG, middle) and measurable PET coincidences (PET with washout, right) when taking biological washout into account and assuming a 5-min acquisition starting 2 min after a 30-s delivery of a proton pencil-like beam (Dose, left) impinging from the left (cf. arrow) on an head-and-neck patient. (Adapted from Moteabbed et al., Phys Med Biol, 56, 1063, 2011.)

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the available nuclear models, differently from the flexible computational approach using experimental cross sections for calculation of proton-induced β+-activity in PET (cf. Section 16.3.4). Hence, clinical applicability will require extensive experimental validation of prompt-gamma yields independent of the proton beam properties and the irradiated tissue type. The final choice of feasible detection solution as well as the strategy for clinical implementation will also considerably depend on the specific beam delivery and time structure at the selected proton therapy facility. Passively shaped scattered broad beams spread typical therapeutic proton beam intensities over large (several cm3) volumes, hence most likely requiring time-integrated 3D reconstruction of prompt-gamma emissions for drawing conclusions on the correctness of the entire dose delivery. Differently, if efficient detection per incident pencil beam might be guaranteed during dynamic beam scanning irradiation, even 1D prompt-gamma imaging might be envisioned as a tool for real-time monitoring of the delivered beam range, with the possibility of prompt interruption of the irradiation if deviations from the expectation are detected. Alternatively, prompt-gamma imaging of a subset of pencil beams could be evaluated as a range probe before the application of the entire treatment (72), similar to the original PET proposition of using low-dose implanted radioactive beams for pretreatment range assessment (cf. Section 16.3.4). Spatial information on the impinging pencil beam direction could be obtained by placing a fast position-sensitive detector (e.g., an hodoscope) in front of the patient and by complementing this entrance information with the most-likely path suffered by protons traveling in the human body, similar to computational approaches developed for image reconstruction in proton radiography or tomography (73). Artistic views of possible clinical implementations originally depicted for application to the less scattering (straight-line approximation) carbon ion beams is reported in Figure 16.13a and b, for the two promising detector solutions of gamma and Compton cameras, respectively. Unfortunately, optimal large-scale instrumentation fulfilling the conflicting requirements of high detection efficiency, good spatial and time resolution, and effective suppression of the considerable background from secondary neutrons as well as scattered photons and, possibly, enabling recovery of 3D spatial information on the treated volume is still at the research and development phase. Therefore, the promising prompt-gamma imaging technique cannot be considered yet mature for clinical application, differently from the PET methodology described in Section 16.3.

16.5  Magnetic Resonance Imaging The last methodology having being proposed for in vivo range verification of proton therapy relies on the unconventional interpretation of standard

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FIGURE 16.13 Artistic views of possible clinical implementations of real-time prompt gamma imaging of scanned pencil-like ion beams (in this example, carbon) by using either a multicollimated multidetector prompt-gamma camera (a) or a multistage Compton camera (b). The upstream hodoscope detector serves to tag the ions in time and space prior to the entrance in the patient, whereas the TOF technique is used to separate the gamma signal from the neutron background (cf. text). (Adapted from Testa, PhD thesis, University Claude Bernard, 2010.)

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T1-weighted diagnostic magnetic resonance (MR) images. In fact, routine follow-up investigations of patients receiving craniospinal proton irradiation at MGH surprisingly revealed a sharp demarcation of a hyperintense T1-weighted signal in the posterior part of the vertebral bodies (74). This signal, visible on MR images acquired after completion of proton therapy, was attributed to radiation-induced fatty replacement of bone marrow, which can be detected as early as 10 days after radiotherapy and is observed to persist up to 21 months after treatment. Visual comparison with the treatment plans indicated a clear correlation between the sharply delineated bone marrow changes and the distal dose falloff for the considered posterior-anterior fields, directly placing the characteristic proton Bragg peaks only in the posterior part of the vertebral body (thecal sac). Whereas the enthusiasm for this intriguing finding was initially addressed to the “visual” demonstration of the improved sparing of normal tissues in proton radiotherapy, the authors soon recognized the potential of the method to address in vivo verification of the beam range. Although such posttreatment information cannot enable patient-specific IGRT or DGRT for correction of the already entirely delivered therapeutic dose, it can still provide essential clinical information for improvement of population-based treatment margins in specific indications. Therefore, in a second study (75) the same research team attempted a challenging quantification of the relationship between radiation dose and MRI signal intensity (SI). This was done on a populationbased approach by analyzing the correlation of the MR signal with the more controllable lateral penumbra of the proton dose in the irradiated sacrum. Using the so-established general dose-SI relationship, the distal falloff of the “actually delivered” dose was deduced from the MRI images and compared to the planning one in order to estimate proton range delivery errors in the lumbar spine (Figure 16.14). The initial findings indicated a tendency to overshoot about 1.9 mm (95% confidence interval, 0.8–3.1 mm), which is, however, well within the already used clinical margins (75). Moreover, the magnitude of the observed overshoot was judged to be in the same order of magnitude of the inherent uncertainties of the method. The latter are mainly attributed due to the patient-specific validity of a general dose-SI relationship deduced in a different anatomical region than the lumbar spine, to the usage of heuristic rules for determination of the data to be reliably used in the analysis, and to the coregistration between MRI and planning CT data (though the quality of coregistration was claimed to be very good in the presented study). Nevertheless, this work indeed represented the first worldwide demonstration of in vivo proton range verification using posttreatment spine MRI changes. Therefore, further investigations are on-going to improve the methodology and to extend the technique to MRI sequences, which may enable earlier detection of bone marrow changes in the lumbar spine or of other physiological processes in different anatomical sites (e.g., the liver). The ultimate goal is to allow for treatment adaptation already during the course of fractionated therapy by using relatively inexpensive and nonionizing MRI (75).

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FIGURE 16.14 (See color insert.) Illustration of the clinical workflow and results of MRI-based in vivo range verification. The less-controllable lateral penumbra of the beam in the sacrum (a) is used to determine a dose-signal intensity curve (b). From the analysis of more patient data a general dose-SI curve is obtained and used to calculate the 50% distal isodose deduced from the MRI scan (red lines, c) for comparison with the planned one (blue lines), showing in this example a generalized beam overpenetration in the lumbar spine. (Adapted from Gensheimer et al., Int J Radiat Oncol Biol Phys, 78(1), 268, 2010.)

16.6  Conclusion and Outlook This chapter has reviewed the main methods currently under experimental or clinical investigation for in vivo range and dose verification in proton therapy. Although none of the reported techniques can yet achieve the level of accuracy currently obtained for EPID-based dose reconstruction in photon therapy (7), all the methods hold great promise to complement each other and enable proton treatment verification at different time scales (cf. Figure 16.1) and in different anatomical locations. Indeed, despite the discussed shortcomings of delayed emission and biological washout, PET imaging still represents the most mature technique readily available for clinical implementation with relatively moderate efforts. Initial promising clinical results could be already demonstrated at least for favorable anatomical locations such as the head-and-neck (41, 43, 57). Therefore, it can be expected that the on-going developments toward new generation detectors of inbeam TOF-PET and prompt-gamma imaging will eventually enable realtime monitoring of the beam range and DGRT for state-of-the-art proton pencil beam scanning in the near future. For certain indications, fractionspecific information from emission imaging could be complemented by MR imaging at regular time intervals during the treatment course in order to optimize treatment margins for reduction of toxicity and safe dose escalation studies. Finally, extension to time-resolved 4D monitoring of motioncompensated beam delivery could play an important role in promoting safe treatment of moving targets. Therefore, it can be foreseen that the synergetic

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unconventional usage of different imaging modalities within and outside the treatment room will play a fundamental role in promoting full-clinical exploitation of the dosimetric advantages of proton beam therapy.

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17. Tobias CA, Benton EV, Capp MP, et al. Particle radiography and autoactivation, Int J Radiat Oncol Biol Phys 1997;35–44. 18. Tomitani T, Kanazawa M, Yoshikawa K, et al. Effect of target fragmentation on the imaging of autoactivation of heavy ions. J Jpn Soc Ther Radiol Oncol 1997;9(S2):79–82. 19. Llacer J, Chatterjee A, Alpen EL, et al. Imaging by injection of accelerated radioactive particle beams. IEEE Trans Med Imag 1984;80–90. 20. Morrissey DJ. Systematics of momentum distributions from reactions with relativistic ions. Phys Rev C 1989;39:460–70. 21. Parodi K, Enghardt W, Haberer T. In-beam PET measurements of β+-radioactivity induced by proton beams. Phys Med Biol 2002;47:21–36. 22. Daube-Witherspoon ME, Surti S, Perkins A, et al. The imaging performance of a LaBr3-based PET scanner. Phys Med Biol 2010;55(1):45–64. 23. Brasse D, Kinahan PE, Lartizien C, et al. Correction methods for random coincidences in fully 3D whole-body PET: impact on data and image quality. J Nucl Med 2005;46:859–67. 24. Ollinger JM. Model-based scatter correction for fully 3D PET. Phys Med Biol 1996;41:153–76. 25. Shepp LA, Vardi Y. Maximum likelihood reconstruction for emission tomography. IEEE Trans Med Imaging 1982;1:113–22. 26. Hudson HM, Larkin RS. Accelerated image reconstruction using ordered subsets of projection data. IEEE Trans Med Imaging 1994;13:601–9. 27. Parodi K, Pönisch F, Enghardt W. Experimental study on the feasibility of in-beam PET for accurate monitoring of proton therapy. IEEE Trans Nucl Sci 2005;52:778–86. 28. Enghardt W, Crespo P, Fiedler F, et al. Charged hadron tumour therapy monitoring by means of PET. Nucl Instrum Methods A 2004;525:284–88. 29. Parodi K, Paganetti H, Cascio E, et al. PET/CT imaging for treatment verification after proton therapy—a study with plastic phantoms and metallic implants. Med Phys 2007;34:419–39. 30. Vynckier S, Derreumaux S, Richard F, et al. Is it possible to verify directly a proton-treatment plan using positron emission tomography? Radiother Oncol 1993;26:275-77. 31. Bennett GW, Archambeau JO, Archambeau BE, et al. Visualization and transport of positron emission from proton activation in vivo. Science 1978;200:1151–53. 32. Mizuno H, Tomitami T, Kanazawa M, et al. Washout measurements of radioisotopes implanted by radioactive beams in the rabbit. Phys Med Biol 2003;48:2269–81. 33. Nishio T, Ogino T, Nomura K, et al. Dose-volume delivery guided proton therapy using beam on-line PET system. Med Phys 2006;33:4190–97. 34. Parodi K, Crespo P, Eickhoff H, et al. Random coincidences during in-beam PET measurements at microbunched therapeutic ion beams. Nucl Instrum Methods Phys Res A 2005;545:446–58. 35. Enghardt W, Crespo P, Parodi K, et al. Verfahren zur Korrektur der beim Monitoring der strahlentherapeutischen Behandlungen mittels in-beam PET erhaltenen Messwerte. Deutsches Patent- und Markenamt München DE 10 2004 0009 784 A1 (2005). 36. Parodi K, Bortfeld T, Haberer T. Comparison between in-beam and offline PET imaging of proton and carbon ion therapeutic irradiation at synchrotron- and cyclotron-based facilities. Int J Rad Oncol Biol Phys 2008;71:945–56.

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37. Crespo P, Shakirin G, Enghardt W. On the detector arrangement for in-beam PET for hadron therapy monitoring. Phys Med Biol 2006;51:2143–63. 38. Crespo P, Shakirin G, Fiedler F, et al. Wagner A, Direct time-of-flight for quantitative, real-time in-beam PET: a concept and feasibility study. Phys Med Biol 2007;52:6795–6811. 39. Parodi K, Bortfeld T. A filtering approach based on Gaussian-powerlaw convolutions for local PET verification of proton radiotherapy. Phys Med Biol 2006;51(8):1991–2009. 40. Fourkal E, Fan J, Veltchev I. Absolute dose reconstruction in proton therapy using PET imaging modality: feasibility study. Phys Med Biol 2009;54(11):N217–28. 41. Nishio T, Miyatake A, Ogino T, et al. The development and clinical use of a beam ON-LINE PET system mounted on a rotating gantry port in proton therapy. Int J Radiat Oncol Biol Phys 2010;76(1):277–86. 42. Pönisch F, Parodi K, et al. The description of positron emitter production and PET imaging during carbon ion therapy. Phys Med Biol 2004;49:5217–32. 43. Parodi K, Paganetti H, Shih HA, et al. Patient study on in-vivo verification of beam delivery and range using PET/CT imaging after proton therapy. Int J Rad Oncol Biol Phys 2007;68:920–34. 44. Parodi K, Brons S, Cerutti F, et al. FLUKA code for application of Monte Carlo methods to promote high precision ion beam therapy Proc. 12th Int. Conf. on Nuclear Reaction Mechanisms (Varenna, Italy, 2009 June 15–20). 45. España S, Paganetti H. The impact of uncertainties in the CT conversion algorithm when predicting proton beam ranges in patients from dose and PETactivity distributions. Phys Med Biol 2010;55(24):7557–71. 46. Knopf A, Parodi K, Bortfeld T, et al. Systematic analysis of biological and physical limitations of proton beam range verification with offline PET/CT scans. Phys Med Biol 2009;54:4477–95. 47. Pawelke J, Enghardt W, Haberer T, et al. In-beam PET imaging for the control of heavy-ion tumour therapy. IEEE Trans Nucl Sci 1997;44:1492–98. 48. Enghardt W, Parodi K, Crespo P, et al. Dose quantification from in-beam positron emission tomography. Radiother Oncol 2004;73:S96–S98. 49. Rietzel E, Schardt D, Haberer T. Range accuracy in carbon ion treatment planning based on CT-calibration with real tissue samples. Radiat Oncol 2007;23:2–14. 50. Fiedler F, Shakirin G, Skowron J, et al. On the effectiveness of ion range determination from in-beam PET data. Phys Med Biol 2010;55:1989–98. 51. Parodi K, Saito N, Chaudhri N, et al. 4D in-beam positron emission tomography for verification of motion-compensated ion beam therapy. Med Phys 2009;36:4230–43. 52. Paans AMJ, Schippers JM. Proton therapy in combination with PET as monitor: a feasibility study. IEEE Trans Nucl Sci 1993;40:1041–44. 53. Oelfke U, Lam GKY, Atkins MS. Proton dose monitoring with PET: quantitative studies in Lucite. Phys Med Biol 1996;41:177–96. 54. Litzenberg DW, Roberts DA, Lee MY, et al. On-line monitoring of radiotherapy beams: Experimental results with proton beams. Med Phys 1999;26:992–1006. 55. Hishikawa Y, Kagawa K, Murakami M, et al. Usefulness of positron-­emission tomographic images after proton therapy. Int J Radiat Oncol Biol Phys 2002;53:1388–91. 56. Abe M. Charged particle radiotherapy at the Hyogo Ion Beam Medical Center: characteristics, technology and clinical results. Proc Jpn Acad B 2007;83:151–63.

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57. Knopf AC, Parodi K, Paganetti H, et al. Accuracy of proton beam range verification using post-treatment positron emission tomography/computed tomography as function of treatment site. Int J Radiat Oncol Biol Phys 2011;79(1):297–304. 58. Nishio T, Miyatake A, Inoue K, et al. Experimental verification of proton beam monitoring in a human body by use of activity image of positron-emitting nuclei generated by nuclear fragmentation reaction. Radiol Phys Technol 2008;1:44–54. 59. Hsi WC, Indelicato DJ, Vargas C, et al.. In vivo verification of proton beam path by using post-treatment PET/CT imaging. Med Phys 2009;36:4136–46. 60. Yamaguchi S, Ishikawa M, Bengua G, et al. A feasibility study of a molecularbased patient setup verification method using a parallel-plane PET system. Phys Med Biol 2011;56(4):965–77S. 61. España S, Zhu X, Daartz J, Liebsch N, et al. Feasibility of in-room PET imaging for in vivo proton beam range verification. Med Phys 2010;37:3180. 62. Unholtz D, Sommerer F, Haberer T, et al. Quantitativer Vergleich gemessener und simulierter strahleninduzierter Positronenaktivität nach Protonentherapie, Proceedings of the 44th Annual meeting of German Society of Biomedical Technique (DGBMT), BMT2010, Rostock, Germany, 2010 October 5–8. 63. Parodi K, Bortfeld T, Enghardt W, et al. Shih H. PET imaging for treatment verification of ion therapy: implementation and experience at GSI Darmstadt and MGH Boston. Nucl Instrum Meth A 2008;591:282–86. 64. Blanco A, Chepela V, Ferreira-Marquesa R, et al. Perspectives for positron emission tomography with RPCs. Nucl Instrum Methods Phys Res A 2003;508:88–93. 65. Polf J, Peterson S, Ciangaru G, et al. Prompt gamma-ray emission from biological tissues during proton irradiation: a preliminary study. Phys Med Biol 2009;54:731–43. 66. Min CH, Kim CH, Youn MY, et al. Prompt gamma measurements for locating the dose falloff region in the proton therapy. Appl Phys Lett 2006;89:183517, 1–3. 67. Polf JC, Peterson S, McCleskey M, et al. Measurement and calculation of characteristic prompt gamma ray spectra emitted during proton irradiation. Phys Med Biol 2009;54:N519–27. 68. Peterson SW, Robertson D, Polf J. Optimizing a three-stage Compton camera for measuring prompt gamma rays emitted during proton radiotherapy. Phys Med Biol 2010;55:6841–56. 69. Testa M. Physical measurements for ion range verification in charged particle therapy. PhD Thesis, University Claude Bernard Lyon 1, Lyon, France, 2010 (http://tel.archives-ouvertes.fr/docs/00/55/66/28/PDF/PhD_Mauro_Testa_ Last.pdf). 70. Kim J, Kubo H, Tanimori T. Prompt Gamma Measurements for the Verification of Dose Deposition in Proton Therapy, presented at the AAPM Annual meeting, Anaheim, CA, 2009 June 26–30 (http://www.aapm.org/meetings/amos2/ pdf/42-11888-63035-937.pdf/ accessed June 24, 2011). 71. Testa E, Bajard M, Chevallier M, et al. Monitoring the Bragg peak location of 73 MeV/u carbon ions by means of prompt gamma-ray measurements. Appl Phys Lett 2008;93:093506. 72. Moteabbed M, Espana S, Paganetti H. Monte Carlo patient study on the comparison of prompt gamma and PET imaging for range verification in proton therapy. Phys Med Biol 2011;56:1063–83.

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73. Williams DC. The most likely path of an energetic charged particle through a uniform medium. Phys Med Biol 2004;49:2899–2911. 74. Krejcarek SC, Grant PE, Henson JW, et al. Physiological and radiographic evidence of the distal edge of the proton beam in craniospinal irradiation. Int J Rad Biol Phys 2007;68:646–49. 75. Gensheimer MF, Yock TI, Liebsch NJ, et al. In vivo proton beam range verification using spine MRI changes. Int J Radiat Oncol Biol Phys 2010;78(1):268–75.

17 Basic Aspects of Shielding Nisy Elizabeth Ipe CONTENTS 17.1 Introduction................................................................................................. 526 17.2 Secondary Radiation.................................................................................. 526 17.2.1 Physics of Secondary Radiation Production............................... 527 17.2.1.1 Intranuclear Cascade....................................................... 527 17.2.1.2 Production of Muons and Electromagnetic Cascade..... 529 17.2.1.3 Evaporation Nucleons and Activation.......................... 529 17.3 Neutron Energy Classification and Interactions.................................... 530 17.4 Neutron Yield, Average Energy, and Angular Distribution................. 532 17.5 Unshielded Neutron Spectra..................................................................... 535 17.6 Characteristics of Shielded Neutron Field.............................................. 536 17.7 Neutron Monitoring................................................................................... 537 17.8 Calculational Methods............................................................................... 537 17.8.1 Conversion Coefficients................................................................. 537 17.8.2 Analytical Methods........................................................................ 538 17.8.2.1 Point Source...................................................................... 538 17.8.2.2 Removal Cross Section.................................................... 539 17.8.2.3 Attenuation Length..........................................................540 17.8.2.4 Moyer Model..................................................................... 541 17.8.3 Monte Carlo Calculations.............................................................. 541 17.8.4 Computational Models...................................................................542 17.9 Shielding Design Considerations.............................................................544 17.9.1 Beam Losses.....................................................................................544 17.9.1.1 Synchrotron- and Cyclotron-Based Systems................544 17.9.1.2 Treatment Rooms............................................................. 545 17.9.1.3 Fixed Beam and Gantry Rooms..................................... 546 17.9.1.4 Beam-Shaping Techniques.............................................546 17.9.2 Workload.......................................................................................... 546 17.9.3 Regulatory Dose Limits................................................................. 547 17.9.3.1 Occupancy Factor............................................................. 548 17.9.4 Shielding Materials.........................................................................548 17.9.4.1 Earth................................................................................... 548 17.9.4.2 Concrete and Heavy Concretes...................................... 548 17.9.4.3 Steel and Iron.................................................................... 549 525

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17.9.4.4 Polyethylene...................................................................... 550 17.9.4.5 Lead.................................................................................... 550 17.9.5 Transmission................................................................................... 550 References.............................................................................................................. 551

17.1  Introduction Shielding considerations for particle accelerators came into play in the 1930s, when construction and operation of particle accelerators at Cambridge by Cockroft and Walton and at Berkeley by Lawrence and Livingstone (1, 2) first occurred. These accelerators were of low energy and intensity, and many of the early cyclotrons were constructed underground to avoid unexpected radiological problems. However, with the advent of larger accelerators producing particles with much higher energies (e.g., the Cosmotron at Brookhaven and the Bevatron at Berkeley), knowledge of the prompt radiation fields and the requirements for effective shielding design became important. The prompt radiation field produced by protons in the therapeutic energy range of interest, 67–330 MeV, is comprised of a mixture of charged and neutral particles as well as photons, with neutrons being the dominant component. The neutrons have energies as high as the incident proton energy. In contrast, the average energy of neutrons from photon therapy linear accelerators (linacs) is only a few megaelectronvolts (MeV). Therefore, physicists who perform shielding calculations for photon therapy linacs seldom have the expertise to shield proton therapy facilities. The requirements for the physicist performing shielding design for proton therapy facilities include a strong foundation in the basic aspects of shielding as well adequate experience in the shielding of neutrons of all energy ranges, especially high-energy neutrons, that is neutrons with energies > 100 MeV. An extensive coverage of shielding design and radiation safety for charged particle therapy facilities can be found in the Particle Therapy Cooperative Group (PTCOG) Report 1 (3). Basic aspects of shielding such as the production of secondary radiation, characteristics of the prompt radiation field, neutron interactions, and shielding design considerations will be covered in this chapter.

17.2  Secondary Radiation Secondary radiation consists of prompt and residual radiation. Prompt radiation is produced while the machine is on. Residual radiation is produced by activated materials, that is, materials that have become radioactive during beam operation. Thus, residual radiation remains even after the machine is

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turned off, for a time period that is determined by the half-life of the activated material. Secondary radiation is produced by the interaction of protons with beam line components. It is produced at locations where beam losses occur: in the synchrotron and cyclotron during injection, during energy degradation in the cyclotron, during beam transport to the treatment room, and in beam-shaping devices in the treatment nozzle. Thus, the accelerators, beam transport line, and treatment room require shielding. It is also produced in the patient, dosimetric phantom, and beam stop. It is produced at locations where beam losses occur. The large shielding thicknesses for the rooms are determined by the prompt radiation, whereas the residual radiation requires considerably less localized shielding. 17.2.1  Physics of Secondary Radiation Production Proton interactions are described in Chapter 1. Nuclear evaporation and the intranuclear cascade are the two nuclear processes that are important in the determination of particle yields from proton-nuclear interactions (1–3). The interaction of low-energy protons (EP < 10 MeV, where EP is the energy of the incident proton) with a nucleus can be described by the compound nucleus model. The incident particle is absorbed by the target nucleus, resulting in the formation of a compound nucleus. The compound nucleus is in an excited state with a number of allowed decay channels. The preferred decay channel is the entrance channel. As the energy of the incident particle increases, the number of levels available to the incident channel increases considerably. Instead of discrete levels in the quasi-stationary states of the compound nucleus, there is a complete overlapping of levels inside the nucleus. Under these conditions, the emission of particles can be described by an evaporation process similar to the evaporation of a molecule from the surface of a liquid. The interaction of protons in the energy range of 50 to 1000 MeV with matter results in the production of an intranuclear cascade (spray of particles), in which neutrons have energies as high as the incident proton. Thus, the intranuclear cascade is an important consideration for therapeutic protons. There are five distinct and independent stages to be considered, as shown in Figure 17.1 (1): Intranuclear cascade Production of muons Electromagnetic cascade Evaporation of nucleons Activation 17.2.1.1  Intranuclear Cascade An intranuclear cascade is produced when an incoming hadron (proton, neutron, etc.) with energy less than a few hundred MeV, interacts with

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Muon production

π e+

e– π

0

n Incoming hadron

p

n π0

n

Electromagnetic cascade

π

Intranuclear cascade

p n

Evaporation of nucleons and fragments

Activation FIGURE 17.1 Schematic representation of various stages of intranuclear cascade. (From National Council on Radiation Protection and Measurements, Radiation Protection for Particle Accelerator Facilities, Report 144, 2003. With permission.)

individual nucleons in a nucleus, producing a spray of particles, such as protons, neutrons, and π mesons (pions). Pions can be charged (π±) or neutral. Charged pions have a rest mass of 139.6 MeV/c2 (where c is the velocity of light) and neutral pions have a mass of about 135 MeV/c2. Therefore, neutral and charged pions are produced at energies above 135 and 139.6 MeV, respectively. The scattered and recoiling nucleons from the interaction proceed through the nucleus. Each of these nucleons may in turn interact with other nucleons in the nucleus, leading to the development of a cascade. Some of the cascade particles that have sufficiently high energy escape from the nucleus, whereas others do not. The residual nucleus evaporates particles such as alpha particles and other nucleons. In the third stage, after particle emission is no longer energetically possible, the remaining excitation energy is emitted in the form of gamma rays. A large fraction of the energy in the cascade is transferred to a single nucleon. This nucleon, with energy greater than 150 MeV, propagates the cascade. The cascade neutrons that arise from individual nuclear interactions are forward-peaked and have longer attenuation lengths than evaporation neutrons. However, it is important to note that although the high-energy neutrons transport the cascade, the lower-energy neutrons deposit a major fraction of the absorbed dose, even outside thick shields. Nucleons with energies between 20- and 150-MeV transfer energy to several nucleons. Therefore, on an average each nucleon receives energy of

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about 10 MeV. Charged particles at these energies are quickly stopped by ionization. Thus, neutrons predominate at low energies. 17.2.1.2  Production of Muons and Electromagnetic Cascade Charged pions decay into muons and neutrinos. Muons have a mass of 105.7 MeV/ c2 and are very penetrating particles. They deposit energy by ionization. Photonuclear reactions are also possible. Protons and pions with energy less than 450 MeV have a high rate of energy loss. Thus, neutrons are the principal propagators of the cascade with increasing depth in the shielding. Neutral pions decay into two energetic gamma rays that initiate electromagnetic cascades. The photons that are produced interact through pair production or Compton collisions, resulting in the production of electrons. These electrons radiate high-energy photons (bremsstrahlung), which in turn interact to produce more electrons. At each step in the cascade, the number of particles increases, and the average energy decreases. This process continues until the electrons fall into the energy range where collision losses dominate over radiative losses and the energy of the primary electron is completely dissipated in excitation and ionization of the atoms, resulting in heat production. This entire process resulting in a cascade of photons, electrons, and positrons is called an electromagnetic cascade. A very small fraction of the bremsstrahlung energy in the cascade goes into the production of hadrons such as neutrons, protons, and pions. The energy that is transferred is mostly deposited by ionization within a few radiation lengths. The attenuation length is the distance traveled through which the intensity of the radiation is reduced to 37% of its original value. However, the attenuation length of these cascades is much shorter than the absorption length, which is the reciprocal of the inelastic cross section and therefore does not include elastic scattering of neutrons. Thus, the electromagnetic cascade does not contribute significantly to the energy transport. It is important to note that the intranuclear cascade dominates for protons in the therapeutic energy range of interest. 17.2.1.3  Evaporation Nucleons and Activation The energy of those particles that do not escape is assumed to be distributed among the remaining nucleons in the nucleus, leaving it in an excited state. It then de-excites by emitting particles, mainly neutrons and protons that are referred to as evaporation nucleons, alpha particles, and some fragments. The evaporation nucleons are so called because they can be considered as boiling off a nucleus that is heated by the absorption of energy from the incident particle. The energy distribution of emitted neutrons can be described by the following equation:

n(E)dE = aEe–E/τ,

(17.1)

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where a is a constant, E is the energy of the neutron, and τ is the nuclear temperature that has the dimensions of energy with a value that lies between 0.5 and 5 MeV. The evaporated particles are emitted isotropically in the laboratory system, and the energy of the evaporation neutrons extends to 8 MeV (1, 2). Similar equations may be used to describe the emission of charged particles, but the emission of low-energy charged particles is suppressed by the Coulomb barrier. If low-energy particles are emitted, they are stopped near their point of emission. These particles do not contribute to the cascade, but they contribute to local energy deposition. Therefore, charged particles produced by evaporation do not impact the determination of shielding thickness. The evaporation neutrons travel long distances, continuously depositing energy. Evaporation neutrons produced by interactions near the source contribute to dose inside the shield and to leakage dose through doors and openings. However, because they are strongly attenuated in the shield, they do not contribute to dose outside the shield. The dose outside the shield is dominated by evaporation neutrons produced near the outer surface of the shield. The remaining excitation energy may be emitted in the form of gammas. The de-excited nucleus may be radioactive, thus leading to residual radiation.

17.3  Neutron Energy Classification and Interactions The secondary radiation field produced by protons is quite complex; however, neutrons dominate the radiation field. Therefore, it is important to understand how neutrons interact. Neutrons are classified according to their energy as follows:

Thermal: Intermediate: Fast: Relativistic: High-energy neutrons:

En = 0.025 eV at 20º C. Typically En ≤ 0.5 eV 0.5 eV < En ≤ 10 keV 10 keV < En ≤ 20 MeV En > 20 MeV En > 100 MeV

where En is the energy of the neutron and En is the average energy of the neutron. Because neutrons are uncharged, they can travel appreciable distances in matter without undergoing interactions. A neutron can undergo an elastic or an inelastic reaction on collision with an atom (4). An elastic reaction is one in which the total kinetic energy of the incoming particle is conserved. In an inelastic reaction, the nucleus absorbs some energy and is left in an excited state. Inelastic scattering can occur only at energies above the lowest excited state (or inelastic scattering threshold) of the material. The lowest excited states

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in lead and iron are 0.57 and 0.847 MeV, respectively. The neutron can also be captured or absorbed by a nucleus in reactions such as (n, 2n), (n, p), (n, α), or (n, γ). The sum of the inelastic and (n, 2n) cross sections in the energy range < 20 MeV is called the nonelastic cross section (5). The inelastic scattering dominates at lower energies, whereas the (n, 2n) reactions dominate at higher energies. The energy loss in any inelastic collision cannot be determined exactly, but there is a minimum energy loss that equals the energy of the lowest excited state. Usually there is a large energy loss in a single collision, which results in the excitation of energy states above the ground state, followed by the emission of gamma rays. In the (n, 2n) reaction, the minimum energy loss is equal to the binding energy of the neutron. This reaction produces a large number of lowerenergy neutrons because the energies of the two neutrons that are produced are similar. A large amount of elastic scattering takes place in high-Z materials, but results in negligible energy loss. However, elastic scattering increases the path length of the neutrons in the shielding material, thus providing more opportunities for inelastic and (n, 2n) reactions to occur. The mean free path is the average distance traveled by the particle in the material between two interactions. Thermal neutrons (nth) are in approximate thermal equilibrium with their surroundings. They gain and lose only small amounts of energy through elastic scattering, but they diffuse about until captured by atomic nuclei. Thermal neutrons undergo radiative capture, that is, neutron absorption leads to the emission of a gamma ray, such as in the 1H(nth, γ)2H reaction. The capture cross section for this reaction is 0.33 × 10−24 cm2, and the gamma ray energy is 2.22 MeV. This reaction occurs in hydrogenous shielding materials such as polyethylene and concrete. Borated polyethylene is used instead of polyethylene, because the cross section for capture in boron is much higher (3480 × 10−24 cm2) and the subsequent capture gamma ray from the 10B (nth, α)7Li has a much lower energy of 0.48 MeV. The capture cross sections for low-energy neutrons (<1 keV) decrease as the reciprocal of the velocity or as the neutron energy increases. Intermediate energy neutrons lose energy by scattering and are absorbed. Fast neutrons include evaporation neutrons. They interact with matter mainly through a series of elastic and inelastic scattering and are finally absorbed after giving up their energy (6). Approximately 7 MeV is given up to gamma rays, on an average, during the slowing down and capture process. Inelastic scattering is the dominant process in all materials at neutron energies above 10 MeV. Elastic scattering dominates at lower energies. Below 1 MeV, elastic scattering is the principle process by which neutrons interact in hydrogenous materials. When high-Z material is used for shielding, it must always be followed by hydrogenous material. A useful rule of thumb is that the hydrogenous material should have a thickness of at least one high-energy inelastic interaction mean free path (6). The reason for the latter requirement is because the energy of the neutrons may be reduced by inelastic scattering to a lower energy where they may be transparent to the

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nonhydrogenous material. For example, lead is virtually transparent to neutrons with energy below 0.57 MeV (5). Relativistic or “cascade” neutrons arise from cascade processes in proton accelerators. They are important in propagating the radiation field. The high-energy component of the cascade with neutron energies above 100 MeV propagates the neutrons through the shielding and continuously regenerates lower-energy neutrons and charged particles at all depths in the shield via inelastic reactions with the shielding material (7). The reactions occur in three stages for neutrons with energies between 50 and 100 MeV (8). In the first stage, an intranuclear cascade develops, where the incident high-energy neutron interacts with an individual nucleon in the nucleus. In the second stage the residual nucleus is left in an excited state and evaporates particles such as alpha particles and other nucleons. In the third stage, after particle emission is no longer energetically possible, the remaining excitation energy is emitted in the form of gamma rays. The de-excited nucleus may be radioactive. For neutrons with energy below 50 MeV, only the second and third stages are assumed to be operative.

17.4  Neutron Yield, Average Energy, and Angular Distribution The prompt radiation field produced by protons of energies up to 330 MeV encountered in proton therapy is quite complex, consisting of a mixture of charged and neutral particles as well as photons. However, neutrons are the dominant component. As the proton energy increases, the threshold for nuclear reactions is exceeded, and more nuclear interactions can occur. At energies above 50 MeV, the intranuclear cascade process becomes important. The neutron yield of a target is defined as the number of neutrons emitted per incident primary particle. Between proton energies of 50 and 500 MeV the neutron yields increase as approximately EP2, for all target materials, where EP is the energy of the incident proton (2). The neutron yield from a target depends on the target material and dimensions. Thick targets are targets in which the protons are completely stopped, that is, the thickness is greater than or equal to the particle range. By contrast, thin targets are targets with thicknesses that are significantly less than the particle range. Thus, for example, the protons lose an insignificant amount of energy in the target, and the kinetic energy available for neutron production in the target is the full incident proton energy (2). Calculations and measurements of neutron yields, energy spectra, and angular distributions for protons of various energies incident on different types of materials have been reported in the literature (2, 9–15). Comparisons between calculations and measurements have also been made (12–14). Table 17.1 shows the neutron yield (integrated over all angles) for protons with energies ranging from 100 to 250 MeV, incident on thick iron targets.

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Basic Aspects of Shielding

TABLE 17.1 Neutron Yields for 100- to 250-MeV Protons Incident on a Thick Iron Target Proton Energy EP (MeV) 100 150 200 250

Neutron Yield (neutrons per proton)

Range (mm)

Iron Target Radius (mm)

Iron Target Thickness (mm)

En < 19.6 MeV

En >19.6 MeV

ntot

14.45 29.17 47.65 69.30

10 15 25 58

20 30 50 75

0.118 0.233 0.381 0.586

0.017 0.051 0.096 0.140

0.135 0.284 0.477 0.726

Source: Particle Therapy Cooperative Group, Report 1, 2010. With permission.

The data is based on calculations with the Monte Carlo code, FLUKA (11, 16). The total yield (ntot), and yields for neutron energy (En ) less than and greater than 19.6 MeV are shown. FLUKA uses cross section tables below 19.6 MeV and models above 19.6 MeV. As expected, the neutron yield increases with increasing proton energy. The average neutron energies (E n) for various emission angles are shown in Table 17.2 for the targets described in Table 17.1 (11). As the proton energy increases, the average neutron energy in the forward direction (0°  to 10°) increases, thus resulting in the hardening of the spectra. However, at very large angles (130° to 140°) the average energy does not change significantly with increasing proton energies; therefore the spectra does not change much. Table 17.3 shows the neutron yield as a function of target dimensions for 250-MeV protons (11). Table 17.4 shows the average neutron energies at 250 MeV as a function of iron target dimensions. The total neutron yield and the yield for En <19.6 MeV increases with both target radius and target thickness, but the yield for En >19.6 MeV decreases. The data indicate that the average TABLE 17.2 Average Neutron Energies for Various Emission Angles as a Function of Proton Energya Emission Angles 0° to 10° Proton energy (MeV)   100   150   200   250

22.58 40.41 57.73 67.72

40° to 50° 12.06 17.26 22.03 22.90

80° to 90° 4.96 6.29 7.38 8.09

130° to 140° 3.56 3.93 3.98 3.62

Average neutron energy, En, is expressed as megaelectron volts (MeV). Source: Particle Therapy Cooperative Group, Report 1, 2010. With permission. a

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TABLE 17.3 Neutron Yield for 250-MeV Protons as a Function of Iron Target Dimensions Iron Target Radius (mm) 37.5 58.0 75.0 75.0

Iron Target Thickness (mm) 75.0 75.0 75.0 150.0

Neutron Yield (neutrons per proton) En < 19.6 MeV

En >19.6 MeV

0.567 0.586 0.596 0.671

0.148 0.140 0.136 0.111

ntot 0.715 0.726 0.732 0.782

Source: Particle Therapy Cooperative Group, Report 1, 2010. With permission.

TABLE 17.4 Average Neutron Energies at 250 MeV for Various Emission Angles as a Function of Iron Target Dimensions Emission Angles Iron Target Radius (mm) 37.5 58.0 75.0 75.0

Iron Target Thickness (mm)

0° to 10°

40° to 50°

80° to 90°

130° to 140°

75.0 75.0 75.0 150.0

73.6 67.7 64.7 70.3

25.9 22.9 21.3 23.5

8.1 8.1 8.1 6.9

3.9 3.6 3.5 3.2

Average neutron energy, En, is expressed as megaelectron volts (MeV). Source: Particle Therapy Cooperative Group, Report 1, 2010. With permission.

neutron energy increases with increasing target thickness at the 0° to 10° and 40° to 50° emission angles, but decreases for emission angles larger than 80° to 90°. As the target thickness increases, the proton interactions increase, resulting in an increase in the secondary neutron yield. At first, the yield is dominated by the high-energy neutrons, but as the thickness is further increased, the high-energy neutrons interact, producing more low-energy neutrons. Therefore, the high-energy neutron yield decreases and the lowenergy neutron yield increases, whereas the overall neutron yield increases. The low-energy neutrons get attenuated in the target as the thickness is further increased. The net result is an increase in total neutron yield with increasing target thickness until it reaches a maximum and then a decrease due to the attenuation of low-energy neutrons in the target material. According to data provided by Tesch (15), the ratios of neutron yields from different target materials for thick targets are independent of EP in the energy range of 20 MeV to 1 GeV, (which covers the therapeutic energy range of interest). The data are given relative to medium mass number (A) by C:Al:CuFe:Sn:Ta-Pb = (0.3 ± 0.1):(0.6 ± 0.2):(1.0):(1.5 ± 0.4):(1.7 ± 0.2). This indicates that as the mass number increases the neutron yield increases.

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17.5  Unshielded Neutron Spectra Figure 17.2 shows the unshielded neutron spectra for neutrons at various emission angles, produced by 250-MeV protons incident on a thick iron target (without any concrete shielding) described in Table 17.1 (11). The double differential neutron spectra shown as lethargy plots were calculated with FLUKA. Neutron lethargy, or logarithmic energy decrement, u, is a dimensionless logarithm of the ratio of the energy of source neutrons (E0) to the energy of neutrons (E) after a collision: u = In



E0 E

(17.2)

E = E0 exp(−u).



(17.3)

A plot of E versus u will show an exponential decay of energy per unit collision,  indicating that the greatest changes of energy (ΔE) result from the early collisions. The energy distributions in these figures are typically characterized by two peaks: a high-energy peak (produced by the scattered primary beam particle) and an evaporation peak at ~2 MeV. The high-energy peaks shift to higher energies with increasing proton energies, which are particularly evident in the forward direction (0° to 10°). The high-energy peak for the unshielded target is not the usual 100-MeV peak that is observed outside thick concrete shielding, which will be discussed in the next section.

Φ(E)·E [cm–2 sr–1 per proton]

9.0 × 10–10

0° - 10° 40° - 50° 80° - 90° 130° - 140°

8.0 × 10–10 7.0 × 10–10 6.0 × 10–10 5.0 × 10–10 4.0 × 10–10 3.0 × 10–10 2.0 × 10–10 1.0 × 10–10 0.0

0.1

1 10 Neutron energy [MeV]

100

FIGURE 17.2 Unshielded neutron spectra for neutrons at various emission angles, produced by 250-MeV protons incident on a thick iron target (without any concrete shielding). (From Agosteo, Magistris, Mereghetti, Silari, Zajacova. Nucl Instrum Methods Phys Res B 2007; 265:581–89. With permission.)

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17.6  Characteristics of Shielded Neutron Field The high-energy component of the cascade with neutron energies (En) above 100 MeV propagates the neutrons through the shielding and continuously regenerates lower-energy neutrons and charged particles at all depths in the shield via inelastic reactions with the shielding material (7). However, the greater yield of low-energy neutrons is more than compensated for by greater attenuation in the shield due to a higher cross section at low energy. Shielding studies indicate that the radiation field reaches an equilibrium condition beyond a few mean-free paths within the shield. Neutrons with energies greater than 150 MeV regenerate the cascade even though they are present in relatively small numbers. They are accompanied by numerous low-energy neutrons produced in the interactions. The typical neutron spectrum observed outside a thick concrete shield consists of peaks at a few MeV and at ~100 MeV. Figure 17.3 shows normalized neutron spectra in the transverse direction at the surface of the concrete and at various depths in the concrete, for 250MeV protons incident on a thick iron target (11). The low-energy neutron component is attenuated up to about a depth of 100 cm with a short attenuation length, thus, giving rise to a less intense but more penetrating spectrum with a longer attenuation length. A fast attenuation region is observed at small thicknesses. Beyond 100 cm, the spectrum reaches equilibrium. Thus, the neutron energy distribution consists of two components: highenergy neutrons produced by the cascade and evaporation neutrons with energy peaked at ~2 MeV. As previously mentioned, the high-energy neutrons 0.8 0 cm 20 cm 40 cm

Normalized Φ(E)·E [a.u.]

0.7 0.6

60 cm 100 cm 600 cm

0.5 0.4 0.3 0.2 0.1 0.0

0.1

1 10 Neutron energy [MeV]

100

FIGURE 17.3 Normalized neutron spectra in transverse direction at surface of a concrete shield, and at ­various depths, produced by 250-MeV protons incident on a thick iron target. (From Agosteo, Magistris, Mereghetti, Silari, Zajacova. Nucl Instrum Methods Phys Res B 2007; 265:581–89. With permisson.)

Basic Aspects of Shielding

537

are anisotropic and forward peaked, but the evaporation neutrons are isotropic. The highest-energy neutrons detected outside the shielding are those that arrive without interaction or that have undergone only elastic scattering or direct inelastic scattering with little loss of energy, and a small change in direction. Low-energy neutrons and charged particles detected outside the shielding are those that have been generated at the outer surface of the shield. Thus, the yield of high-energy neutrons (En > 100 MeV) in the primary collision of the protons with the target material determines the magnitude of the prompt radiation field outside the shield in the therapeutic proton energy range of interest. The charged particles produced by the protons will be absorbed in shielding that is sufficiently thick to protect against neutrons. Thus, neutrons dominate the radiation field outside the shielding. Degraded neutrons might undergo capture reactions in the shielding, giving rise to neutron-capture gamma rays.

17.7  Neutron Monitoring Because the neutron energy spectra extend to the energy of the incident proton, it is important to use wide-energy range instruments for neutron monitoring. Rem-meters are typically used for neutron monitoring. A rem-meter is comprised of a thermal neutron detector such as a BF3 (boron trifluoride) or 3He (helium) proportional counter or a 6Li (lithium) glass scintillation counter that is surrounded by a polyethylene neutron moderator. The moderator slows down fast and intermediate energy neutrons to thermal neutrons, which are then detected by the thermal neutron detector. Most conventional rem-meters are insensitive to neutrons of energies above 15 MeV, and many of them have rapidly decreasing responses above about 7  MeV. Therefore, they can underestimate the neutron dose equivalent by as much as a factor of 3 when used outside the shielding of a particle therapy facility (1). Wideenergy rem-meters consist of high-atomic number inserts such as lead or tungsten in the polyethylene moderator (17, 18), which cause neutron multiplication and energy degrading reactions such as (n, 2n). Thus, the sensitivity to high-energy neutrons is improved. An example of such a rem-meter is the FHT 762 Wendi-2 (Thermo Fisher Scientific, Waltham, MA), which has an excellent energy response from thermal to 5 GeV.

17.8  Calculational Methods 17.8.1  Conversion Coefficients The concept of effective dose (E) is discussed in Chapter 18. The ambient dose equivalent, H*(d), at a point in a radiation field, is the dose equivalent

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that would be produced by the corresponding expanded and aligned field, in the International Commission on Radiation Units and Measurements (ICRU) sphere (diameter = 30 cm, 76.2% O, 10.1% H, 11.1% C, and 2.6% N) at a depth, d, on the radius opposing the direction of the aligned field (19). The ambient dose equivalent is measured in Sv. For strongly penetrating radiation, a depth of 10 mm is recommended, and for weakly penetrating radiation, a depth of 0.07 mm is recommended. In the expanded and aligned field, the fluence and its energy distribution have the same values throughout the volume of interest as in the actual field at the point of reference, but the fluence is unidirectional. Conversion coefficients are used to relate the protection and operational quantities to physical quantities characterizing the radiation field (19). Frequently radiation fields are characterized in terms of absorbed dose or fluence. The fluence, Φ, is the quotient of dN by da, where dN is the number of particles incident on a sphere of cross-sectional area da. The unit is m−2 or cm−2. Thus, for example, the effective dose, E, can be obtained by multiplying the fluence with the fluence-to-effective dose conversion coefficient. The ambient dose equivalent, H*(d), can be obtained by multiplying the fluence with the fluence-to-ambient dose equivalent conversion coefficient. Conversion coefficients have been calculated by various authors using the Monte Carlo transport codes (16, 19–21) for many types of radiation (photons, electrons, positrons, protons, neutrons, muons, charged pions, and kaons) and incident energies (up to 10 TeV). Pelliccioni (20) has summarized most of the data. Because the conversion coefficient for H*(10) for neutrons becomes smaller than that for E(AP) (where AP refers to anterior-posterior) above 50 MeV, use of E(AP) may be considered more conservative for highenergy neutrons. The conversion coefficient for E(AP) becomes smaller than that for posterior-anterior (PA) irradiation geometry, E(PA), at neutron energies above 50 MeV. However, the integrated dose from thermal neutrons to high-energy neutrons is highest for AP geometry, and therefore the choice of E(AP) is more conservative than the choice of E(PA). The term “dose” is used in a generic sense for the dose equivalent or effective dose in this chapter. 17.8.2  Analytical Methods Most analytical models consist of line-of-sight or “point kernel” models. They are limited in their use because they are based on simplistic assumptions and geometry. Many of the models are restricted to transverse shielding. Further, they do not account for changes in energy, angle of production, target material and dimensions, and concrete material composition and density. 17.8.2.1  Point Source A radiation source can be considered a point source if the distance at which the dose is determined is at least five times the dimension of the radiation

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source. For a point source, the dose decreases as the square of the distance. Because protons have a defined range in the target material, the dimension of the source can be considered to be the range of the proton in the target material. For example, the range of a 230-MeV proton in tissue is 32 cm, whereas the distance from the target to the point of interest outside the shielding walls is typically greater than 1.6 m (5 × 32 cm). 17.8.2.2  Removal Cross Section For fast neutrons (En < 20 MeV), the most common approach to calculate shielding thicknesses is that of the removal cross-section theory (8). To use this approach, the following principles must hold:





1. The shield must have adequate thickness, and the neutron energy distribution must be such so that only a narrow band of the most penetrating neutrons contribute to the dose outside the shield. 2. There must be sufficient hydrogen distributed homogeneously in the shield or in the outer portion of the shield, to ensure that there is a very short characteristic transport length for neutrons with energies lying in the range of thermal to 1 MeV. 3. The source energy distribution and the shield material (nonhydrogenous) properties must be such that they ensure a short transport length for slowing down neutrons from the highest energy to 1 MeV.

The dose equivalent, H(d), as a function of shield thickness, is approximately given by the line of-sight equation:



H (d) =

H 0 e ∑r d r2  

(17.4)

where H0 is the unshielded dose at a distance of 1 m from the source, r is the distance from the source to the point of interest outside the shield, and d is the thickness of the shield in centimeters, and ∑r is the macroscopic removal cross section in cm−1:



Σr =

N 0 σr ρ A

(17.5)

where σr is the microscopic removal cross section in cm, N0 is Avogadro’s number, ρ is the density (g cm−3), and A is the mass number. The attenuation data for fast neutrons can be adequately described by removal cross sections even though neutrons of energy lower than a few MeV dominate at greater depths in the shielding.

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17.8.2.3  Attenuation Length Radiation transmission can be approximated by an exponential function over a limited range of thickness (2). The attenuation length, λ, is usually expressed in centimeters (or meters) and in g cm−2 (or kg m−2) when multiplied by the density (ρ). The value of λ changes with increasing depth in the shield for thicknesses (ρd) that are less than ~100 g cm−2, because the “softer” radiations are more easily attenuated, and the neutron spectrum “hardens.” Figure 17.4 shows the attenuation length (ρλ) for mono-energetic neutrons in concrete as a function of energy. The attenuation length increases with increasing neutron energy at energies greater than ~20 MeV. The increase in attenuation length is indicative of the change from the energy region in which neutrons interact mainly by elastic scattering with the target nuclei as a whole, to the region where interaction occurs more likely with individual nucleons in a target, thus, leading to an intranuclear cascade. In the past, it has typically been assumed that the attenuation length reaches a highenergy limiting value of about 120 g cm−2., even though the data in Figure 17.4 show a slightly increasing trend above 200 MeV. Comparison of neutron dose attenuation lengths measured at various facilities, for concrete and iron, respectively, as a function of the effective maximum energy (Emax) of the source neutrons, for neutrons with energies from thermal to maximum has been made by Nakamura (22) and include measurements for Emax ranging from 22 to 700 MeV and various production angles for a variety of neutron sources. According to Nakamura, the measured neutron dose attenuation length (thermal to maximum energy) for concrete at 22 MeV is about 30 g cm−2, in the forward direction, and then gradually increases above 100 MeV to a maximum value of about 130 g cm−2, which may be considered the high-energy limit. It is important to note that, in addition

Attenuation length [ρλ(kg m–2)]

1500 High energy limit

1000

500

0

Concrete ρ = 2.4 g cm–3

1

10 100 Neutron energy [MeV]

1000

FIGURE 17.4 Attenuation length (ρλ) for monoenergetic neutrons in concrete as a function of energy. (From National Council on Radiation Protection and Measurements, Radiation Protection for Particle Accelerator Facilities, Report 144, 2003. With permission.)

541

Basic Aspects of Shielding

to particle type and energy, λ also depends on the production angle (θ), material composition and density. Monte Carlo calculations by the author indicate that, for concrete, shielding for 250-MeV protons in the forward direction can differ by about 30 cm for shielding thicknesses of the order of 2 to 3 m when two concretes with the same density but differing compositions are used. Therefore, all concretes will not have the same λ at a given angle and energy, and the differences can be fairly significant, especially in the forward direction for concretes with different compositions and densities. 17.8.2.4  Moyer Model Burton Moyer developed a semi-empirical method for the shield design of the 6-GeV proton Bevatron (1) in 1961. This model is only applicable to angles close to 90°, and the transverse shielding for a high-energy proton accelerator is determined using the following simple form of the Moyer model (23): α



H E   d H = 20  P  exp −  r  E0   λ  

(17.6)

where H is maximum dose equivalent rate at a given radial distance (r) from the target, d is shield thickness, EP is proton energy, E0 is 1 GeV, H0 = 2.6 × 10−14 Sv m2, and α is about 0.8. The Moyer model is effective in the gigaelectronvolt (GeV) region because the neutron dose attenuation length (λ) is nearly constant regardless of energy. However, the model is restricted to the determination of neutron dose equivalent produced at an angle between 60° and 120°. At proton energies in the therapeutic range of interest, the neutron attenuation length increases considerably with energy. Therefore, the Moyer model is ineffective and inappropriate for use in proton therapy shielding. Kato and Nakamura have developed a modified version of the Moyer model that includes changes in attenuation length with shield thickness and also includes a correction for oblique penetration through the shield (24). In the past, high-energy accelerators were shielded using analytical methods. However, with the advent of powerful computers, sophisticated Monte Carlo codes have superseded analytical methods. 17.8.3  Monte Carlo Calculations Monte Carlo codes such as FLUKA, MCNPX, and MCNP are used extensively for shielding calculations. These codes can be used to do a full simulation, modeling the accelerator or beam line and the room geometry in its entirety. They can also be used to derive computational models as discussed in the next section. Monte Carlo codes have been used in the shielding design of several particle therapy facilities (25–30). One unique feature of these codes

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Proton Therapy Physics

is their ability to generate isodose curves (dose contours), which provide a visualization of the secondary radiation field, thus, facilitating the identification of weak spots in the shielding design (26). For comparison of Monte Carlo calculations to experimental data, the actual experimental configuration should be modeled, including the instrument response and the concrete composition. Further, the experiment should have been performed using the appropriate instrumentation such as wide-energy neutron rem-meters. Any deviations from the above conditions will result in large discrepancies between measurements and simulations. Unfortunately, there is a paucity of published data for charged particle therapy facilities that meet all these conditions. The use of Monte Carlo codes is time consuming. In the early stages of design, the facility undergoes several iterations of changes in layout, and therefore, a full Monte Carlo simulation is not practical or cost effective. Full simulations should be performed only after the layout has been finalized. Monte Carlo simulations are especially effective for special issues such as maze design, penetration shielding, skyshine, and groundshine. Skyshine is the radiation reflected back to earth by the atmosphere above a radiationproducing facility. Therefore, even if there is no occupancy above the roof of a radiation-producing facility, a minimal thickness of roof shielding is required to minimize skyshine. Groundshine is the radiation reflected back to the point of interest by the earth below the floor slab to the point of interest. For the same reasons mentioned above, the floor slab will also require a minimal shielding thickness to minimize groundshine. 17.8.4  Computational Models Computational models (derived using Monte Carlo codes) that are independent of geometry typically consist of a source term and an exponential term that describes the attenuation of the radiation. Both the source term and the attenuation length are dependent on particle type, incident proton energy, and angle. Such models were first determined by Agosteo et al. (10) using experimental double differential neutron spectra, but the early data are now obsolete (11). Computational models have also been published by Ipe (30). Shielding can be estimated over a wide range of thicknesses by the following equation for a point source, which combines the inverse square law and an exponential attenuation through the shield and is independent of geometry (10):

H(Ep, θ, d/λ(θ)) =

H 0 (Ep , θ) r

2

  d exp −   λ(θ) g(θ) 

(17.7)

where H is the dose equivalent outside the shielding; H0 is source term at a production angle θ with respect to the incident beam and is assumed to

Basic Aspects of Shielding

543

be geometry independent; Ep is the energy of the incident particle; r is the distance between the target and the point at which the dose equivalent is scored; d is the thickness of the shield; d/g(θ) is the slant thickness of the shield at an angle θ; λ(θ) is the attenuation length for dose equivalent at an angle θ and is defined as the penetration distance in which the intensity of the radiation is attenuated by a factor of e; and g(θ) = cosθ for forward shielding; g(θ) = sinθ for lateral shielding; g(θ) = 1 for spherical geometry. Computational models are useful especially during the schematic phase of the facility design, when the design undergoes several changes, to determine the barrier shielding (31). The entire room geometry is not modeled, but usually spherical shells of shielding material are placed around the target, and Monte Carlo codes are used to score dose at given angular intervals and in each shell of shielding material. Plots of dose versus shielding thickness can be fitted to obtain source terms and attenuation lengths as a function of angle, and at the energies of interest, with the appropriate target. In some cases the data may require a double exponential fit. For example, Agosteo (11) notes that the source term and attenuation length in the forward direction (0°–10°) for total ambient dose equivalent, H(10), in ordinary concrete, produced by 250-MeV protons incident on a thick iron target are given by H0 = (9.8 ± 1.0) × 10−15 Sv m2 per proton and λ = 105.4 ± 1.4 g cm−2, respectively. In contrast, the data in the 80°–90° direction can be fitted with a double exponential. The first source term and attenuation length are given by H01 = (1.4 ± 0.4) × 10−15 Sv m2 per proton and λ1 = 49.7 ± 5.7 g cm−2, respectively; and the second source term and attenuation length are given by H02 = (1.4 ± 0.4) × 10−15 Sv m2 per proton and λ2 = 83.7 ± 2.0 g cm−2. Plots of dose equivalent versus shielding indicate that there is a dose build-up in the forward direction, at small depths. However, at large angles, the low energy component of the radiation is attenuated quickly in small thicknesses. This is because the neutron spectrum changes with depth in the shield. The spectrum hardens with depth and reaches equilibrium after a depth of about 100 cm. Thus, there are two attenuation lengths. The second attenuation length is also referred to as the effective attenuation length and is valid for thicknesses greater than 100 cm of concrete. The source terms and attenuation lengths will depend on the composition and density of the shielding material. A thick target can be used to determine dose rates from the beam incident on the patient. However, it is important to note that the use of a thick target is not necessarily conservative in all cases, because for a thin target, the intranuclear cascade may propagate in the downstream shielding. Ray traces can be performed at various angles and the source terms and attenuation lengths can be used for dose calculations. These models are also useful in identifying thin shielding and facilitate improved shield design. Published computational models should not be used for calculations, but computational models for energies, targets, and concrete composition that are facility specific should be derived.

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17.9  Shielding Design Considerations In radiation protection, the primary goal of shielding is to attenuate secondary radiation to levels that are within regulatory or design limits for individual exposure. This requires knowledge of the various parameters such as beam losses (including location, target material, and dimensions), treatment parameters, facility layout, adjacent occupancies, shielding material composition, and density and regulatory dose limits (1, 31). 17.9.1  Beam Losses The shielding thicknesses for various parts of the facility may range from about 60 cm to about 7 m of concrete. Beam losses result in the production of secondary radiation. Therefore, to design effective shielding, the beam losses and sources of radiation for proton therapy facilities must be well understood. This requires knowledge of how the accelerators operate and deliver beam to the treatment rooms. The equipment vendor should provide specific details of beam losses, duration, frequency, targets (material and dimensions), and locations. Higher beam losses will occur during start-up and commissioning as the beam is tuned and delivered to the final destination and should be planned for. 17.9.1.1  Synchrotron- and Cyclotron-Based Systems Synchrotrons are designed to accelerate protons to the exact energy required for therapy, thus eliminating the need for energy degraders (see Chapter 3). This results in less local shielding and less activation of beam-line components. Sources of radiation for the synchrotron injector include x-rays from the ion source, x-rays produced by back-streaming electrons striking the linac (linear accelerator) structure, and neutrons produced by the interaction of the ions with the linac structure toward the end of the linac. The target material is typically copper or iron. The production of x-rays from back-streaming electrons will depend on the vacuum conditions and the design of the accelerator (32). The use of a Faraday cup to intercept the beam downstream of the linac must also be considered. Typically for synchrotrons, beam losses can occur during the injection process, radiofrequency (RF) capture and acceleration, and during extraction. Some of these losses may be distributed in the synchrotron, whereas others may occur locally. Losses will be machine-specific, and therefore the equipment vendor should provide this information. Particles that are not used in a spill may be deflected on to a beam dump or stopper and will need to be considered in the shielding design and activation analysis. If the particles are decelerated before being dumped, they are not of concern in the shielding design or activation analysis. X-rays may be produced at the injection and extraction

Basic Aspects of Shielding

545

septa due to the voltage applied across electrostatic deflectors and may need to be considered in special cases. About 20% to 50% of the accelerated beam particles can be lost continuously in the cyclotron. Significant self-shielding is provided by the steel in the magnet yoke, except in regions where there are holes through the yoke. These holes need to be considered in the shielding design. Losses at very low proton energies are not of concern for prompt radiation shielding, but can contribute to activation of the cyclotron. The shielding is determined by beam losses that occur at higher energies and those due to protons that are close to their extraction energy (230–250 MeV depending on the cyclotron type), striking the dees and the extraction septum, which are made of copper. These beam losses also result in activation of the cyclotron. The energy selection system (ESS) consists of an energy degrader, collimators, spectrometer, energy slits, and a beam stop. The ESS allows the proton energy to be lowered after extraction. The intensity from the cyclotron is increased as the degraded energy is decreased in order to maintain the same dose rate at the patient. Thus, copious amounts of neutrons are produced in the degrader, especially at the lower energies, resulting in thicker local shielding requirements in this area. The degrader scatters the protons and increases the energy spread. A collimator is used to reduce the beam emittance. A magnetic spectrometer and energy slits are used to reduce the energy spread. Beam stops are used to tune the beam. Neutrons are also produced in the collimator, slits, and beam stop. Losses in the ESS are large and also result in activation. Losses occur in the beam transport line for synchrotron- and cyclotronbased systems. Although these losses are usually very low (~1 %) and are distributed along the beam line, they need to be considered for shielding design. The target material is typically copper or iron. During operation, the beam is steered onto Faraday cups, beam stoppers. Beam incident on these components also needs to be considered in the shielding design. 17.9.1.2  Treatment Rooms The radiation produced from the beam impinging on the patient (or phantom) is a dominant source for the treatment rooms. Thus, a thick-tissue target should be assumed in computer simulations for shielding calculations. In addition, losses in the nozzle, beam-shaping, and range-shifting devices must also be considered in the shielding design. The contributions from adjacent areas, such as the beam transport and other treatment rooms, should also be taken into account. Typically, the large facility treatment rooms do not have shielded doors, and therefore the effectiveness of the maze design is critical. The smaller single-room facilities have shielded doors. In such cases, a full computer simulation for the maze is recommended. Treatment rooms either have fixed beam rooms or gantries.

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17.9.1.3  Fixed Beam and Gantry Rooms Either a single horizontal fixed beam or dual (horizontal and vertical or oblique) beams are used in fixed beam rooms. Shielding walls in the forward direction are much thicker than the lateral walls and the walls in the backward direction. The Use Factor (U) is defined as the fraction of time that the primary proton beam is directed toward the barrier. For rooms with dual beams the Use Factor for the wall in the forward (0°) direction for each beam should be considered. This may be either one-half for both beams and twothirds for one beam and one-third for the other. For a single beam, the use factor is one for the wall in the forward direction. The beam is rotated about the patient in gantry rooms. In some cases, the gantries may rotate completely (360°), but in other cases only partial rotation is possible (~180°). For full rotation, on average, it can be assumed that the use factor for each of the four barriers (two walls, floor, and ceiling) is 0.25. In some designs, the gantry counterweight (made of large thicknesses of steel) acts as a stopper in the forward direction. However, it usually covers a small angle and is asymmetric. The ceiling, lateral walls, and floor are exposed to the forward-directed radiation. The walls in the forward direction can be thinner than for fixed beams, because of the lower use factor. 17.9.1.4  Beam-Shaping Techniques The various techniques used to shape and deliver the beam to the patient can be divided into two categories: passive scattering and pencil beam scanning. In passive scattering, a spread-out Bragg peak (SOBP) is produced by a range modulation wheel or a ridge filter located in the nozzle (33). Lateral spread of the beam is achieved by scatterers located downstream. Typically, for small fields, a single scatterer is used, whereas for large fields, a double scatterer is used. A collimator (specific to the treatment field) located between the nozzle exit and the patient is used to shape the field laterally. A range compensator is used to correct for the shape of the patient surface, inhomogeneities in the tissues traversed by the beam, and the shape of the distal target volume. A much higher beam current is required at the nozzle entrance when compared to the other delivery techniques, because there are losses due to the incidence of the primary beam on the various delivery and shaping devices. The typical maximum efficiency of a passive scattering system with a patient field is about 45%. Thus, more shielding is required for passive scattering when compared to pencil beam scanning. 17.9.2  Workload The term workload is used in a generic sense to include for each treatment room the following: each proton energy, the beam-shaping method, the number of fractions per week and the time per fraction, the dose per fraction, and the proton current required to deliver a specific dose rate. Once the

547

Basic Aspects of Shielding

workload for the treatment room has been established, one must determine the corresponding energies and currents from the cyclotron or the synchrotron. The workload for each facility will be facility specific and equipment specific. Therefore, the workload will vary from facility to facility and from one equipment vendor to the other. An example of a workload can be found in PTCOG Report 1 (1). 17.9.3  Regulatory Dose Limits The use of protons for therapy purposes is associated with the generation of secondary radiation. Therefore, protection of the occupationally exposed workers and members of the public must be considered. Most of the national radiation protection regulations are based on international guidelines or standards. In the United States, medical facilities are subject to state regulations. These regulations are based on standards of protection issued by the U.S. Nuclear Regulatory Commission (34). Table 17.5 shows the radiological areas and the dose limits for the following countries: United States (34), Japan (35), Italy (36), and Germany (37). The dose limits for the countries of Italy and Germany are similar for controlled, supervised, and public areas. In Germany, areas with dose rates > 3 mSv/h are defined as restricted areas. In the United States, controlled areas have dose limits that are much lower than the dose limits for other countries. Thus, for example, although in the United States the control room adjacent to the treatment room has a design dose limit of 5 mSv/yr, dose limits for controlled areas in other countries are much higher. Therefore, a cookie-cutter design originating in one country could potentially underestimate or overestimate the shielding in some areas for a proton therapy facility in another country, assuming similar patient workload, usage, and beam parameters. TABLE 17.5 Classification of Radiological Areas and Dose Limits in Various Countries Area Restricted Controlled

United States

Japan

—

—

≤5 mSv/y

Supervised (area near controlled area) Public ≤1 mSv/y, 20 µSv in 1 h with T = 1

Italy

<1 mSv/week <1.3 mSv/3 months at boundary of controlled area <250 µSv/3 months (outside of site boundary)

Germany

No general regulation (RSOa judgement) <3 mSv/h <6 mSv/y

<6 mSv/y

<1 mSv/y, <1 mSv/y recommended operational limit = 0.25 mSv/y

RSO, radiation safety officer Source: Modified from Particle Therapy Cooperative Group, Report 1, 2010. With permission. a

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17.9.3.1  Occupancy Factor The occupancy factor (T) for an area is the average fraction of the time that the maximally exposed individual is present in the area while the beam is on (38). If the use of the machine is spread out uniformly during the week, the occupancy factor is the fraction of the working hours in the week during which the individual occupies the area. For instance, corridors, stairways, bathrooms, or outside areas have lower occupancy factors than offices, nurses’ stations, wards, staff, or control rooms. The occupancy factor for controlled areas is typically assumed to be 1 and is based on the premise that a radiation worker works 100% of the time in one controlled area or another. In the United States, the regulatory agencies allow the use of occupancy factors. 17.9.4  Shielding Materials Earth, concrete, and steel are typically used for particle accelerator shielding (2). Other materials such as polyethylene and lead are used to a limited extent. For particle therapy facilities, neutrons are the dominant secondary radiation, and when steel is used, a layer of hydrogenous material must be used in conjunction with the steel. 17.9.4.1  Earth Earth is often used as shielding material at underground accelerator facilities. However, it must be compacted to minimize cracks and voids, and attain a consistent density. Because earth is primarily composed of silicon dioxide (SiO2), it is suitable for shielding of both gamma radiation and neutrons (2). Its water content improves the shielding of neutrons. However, the water content can vary from 0% to 30%. The density of earth typically ranges from 1.7 to 2.2 g/cm3 and depends on the soil type, water content, and degree of compaction. The activation of the ground water must also be considered for underground facilities. 17.9.4.2  Concrete and Heavy Concretes Concrete is a mixture of cement, coarse and fine aggregates, water, and sometimes supplementary cementing materials and/or chemical admixtures. The density of concrete depends on the amount and density of the aggregate, the amount of air that is entrapped or purposely entrained, and the water and cement contents. Typically, ordinary concrete has a density that varies between 2.2 and 2.4 g cm−3. Concrete has many advantages compared to other shielding materials (2). For example, it can be poured in almost any configuration, provides shielding for both photons and neutrons, and is relatively inexpensive. Poured-in-place concrete has sufficient structural strength that it can be used to support the building and any additional shielding. It is important to ensure that there are no hollow structural support columns in

Basic Aspects of Shielding

549

the concrete shielding walls. Concrete is also available in the form of blocks. If blocks are used, they should be interlocked or staggered both horizontally and vertically to minimize gaps. Water exists in concrete in both the free and bound form. As previously mentioned, the water content of concrete plays a significant role in the shielding of neutrons. With time, the free water evaporates, but the concrete also hydrates, that is, it absorbs moisture from the surrounding environment until it reaches some equilibrium. About 3% of the water may evaporate in the first 30 days or so. Therefore, all shielding calculations should be performed using the equilibrium density and not the wet density. For neutron shielding, a minimum water content of about 5.5% is recommended. In the United States, ordinary concrete is usually considered to have a density of 2.35 g cm−3 (147 lb feet−3). Concrete used for floor slabs in buildings is typically lightweight with a density that varies between 1.6 and 1.7 g cm−3. The poured-in-place concrete is usually reinforced with steel rebar, which makes it more effective for neutrons. Measured radiation doses with heavily reinforced concrete may be lower than calculated doses because the steel rebar is not included in the concrete composition. The disadvantage of concrete is that takes months to pour. Continuous pours are preferred for the concrete walls and ceiling. For noncontinuous concrete pours, appropriate measures (e.g., such as sandblasting of poured surface before pouring the next portion, use of keyways, and staggered joints) should be used to ensure that there are no thin spots at the cold joint. Also, for noncontinuous pours, the ceiling should be notched into lateral walls. Heavy concretes contain high-Z aggregates or small pieces of scrap steel or iron that increase their density and effective Z. Densities as high as 4.8 g cm−3 can be achieved. The pouring of such high-Z aggregate-enhanced concrete is a special skill and should not be undertaken by an ordinary concrete contractor because of settling, handling, and structural issues (38). Ordinary concrete pumps are not capable of handling such dense concrete. The high-Z aggregates could sink to the bottom, resulting in a nonuniform composition and density. The high-Z aggregate–enhanced concrete is also sold in the form of prefabricated interlocking or noninterlocking modular blocks. It is preferable to use the interlocking blocks to avoid the streaming of radiation. Concrete enhanced with iron ore is particularly effective for the shielding of relativistic neutrons. One important consideration in the choice of shielding materials is their susceptibility to radioactivation by neutrons, which can last for decades. Activation of concrete is discussed in PTCOG Report 1 (1). 17.9.4.3  Steel and Iron Steel is an alloy of iron and is used for shielding photons and high-energy neutrons. The high density of steel (~7.4 g/cm3) together with its physical properties leads to tenth-value thickness for high-energy neutrons of about 41 cm (39). Therefore, steel is often used when space is at a premium. Steel or iron are usually available in the form of blocks (2). Iron has an important

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deficiency in shielding neutrons because it contains no hydrogen. Natural iron is composed of 91.7% 56Fe, 2.2% 57Fe, and 0.3% 58Fe. The lowest inelastic energy level of 56Fe is 0.847 MeV (2). Neutrons with energy above 0.847 MeV will lose energy by inelastic scattering in 56Fe, but below this energy, neutrons can only lose energy by elastic scattering, which is a very inefficient process. Therefore, there is a build-up of neutrons below this energy. Furthermore, the neutron quality factor is at a maximum near 0.7 MeV. In addition, natural iron has two regions where the total cross section is very low because of resonances in 56Fe. There is one resonance at 27.7 keV (minimum cross section = 0.5 barn) and another at 73.9 keV (minimum cross section = 0.6 barn). The net result is an increased attenuation length. Thus, large fluxes of lowenergy neutrons are found outside steel or iron shielding. If steel is used for the shielding of high-energy neutrons, it must be followed by a hydrogenous material for shielding the low-energy neutrons that are generated. Because of the large variety of nuclear processes, including neutron capture reactions of thermalized neutrons, steel can be highly activated (1). 17.9.4.4  Polyethylene Polyethylene (CH2)n is used for neutron shielding. Attenuation curves in polyethylene of neutrons from 72-MeV protons incident on a thick iron target have been published by Teichmann (40). The thermal neutron capture in polyethylene yields a 2.2-MeV gamma ray that is quite penetrating. Therefore, boron-loaded polyethylene can be used. Thermal neutron capture in boron yields a 0.475-MeV gamma ray. Borated polyethylene can be used for shielding of doors and ducts and other penetrations. 17.9.4.5  Lead Lead is used primarily for the shielding of photons. It has a very high density (11.35 g cm−3) and is available in bricks, sheets, and plates. Lead is malleable (2) and cannot support its own weight when stacked to large heights. Therefore, it will require a secondary support system. Lead is transparent to fast neutrons, and therefore it should not be used for door sills or thresholds for proton therapy facilities where secondary neutrons dominate the radiation field. However, it does decrease the energy of higher-energy neutrons by inelastic scattering down to about 5 MeV, making the hydrogenous material following it, more effective. Below 5 MeV, the inelastic cross section for neutrons drops sharply. Lead is toxic and should be protected by paint or encased in other materials. 17.9.5  Transmission The transmission of a given thickness of shielding material is defined as the ratio of the dose at a given angle with shielding to the dose at the same angle

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Basic Aspects of Shielding

20 to 30 degrees

1.00E+01 1.00E+00

Concrete

Transmission

1.00E-01

30 cm Fe +Concrete

1.00E-02

60 cm Fe + Concrete

1.00E-03

90 cm Fe + Concrete

1.00E-04

120 cm Fe + Concrete

1.00E-05

Fe

1.00E-06 1.00E-07

0

100

200 300 400 Shielding thickness (cm)

500

600

FIGURE 17.5 Transmission curves for 250-MeV protons incident on 30-cm ICRU tissue sphere (20°–30°).

without shielding. Transmission curves are useful for comparing different shielding materials. Transmission curves for various shielding materials, for 250-MeV protons incident on tissue have been reported by Ipe (40) for three different production angles. Figure 17.5 shows the total particle dose equivalent transmission (based on FLUKA calculations) of composite shields (iron and concrete) and iron and concrete as a function of shielding thickness at 20°–30° for 250-MeV protons incident on a 30-cm ICRU tissue sphere. These transmission curves can be used to determine the composite shielding thickness that can be used to replace large concrete thicknesses in the forward direction in the treatment room and thus save space. For example, from Figure 17.5 it can be observed that 4.65 m of concrete provides about the same attenuation as about 2.85 m of composite shield (1.2 m of iron plus 1.65 m of concrete), thus resulting in a space savings of 1.8 m.

References

1. NCRP. Radiation Protection for Particle Accelerator Facilities. National Council on Radiation Protection and Measurements Report. 2003:144. 2. IAEA. Radiological Safety Aspects of the Operation of Proton Accelerators, Technical Reports Series No. 283, International Atomic Energy Agency, Vienna, 1988.

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3. PTCOG. Shielding Design and Radiation Safety of Charged Particle Therapy Facilities. PTCOG Report 1, Particle Therapy Cooperative Group, 2010. Available from: URL: http://ptcog.web.psi.ch/Archive/Shielding_radiation_protection. pdf. 4. Turner JE. Atoms, Radiation, and Radiation Protection, NY: Pergamon Press, 1986. 5. NCRP. Neutron Contamination from Medical Electron Accelerators. National Council on Radiation Protection and Measurements Report 79. 1984:79. 6. ICRU. Basic Aspects of High Energy Particle Interactions and Radiation Dosimetry. International Commission on Radiation Measurements and Units Report 28. 1978:28. 7. Moritz LE. Radiation Protection at Low Energy Proton Accelerators. Radiat Protect Dosim 2001: 96(4):297–309. 8. NCRP. Protection against Neutron Radiation. National Council on Radiation Protection and Measurements, NCRP Report 38.1971:38. 9. Agosteo S, Fasso A, Ferrari A, Sala PR, Silari M, Tabarelli de Fatis P. Double differential distributions, attenuation lengths, and source terms for proton accelerator shielding. In: Proceedings of SATIF-2 Shielding Aspects of Accelerators, Targets and Irradiation Facilities; 1995 Oct 12–13; Geneva, Switzerland. Paris: Nuclear Energy Agency, Organization for Economic Co-operation and Development; 1996. 99–113. 10. Agosteo S, Fasso A, Ferrari A, Sala PR, Silari M, Tabarelli de Fatis P. Double differential distributions and attenuation in concrete for neutrons produced by 100-400-MeV protons on iron and tissue targets. Nucl Instrum Methods Phys Res B 1996;114:70–80. 11. Agosteo S, Magistris M, Mereghetti A, Silari M, Zajacova Z. Shielding data for 100 to 250 MeV proton accelerators: double differential neutron distributions and attenuation in concrete. Nucl Instrum Methods Phys Res B 2007; 265:581–89. 12. Kato T, Kurosawa K, Nakamura T. Systematic analysis of neutron yields from thick targets bombarded by heavy ions and protons with moving source mode. Nucl Instrum Methods Phys Res A 2002; 480:571–90. 13. Nakashima H, Takada H, Meigo S, Maekawa F, Fukahori T, Chiba S, et al. Accelerator shielding benchmark experiment analyses. In: Proceedings of SATIF2, Shielding Aspects of Accelerators, Targets and Irradiation Facilities; 1995 Oct 12–13; Geneva, Switzerland. Paris: Nuclear Energy Agency, Organization for Economic Co-operation and Development; 1996. 115–45. 14. Tayama R, Handa H, Hayashi H, Nakano H, Sasmoto N, Nakashima H, Masukawa F. Benchmark calculations of neutron yields and dose equivalent from thick iron target for 52–256 MeV protons. Nucl Eng Design 2002; 213:119–31. 15. Tesch K. A simple estimation of the lateral shielding for proton accelerators in the energy range 50 to 1000 MeV. Radiat Protect Dosim1985; 11(3):165–72. 16. Ferrari A, Sala PR, Fasso A, Ranft J. FLUKA: a multi-particle transport code. CERN Yellow Report CERN 2005-10; INFN/TC 05/11, SLAC-R-773. CERN, Geneva, Switzerland; 2005. 17. Birattari C, Ferrari A, Nuccetelli C, Pelliccioni M, Silari M. An extended range neutron rem counter. Nucl Instrum Methods 1990; A297:250–57. 18. Olsher RH, Hsu HH, Beverding A, Kleck JH, Casson WH, Vasilik DG, et  al. WENDI: an improved neutron rem meter. Health Phys 2000; 70:171–81.

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19. ICRU. Conversion coefficients for use in radiological protection against external radiation. International Commission on Radiation Units and Measurements Report 57. 1998:57. 20. Pelliccioni M. Overview of fluence-to-effective dose and fluence-to-ambient dose equivalent conversion coefficients for high energy radiation calculated using the FLUKA Code. Radiat Protect Dosim 2000; 88(4):277–97. 21. Battistoni G, Muraro S, Sala, PR, Cerutti F, Ferrari A, Roesler S, et al. The FLUKA code: description and benchmarking. In: Albrow M, Raja R, eds., Proceedings of the Hadronic Shower Simulation Workshop 2006; 2006 Sep 6–8; Fermilab, Battavia, IL. AIP Conference Proceedings 2007: 896:31–49. 22. Nakamura T. Summarized experimental results of neutron shielding and attenuation length; In: Proceedinfs of SATIF 7, Shielding Aspects of Accelerators, Targets and Irradiation Facilities, 17–18 May 2004, Portugal, Nuclear Energy Agency, Organization for Economic Co-operation and Development, Paris, 2004. 23. Thomas RH. Practical Aspects of Shielding High-Energy Particle Accelerators. Report UCRL-JC-115068. U.S. Department of Energy, Washington, D.C. 1993. 24. Kato T, Nakamura T. Analytical method for calculating neutron bulk shielding in a medium-energy facility. Nucl Instrum Methods Phys Res B 2001; 174: 482–90. 25. Agosteo S, Arduini G, Bodei G, Monti S, Padoani F, Silari M, et al. Shielding calculations for a 250 MeV hospital-based proton accelerator. Nucl Instrum Methods Phys Res A 1996; 374:254–68. 26. Dittrich W, Hansmann T. Radiation Measurements at the RPTC in Munich for Verification of Shielding Measures around the Cyclotron Area. In: Proceedings of SATIF 8, Shielding Aspects of Accelerators, Targets and Irradiation Facilities; 2006 May 22–24; Gyongbuk, Republic of Korea; Paris: Nuclear Energy Agency, Organization for Economic Co-operation and Development; 2007. 27. Hofmann W, Dittrich W. Use of Isodose Rate Pictures for the Shielding Design of a Proton Therapy Centre. In: Proceedings of SATIF 7, Shielding Aspects of Accelerators, Targets and Irradiation Facilities; 2004 May 17–18; Portugal, Paris: Nuclear Energy Agency, Organization for Economic Co-operation and Development; 2005. 181–87. 28. Kim J. Proton therapy facility project in National Cancer Center, Republic of Korea. J Republ Korean Physl Soc 2003 Sep; 43:50–54. 29. Porta A, Agosteo S, Campi F. Monte Carlo Simulations for the design of the treatment rooms and synchrotron access mazes in the CNAO hadrontherapy facility. Radiat Protect Dosim 2005; 113(3):266–74. 30. Ipe NE, Fasso A. Preliminary computational models for shielding design of particle therapy facilities. In: Proceeedings of SATIF 8, Shielding Aspects of Accelerators, Targets and Irradiation Facilities; 2006 May 22–24; Gyongbuk, Republic of Korea; Paris: Nuclear Energy Agency, Organization for Economic Co-operation and Development; 2007. 351–359. 31. Ipe NE. Particle accelerators in particle therapy: the new wave. In: Procedings of the 2008 Mid-Year Meeting of the Health Physics Society on Radiation Generating Devices; 2008; Oakland, CA. McLean, VA: Health Physics Society; 2008. 32. NCRP. Radiation Protection Design Guidelines for 0.1–100 MeV Particle Accelerator Facilities. National Council on Radiation Protection and Measurements Report 51. 1977:51.

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33. Smith AR. Vision 20/20: proton therapy. Med Phys 2009; 36(2):556–68. 34. USNRC United States Nuclear Regulatory Commission 2009. Standards for Protection Against Radiation 10CFR20, Code of Federal Regulations. Available from URL: http://www.nrc.gov/reading-rm/doc-collections/cfr/part020. 35. JRPL Japanese Radiation Protection Laws (Prevention Law) 2004. Law concerning Prevention from Radiation Hazards due to Radioisotopes, etc. 167. 36. IRPL (2000). Italian Radiation Protection Laws, Decreto Legislativo del Governo n° 230/1995 modificato dal 187/2000 e dal 241/2000 (Ministero dell’Ambiente e della Tutela del Territorio, Italy). 37. GRPO (2005). German Radiation Protection Ordinance, Veordnung über den Schutz vor Schäden durch ionisierende Strahlen (Strahlenschutzverordnung– StrlSchV). (Bundesministerium der Justis, Germany.) 38. NCRP. Structural Shielding Design and Evaluation for Megavoltage X- and Gamma-Ray Radiotherapy Facilities, National Council on Radiation Protection and Measurements Report 151. 2005:151. 39. Sullivan AH. A Guide to Radiation and Radioactivity Levels near High-Energy Particle Accelerators. Nuclear Technology Publishing, Kent, UK, 1992. 40. Teichmann S. Shielding Parameters of Concrete and Polyethylene for the PSI Proton Accelerator Facilities In: Proceeedings of SATIF 8, Shielding Aspects of Accelerators, Targets and Irradiation Facilities; 2006 May 22–24; Gyongbuk, Republic of Korea; Paris: Nuclear Energy Agency, Organization for Economic Co-operation and Development; 2007. 45–49. 41. Ipe NE. Transmission of Shielding Materials for Particle Therapy Facilities. Nucl Technol 2009; 168(2):559–63.

18 Late Effects from Scattered and Secondary Radiation Harald Paganetti CONTENTS 18.1 Late Effects on the Example of Second Malignancies........................... 555 18.2 Volume Definition....................................................................................... 557 18.3 Secondary Radiation (Neutrons) in the OFV.......................................... 559 18.3.1 Physics of the Neutron Background............................................ 559 18.3.2 Neutron Energy Distributions...................................................... 559 18.3.3 Radiation Quality Factors and Weighting Factors..................... 560 18.3.4 Biological Effectiveness of Neutrons............................................ 562 18.3.5 Neutron Sources in the Treatment Head..................................... 563 18.3.6 Neutron Doses as a Function of Distance to the Beam Axis.....564 18.3.7 Field Parameters That Influence the Neutron Field from the Treatment Head........................................................................ 566 18.3.8 Field Parameters That Influence the Neutron Field Generated in the Patient................................................................ 568 18.4 Modeling Cancer Risk................................................................................ 570 18.4.1 Risk Parameters............................................................................... 570 18.4.2 Low-Dose Effects (in the OFV)..................................................... 571 18.4.3 Risk Modeling Formalism in the OFV......................................... 572 18.4.4 Results for the OFV......................................................................... 574 18.4.5 Effects in the IFV............................................................................. 575 18.4.6 Risk Modeling Formalism for the IFV......................................... 576 18.4.7 Results for IFV................................................................................. 579 Acknowledgments............................................................................................... 580 References.............................................................................................................. 580

18.1  Late Effects on the Example of Second Malignancies Dose received by healthy tissue can lead to severe side effects, such as influencing cognitive function in children (1), affecting the functionality of organs, or causing a second cancer later in life. This chapter focuses on the 555

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latter. Criteria for a malignancy to be classified as a radiation-induced second tumor include, for example, that the histology of the second tumor be different from that of the original disease. Furthermore, one needs to consider a latency period of typically several years for a radiation-a­ssociated tumor. Treatment-related cancers are a well-recognized side effect in radiation therapy (2–8). The SEER (Surveillance Epidemiology and End Results) report (9) gives an overview of new malignancies after the successful treatment for a primary cancer, as well as the parameters influencing the risk factors. Excess risks have been reported for many treatment sites and second tumor locations. It is known that, even 30–40 years after initial radiation treatment, cancer survivors remain at an increased risk of developing a second cancer (10). The cumulative risk for the development of second cancers has been estimated to be 2–12% according to a 25-year follow-up (11–19). The risk might level off after ~10 years for some tumor types (e.g., acute nonlymphocytic leukemia and non-Hodgkin’s lymphoma), whereas for others it may increase more than 20 years after treatment (20). An analysis of patients with pituitary adenoma resulted in an estimation of the cumulative risk of second brain tumors of 1.9–2.4% at ~20 years after radiotherapy and a latency period for tumor occurrence of 6 to 21 years (15, 16, 19, 21). The likelihood of developing second cancer depends on both the entire irradiated volume and on the volume of the high-dose region. It has been confirmed that the majority of second tumors occur within the margins of the treatment volume (22). Solid cancers are mostly found within or close to the primary cancer treatment field (20, 23, 24), where higher doses may cause bone and soft tissue sarcoma (19, 25). Other than carcinoma, radiation induced sarcoma can be expected in high-dose regions. Low doses delivered far outside the main field have also been associated with second tumors (3, 26). When treating adults, the latent period might exceed the life expectancy. Second malignancies are of particular concern for pediatric patients (27, 28), because children, and young adults are especially prone to the carcinogenic effects of radiation (20, 29, 30) and these patients are likely to live longer than the average latent period. There is an increasing risk with decreasing patient age (31, 32) due to a greater radiation effect in humans during the period of rapid cell proliferation, for example, during development of the thyroid gland (33). It was shown that there is a statistically significant correlation between radiation therapy and second tumors after childhood cancer (28). Gliomas occurred typically within 15 years after treatment, whereas meningiomas typically occurred beyond 15 years after treatment. The Childhood Cancer Survivor Study presents an ongoing multi-institutional retrospective study of more than 14,000 cases (34–38). Children are preferably treated with highly conformal treatment techniques (39), and there is an interest in using protons

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because of the reduction in dose to healthy tissue compared with photon techniques. The knowledge about risk in medium or high dose levels for second malignancies is very limited because of the scarcity of second cancer from radiation therapy. Our understanding of radiation late effects at low doses is based on incidence and cancer mortality data for atomic bomb survivors (29, 40–43). However, in these cases the radiation exposure was acute over a very short period of time, unlike in the fractionated radiation treatment. Furthermore, the radiation field, consisting of neutron, photons, and other particles, was much different from those in radiation therapy. One might thus expect different biological damage mechanisms.

18.2  Volume Definition The irradiated volume considered in treatment planning includes the target volume receiving a prescribed dose as well as the organs at risk (see Chapter  10). The most common volume definitions in radiation therapy are illustrated in Figure 18.1. Target volumes might be defined as the gross tumor volume (GTV), the clinical target volume (CTV), and the planning target volume (PTV) (44). For critical structures, the organ(s) at risk (OAR) and the planning organ at risk volume (PRV) are defined (44). When ­analyzing IFV PRV OAR

GTV CTV PTV

OFV FIGURE 18.1 Volumes considered in treatment planning as defined by the ICRU (44) for the target and for the organ(s) at risk (OAR). Gross tumor volume (GTV); clinical target volume (CTV); planning target volume (PTV), organ(s) at risk (OAR); planning organ at risk volume (PRV). Also shown are the volume definitions introduced here for the analysis of scattered and secondary doses: in-field volume (IFV) and out-of-field volume (OFV).

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late effects from scattered and secondary radiation one can define three (overlapping) volumes in the patient: • The target (e.g., CTV), treated with the therapeutic dose. • OAR in the tumor vicinity that are imaged (considered) in treatment planning that may intersect with the beam path and are allowed to receive low-to-intermediate doses, here defined as in-field volume (IFV). • The rest of the patient’s body, which typically receives low doses (way below 1% of the target dose) that are not considered, or even imaged, for treatment planning, here defined as out-of-field volume (OFV). In this definition the CTV is excluded from the IFV because presumably all cells in the CTV will be killed during treatment. The definitions of IFV and OFV are arbitrary. One might also distinguish between low and intermediate dose levels. However, there is a distinct difference in dosimetry when analyzing risk for the IFV and the OFV. With some exceptions, dose distributions within the human body are not directly measurable. Organ doses in the IFV can typically be extracted from the treatment-planning system. On the other hand, organ doses in the OFV can typically only be calculated using Monte Carlo simulations (see Chapter 9). Treatment-planning systems cannot be applied for this purpose, even if whole-body computed tomography (CT) is available, because they are not commissioned for very low doses and do not explicitly take into account the particle type and energy distribution of secondary radiation. Furthermore, as will be discussed later in this chapter, the dose-response relationships and dose distributions differ between the IFV and the OFV (i.e., the OFV and the IFV have to be considered separately). Note that the term “integral dose” (a more correct terminology is the total energy deposited) is often used to describe the dose deposited in the patient including the tumor as well as all healthy tissues (target, IFV, and OFV). Proton therapy reduces the total energy deposited in the patient by a factor of 2 to 3 compared to photon therapy. This typically causes a significant reduction in early and late side effects when using protons in favor of photons (1, 45). Side effects do not simply scale with total energy deposited because the distribution of dose also plays a role. Many studies have compared different radiation modalities regarding the potential risk of late effects (46, 47). When comparing scattered and secondary dose from photon (intensity-­modulated radiation therapy [IMRT]) and proton (passive scattered) treatments, it seems that, in locations far away from the target (OFV), proton therapy offers an advantage, but within approximately 20–25 cm from the field edge (still OFV), the scattered photon dose in IMRT might be lower than the neutron equivalent dose from passive scattered proton therapy (48). In total, IFV risks seem to be higher than OFV risks, and it appears that there is an overall advantage for proton therapy for the majority of field arrangements (49–50).

Late Effects from Scattered and Secondary Radiation

559

18.3  Secondary Radiation (Neutrons) in the OFV 18.3.1  Physics of the Neutron Background Particles generated in nuclear interactions of primary protons can be very short ranged (<1 mm; e.g., recoil nuclei, α-particles), medium ranged (less than or equal to the range of the primary proton; secondary protons), or longranged (secondary neutrons) (Chapter 17). The first two types are included in the planned dose distribution, as the treatment-planning system would be commissioned for these dose levels. Neutrons can be generated when the primary proton beam interacts with devices in the treatment head but also when interacting inside the patient. At low energies (<1 MeV) neutrons undergo elastic scattering processes and cause protons and γ-rays produced by neutron capture. The most likely interaction in hydrogen-rich media, and thus mainly responsible for the neutrons to lose energy, is elastic scattering. In the low/thermal energy region, there is a decreasing probability of neutrons slowing down, as low-energy neutrons sparsely interact with material. For higher-energy neutrons, roughly 90% of the energy transfer (dose) occurs via secondary protons in only a few interaction events. This process causes protons with a wide range of energies between zero and the incident neutron energies. Secondary protons can be produced anywhere in the human body (it is thus feasible to encounter a proton downstream of the maximum range predicted for the primary proton beam). As a result, an extensive part of the patient’s body may be exposed to the secondary radiation field. The small amount of dose and the fact that neutrons are uncharged particles make measurements and simulations difficult and/or time consuming. 18.3.2  Neutron Energy Distributions The biological effectiveness of neutrons depends on their energy. Consequently, when assessing the impact of neutron doses, not only the absorbed dose but also the neutron energy distribution is important. Secondary neutrons can have energies up to the maximum proton energy. Neutrons with energy in excess of 10 MeV and high-energy protons produced by an intranuclear cascade processes are mainly forward-peaked. The majority of neutrons produced are in the energy region below 10 MeV, produced by an evaporation process, and are emitted more isotropically. Even though neutrons are predominantly emitted in a forward direction, the patient might be exposed to a relatively uniform neutron field, depending upon the distance between the patient and the neutron-emitting elements in the treatment head. Because of a 1/r2 dependency of the neutron fluence on the distance r, the relative position of devices in the treatment head plays a role when analyzing the neutron dose caused by the treatment

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Protons

Neutrons/proton/5keV

5e-4

Brass

H2O

10 cm

100 cm

Neutrons entering H2O

5e-5

Neutrons undergoing (n, xp) in H2O

5e-6 5e-7 0

50

150 100 Neutron energy [MeV]

200

FIGURE 18.2 Results of a Monte Carlo simulation of a 200-MeV proton beam stopping in a brass block and the generated neutrons entering a water tank. The simulated setup is shown in the top right with the protons indicated by an arrow and entering a 10-cm brass block, which stops all primary particles. The figure shows the neutron energy distributions of those neutrons entering the water tank downstream of the brass block as well as those neutrons causing a secondary proton in a nuclear interaction, the main mechanism of dose deposition. The unit is in neutrons per incident proton per 5-keV bin.

head. Neutrons produced in the patient, on the other hand, are generated by protons, which have, on average, lower energies and a much wider angular distribution. Because of the large number of elastic scatterings in soft tissue there is a prevailing field of low-energy neutrons inside the patient. Neutron energy distributions in patients (or phantoms) can be calculated using Monte Carlo simulations (51–54). Figure 18.2 shows the simulated energy distribution of neutrons entering a water tank after being generated in a brass block by a 200-MeV proton beam. Although the neutron energy distribution peaks at low neutron energies, the majority of the neutrongenerated dose is deposited by high-energy neutrons. About two-thirds of the neutron dose in a typical proton therapy scenario is deposited via neutrons with energy above 100 MeV (55). 18.3.3  Radiation Quality Factors and Weighting Factors The dose from secondary radiation might be low. Nevertheless, compared to high-dose photon radiation (the typical reference), there are concerns because of an elevated relative biological effect (RBE) of neutrons that may cause long-term side effects (56–58). The RBE is used when comparing different modalities with a reference radiation. It depends on the type of radiation, the particle energy, the dose, and the biological endpoint. The rationale behind the use of RBE and the determinants of RBE are discussed in Chapter 19. The RBE is used at a dose higher than ~0.5 Gy. The biological effectiveness

Late Effects from Scattered and Secondary Radiation

561

relative to photons increases with decreasing dose, causing the difference between photons and neutrons to be considerable at low doses. A conservative approach at low doses is to use a maximum RBE, RBEmax, which is the ratio of the initial slopes of the dose-response curves. This maximum RBE value is related to conservative regulatory quantities such as the radiation quality factors and the radiation weighting factors, which are defined independently of dose and biological endpoint. The equivalent dose is the average absorbed dose in an organ or tissue, modified by the radiation weighting factor for the type and energy of the radiation (59–62). The radiation weighting factors, wR, convert the absorbed dose in Gray (Gy) to Sievert (Sv) and are defined by the International Commission on Radiological Protection (ICRP) (63, 64):

H [Sv] = wR ⋅ D [Gy ].

(18.1)

The ICRP recommends for photons and electrons a radiation weighting factor of 1, for protons a weighting factor of 2, and for alpha particles a weighting factor of 20 (63). In the case of neutrons, the weighting factor depends on energy, and the ICRP defines an energy-dependent bell-shaped curve with a maximum weighting factor of 20 at about 1 MeV (63–65). For energies above 10 MeV, however, there is a significant uncertainty in the radiation weighting factors due to a lack of relevant animal studies (66). Nevertheless, a continuous function is suggested by the ICRP for the calculation of radiation weighting factors for neutrons (64):



2.5 + 18.2 ⋅ exp ( −[In {En }]2 / 6 ) En < 1 MeV  wR = 5.0 + 17.0 ⋅ exp ( −[In {2En }]2 / 6 ) 1 MeV ≤ En ≤ 50 MeV  2 2.5 + 3.25 ⋅ exp ( −[In {0.04En }] / 6 ) En > 50 MeV.

(18.2)

Several alternative fits have been presented as well (61). The interaction probability as a function of neutron energy is important in the understanding of the efficiency of neutron radiation. Most of the dose from high-energy neutrons is deposited via recoil protons, whereas for low-energy neutrons most of the dose is deposited via photons caused by neutron capture in hydrogen. It has been shown that, for a neutron field of 1-MeV neutrons, 25% of the dose would be deposited by photons (67). Most importantly, the weighting factors are only applicable for wholebody irradiation by external radiation fields, for which they are designed. Radiation weighting factors have also been used for internal radiation (e.g., neutrons generated in the patient). This can cause inconsistencies when assigning proton weighting factors for primary protons and neutron weighting factors for protons generated by neutrons because the latter protons would be scaled by a higher weighting factor (68). Furthermore, because the ICRP equation is defined for an external neutron field, it

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also contains the contribution of secondary photons that might be created in the body. For the size of a human body, however, some of the captured gamma rays will deposit a noticeable portion of the overall dose in the body. The equivalent dose defined via weighting factors was originally introduced to replace the “dose equivalent,” which is based on quality factors and is defined for a point instead of an organ (65). For estimating side effects from low doses in (proton) radiation therapy, however, the quality factor concept is in fact more meaningful for the reasons discussed above. The quality factor is based on the LET (linear energy transfer), independent of the energy-depositing particle. Thus, it allows proper consideration of internal and external radiation (66). The dose equivalent is written as H [Sv] = Q ⋅ D [Gy ].



(18.3)

The quality factor is defined as a function of the unrestricted linear energy transfer of charged particles in water (LET∞). Its maximum value is ~30 as defined by the ICRP (63):



 1 LET∞ < 10 keV / µm  Q(LET∞ ) =  0.32 ⋅ LET∞ − 2.2 10 ≤ LET∞ ≤ 10 keV / µm  LET∞ > 100 keV / µm.  300 / LET∞

(18.4)

For a given volume, the quality factor is obtained by integrating over the dose-weighted contributions of charged particles: Q=

∞

1 dD ⋅ ∫ Q(LET∞ ) ⋅ dLET∞ . D LET∞ = 0 dLET∞

(18.5)

Another radiation protection quantity is the “effective dose” as the weighted sum of various organ or tissue doses. It normalizes partial-body exposure in terms of whole-body stochastic risk using “tissue weighting factors” (63, 65). It was developed to recommend a risk-based occupational dose limit for radiation protection. The effective dose is not measurable or additive and carries significant uncertainty in the assessed risk values because it is based on not only radiation weighting factors but also tissue weighting factors for specific organs. The effective dose concept should be used only for overall radiation protection for the general public, but not for patient-specific radiation therapy risk assessments. 18.3.4  Biological Effectiveness of Neutrons Most second cancer risk studies have been done using the weighting factor concept. The energy averaged neutron weighting factors in the human body

Late Effects from Scattered and Secondary Radiation

563

for a proton beam entering the patient are typically between 2 and 11 (51, 69, 70). Independent of the problems when dealing with regulatory quantities discussed above, the radiation effectiveness as a function of particle and dose for carcinogenesis in human tissues or organs is not well known. It has been estimated that the neutron RBE at low doses (e.g., the weighting factor) might be about 25 for carcinogenesis (71). It is undisputed that the neutron quality factors are subject to significant uncertainties (46, 62, 66, 71–75). There is a paucity of data on RBEs at energies outside the range of about 0.1–2 MeV. Because of the lack of high-energy neutron carcinogenesis data, extrapolations have been made to much higher neutron energies (63–65, 76–79). Furthermore, RBE values obtained at high doses might be extrapolated to low-dose values (80). For the atomic bomb survivor data it was estimated that the neutron RBE for tumor induction was 70 ± 50 (81). Values up to 80 have been reported considering several endpoints (59, 79, 82). A comprehensive study on neutron values for RBEmax for the induction of dicentric chromosomes found a value of ~11 for a 60- and a 192-MeV mono-energetic neutron beam, demonstrating that the RBE is probably constant above ~20 MeV (83, 84). An RBE of 96 (relative to 60Co) was measured for chromosome aberrations at low dose (2.5 mGy) using a neutron energy spectrum that was similar to that produced by a clinical proton therapy nozzle (85). This may overestimate the RBE in the patient, because the neutron energy spectrum is modified by moderation and absorption. Most experimental data are for fission neutrons with energies between 1 and 1.5 MeV, much lower than the energy of neutrons responsible for most of the secondary dose in proton therapy. The RBE for oncogenic transformation, a relevant endpoint for carcinogenesis, was measured for low-energy neutrons in vitro, resulting in values of RBEmax relative to x-rays of 3.7, 6.6, and 7.2 for 40-, 70-, and 350-keV neutrons, respectively (86). The maximum RBE for induction of dicentric chromosomes was determined to be 94 ± 39 relative to 60Co for 0.385-MeV neutrons (corresponding to 23.4 ± 2.5 relative to 220-kV x-rays) (87). Based on the human data from neutron dose estimates to Japanese atomic bomb survivors (83, 88), the most likely RBEmax for neutron-induced carcinogenesis in humans has been estimated to be 100 for solid-cancer mortality (89) and 63 for overall cancer incidence (90). However, the radiation field to which the atomic bomb survivors were exposed is much different from the conditions in radiation therapy. One must keep in mind that most of the neutron dose is deposited via secondary protons. Interestingly, the low-dose RBE for chromosome aberrations induced by protons was found to be 5.7 for a proton energy of 4.9 MeV (91). 18.3.5  Neutron Sources in the Treatment Head Neutron production depends on the nuclear interaction cross section of the primary beam and thus on the proton beam energy and the materials in

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the beam path. The neutron production is determined mainly by the atomic number, Z, of the material. Cyclotrons extract a proton beam with a fixed energy. Thus, a significant amount of secondary radiation is produced in the energy selection system, which includes energy degraders of variable thickness and energy-defining slits. These degraders are usually outside the treatment room (in the accelerator vault) and do not cause secondary dose exposure of the patient. However, at some facilities fine-tuning of the beam energy (range) is done directly upstream of the patient position. High-Z materials are used in scattering devices as well as to stop the beam around the patient aperture. Some of the materials typically used in treatment heads are brass, steel, carbon, or nickel. Consequently, the neutron fluence is influenced by the treatment head design, that is, the geometry and the materials used. Design of proton therapy beam delivery systems and treatment heads can vary considerably when comparing different facilities. The neutron background produced by a treatment head can be influenced by appropriately designing the treatment head, particularly for passive scattered proton beam therapy (92–94). Variable collimators can be used to tailor the field size upstream of the final patient collimator. Furthermore, aperture designs can be optimized using low-Z materials and/or preabsorbers (92). 18.3.6  Neutron Doses as a Function of Distance to the Beam Axis Many experiments have been reported to assess secondary radiation from therapeutic proton beams (69, 70, 94–105). Neutron detectors typically include Bonner spheres (70, 102), thermoluminescence dosimeters (106), CR-39 plastic nuclear track detectors (99, 102), bubble detectors (98), solid-state microdosimetry detectors (69, 97, 107), tissue equivalent proportional counters (104), ionization chamber arrays (97), and other survey meters such as WENDI (94, 108). Bonner spheres consist of a proportional chamber filled with BF3 gas at the center of polyethylene sphere in diameter plus some Cd. The polyethylene moderates the neutrons to thermal energies, which are detected by the proportional chamber via the reaction 10B(n,α)7Li. The Bonner spheres can be calibrated by measuring the response when the detector is placed a certain distance (1 m) from an Am/Be source of known activity. These spheres can be set up throughout the treatment room and can also be used as area monitors (see Chapter 17). Experiments to determine neutron doses can be difficult because neutrons are indirectly ionizing and interact only sparsely. Monte Carlo simulations of neutron doses as a function of lateral distance to the field edge have been used in several studies (53–55, 95, 99, 109, 110), whereas analytical models can be used as well (111). The majority of published data on neutron doses as a function of distance to the field edge is shown in Figure 18.3. The results from passive

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Late Effects from Scattered and Secondary Radiation

102

H [mSv/Gy]

101

100

10–1

10–2

0

10

20 30 40 50 60 Lateral distance to the field edge [cm]

70

80

FIGURE 18.3 Equivalent dose per treatment dose [mSv/Gy] as a function of lateral distance to the field. Solid lines: measured (69, 70, 94, 97–99, 107) and simulated (53, 55, 97, 99, 110) data for a variety of proton beam configurations using passive scattered beam delivery. Dashed lines: results for scanned proton beams (97, 102). If more than one configuration was reported in a given publication, two curves showing the maximum and minimum were selected. Also shown for comparison is the scattered photon dose for a randomly chosen 10 × 10-cm 2 intensity-modulated photon field using a 6-MV beam (dotted line) (181).

scattered beams vary significantly because of variations in beam delivery systems and field specifications. Within 5 cm of the edge of the primary treatment field, the reported doses vary between 0.5 and 10 mSv/Gy. At a distance of 60 cm from the edge in lateral direction, the reported doses vary between 0.03 and 8 mSv/Gy. Most of the studies focus on neutron doses lateral to the field. Because neutrons are predominantly emitted in forward direction in the treatment head, one might expect a slightly higher neutron dose downstream of the target. Nevertheless, neutron equivalent doses past the distal falloff were determined to be below 2 mSv/Gy (95, 99, 107). For scanned beams, neutron doses lateral to the field have been measured (using a Bonner sphere and CR39 etch detectors) as below 4 mSv/Gy outside of the target (102). Scanning reduces the equivalent dose in the OFV by a factor of 30–45 in the entrance region. The difference decreases with depth because internal (generated in the patient) neutrons predominate. Because of the ratio of external (generated in the treatment head) versus internal neutrons, the equivalent dose at 15–20 cm from the field edge decreases with depth in passive scattering and increases with depth for scanning (97).

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Proton Therapy Physics

18.3.7 Field Parameters That Influence the Neutron Field from the Treatment Head When proton treatments are delivered in passive scattering mode, various scatterers, beam-flattening devices, collimators, and energy-modulation devices to produce the SOBP are in the beam path. In addition, for each treatment field, individual apertures and range compensators are being used. Doses caused by neutrons depend significantly on the treatment conditions (i.e., the treatment facility) because of differences in position and design of devices in the treatment head. Even for the same facility there are huge variations between fields because the treatment head geometry and the beam characteristics in passive scattered proton therapy are patient field specific (Figure 18.3). The parameters determining the neutron contamination of the primary proton beam include the characteristics of the beam entering the treatment head (energy, angular spread), the material in the double-scattering system and range modulator, and the field size upstream of the final patient-specific aperture (55, 94, 98, 110). The complexity of field delivery in passive scattering techniques, causes considerable variations in neutron doses and prevents the definition of a “typical” neutron background representing proton therapy (46, 74, 110, 112). Neutrons are mainly generated in the modulator wheel as well as in precollimators and patient-specific apertures (99, 113). Double-scattering systems are typically designed to create a homogeneous field with the maximum size commissioned for treatment. The efficiency of most proton therapy treatment heads is quite low (typically between 3% and 30% depending on the field size). Depending on the actual required field size for a treatment, a high percentage of primary protons are being stopped in the treatment head by either precollimators or the patient-specific aperture. A systematic experimental study on secondary neutron dose equivalent using anthropomorphic phantoms confirmed that neutron dose decreased with increasing aperture size and air gap, implying that the brass collimator contributes significantly to the neutron dose because of its proximity to the patient (98). Thus, the neutron dose depends on the ratio of field size to aperture opening; neutron equivalent doses due to external neutrons typically increase with decreasing field size (74, 98, 105, 110, 112). Figure 18.4 shows the neutron dose equivalent as a function of the aperture opening. The neutron production in the treatment head also depends on the beam energy, as higher beam energies might traverse more scattering material to slow down protons in order to cover proximal parts of the target (the proximal part of the spreadout Bragg peak). Neutron equivalent doses to specific organs do depend considerably on patient’s age and size because of the position and distance of the organ relative to the treatment head and the target. Younger patients are thus typically exposed to a higher neutron contribution from the treatment head because of their smaller bodies (110). For example, assuming an 8-year-old patient, the

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Late Effects from Scattered and Secondary Radiation

Neutron dose equivalent (mSv/Gy)

0.35

Double scattering

Rectangular scanning

Spiral scanning

0.3

Circular wobbling

y = –0.0009x + 0.309

0.25

y = –0.0009x + 0.2392

0.2

0.15 y = –0.0009x + 0.1906

0.1

y = –0.0008x + 0.06

0.05 0

0

10

20

30 40 50 Collimator area (cm2)

60

70

80

FIGURE 18.4 Neutron dose equivalent at a position in a water phantom as a function of the aperture opening. Different delivery techniques were considered: passive (double) scattering (squares), rectangular scanning (diamonds), spiral scanning (triangles), and circular wobbling (circles), each representing a different ratio of field size versus aperture opening. (From Hecksel et al., Med Phys., 37(6), 2910, 2010. With permission.)

dose to the brain from spinal fields ranged from 0.04 to 0.10 mSv/Gy, whereas assuming a 9-month-old patient, the dose ranged from 0.5 to 1.0 mSv/Gy for the same field (114). Figure 18.5 illustrates the increase in neutron dose with decreasing patient’s age, considering identical treatment fields. The neutrons produced in the proton treatment nozzle are the main contributor to organ equivalent doses. The ratio of internal versus external 3.0

H [mSv/Gy]

2.5 2.0 1.5 1.0 0.5 0.0

20 30 Patient’s age [years]

40

FIGURE 18.5 Simulated organ neutron equivalent dose for thyroid (circles), esophagus (squares), lungs (triangles), and liver (diamonds) as a function of patient age averaged over eight different proton treatment fields. The simulations were based on computational phantoms resembling representative individuals. (From Zacharatou Jarlskog et al., Phys Med Biol., 53, 693, 2008. With permission.)

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neutron dose depends heavily on the organ and its distance to the treatment target volume (51). It has been shown that for a small target volume, the contribution of neutrons from the treatment head can reach ~99% of the total neutron contribution, whereas for a large target volume it can go down to ~60% (110). Beam scanning typically does not require scattering or compensating devices. Also, no field-shaping apertures stopping a large portion of the beam are necessary. Thus, proton beam scanning reduces the neutron dose exposure significantly, particularly for small treatment fields (i.e., small apertures in scattering systems) (97). A treatment head using the passive scattering technique may show a 10-fold secondary neutron dose disadvantage compared with the spot-scanning technique (45, 51). 18.3.8 Field Parameters That Influence the Neutron Field Generated in the Patient

H [mSv/Gy]

Neutrons are also generated in the patient. Here, the bigger the target, the more protons are entering the patient. Thus, the main parameter influencing the neutron dose is the treatment volume (102). Figure 18.6 shows the relationship of treatment volume and neutron dose from internally created neutrons assuming different patient age. Neutron doses increase with increasing range and modulation width (53, 110). The greater the penetration of the beam, the greater is the overall likelihood of a nuclear interaction producing neutrons. The treatment volume is slightly affected by the delivery technique. One can assume that the patient generated neutron dose for scanned beams is roughly the same as in passive scattering beams. Neutron production is not homogeneous as a function of proton penetration depth. Figure 18.7 shows the nonelastic cross section for protons on carbon and oxygen. Clearly, the cross section is more or less independent of proton energy down to ~100 MeV, after which it increases with decreasing proton energy. The maximum is reached at ~25 MeV. To understand the 0.5 0.4 0.3 0.2 0.1 0.0

0

100 200 300 Treatment volume [cm3]

FIGURE 18.6 Simulated internally created neutron equivalent dose to the thymus as a function of treatment volume of a brain tumor: 4-year-old patient (circles), 11-year-old patient (squares), 14-year-old patient (triangles), and adult patient (diamonds). (From Zacharatou Jarlskog et al., Phys Med Biol., 53, 693, 2008. With permission.)

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Late Effects from Scattered and Secondary Radiation

Nonelastic cross section [barn]

0.6 0.5 0.4 0.3 0.2 0.1

20

0

40

60 80 100 120 140 160 180 200 Proton energy [MeV]

FIGURE 18.7 Total nonelastic cross sections for protons on carbon ( ) and oxygen ( ). (Based on EXFOR/ CSISRS, Experimental Nuclear Reaction Data. International Atomic Energy Agency, Nuclear Data Section, Vienna, Austria, 2010. (182))

neutron emission as a function of depth, one has to consider the average proton energy as a function of depth, which is shown for a 160-MeV proton beam in water in Figure 18.8. Epidemiological studies require the use of organ-specific doses for proper risk analysis. Accurate dosimetry information exists for organs delineated in a treatment plan. However, dosimetry for organs or tissues outside the portion of the body that was imaged for treatment planning will need to be reconstructed using whole-body patient models and Monte Carlo simulations (see Chapter 9). Many models representing male and female adults, children, and pregnant women have been developed,

Average proton energy [MeV]

160 Dose [relative units]

140 120 100 80 60 40 20 0

0

50

100 150 Depth in water [mm]

200

FIGURE 18.8 Average proton energy for primary protons (solid line) and secondary protons from nuclear interactions (dotted line) as a function of depth in a 160-MeV proton beam leading to the depthdose distribution shown as dashed line.

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Proton Therapy Physics

mostly from segmented whole-body images (115, 116). A number of studies have used whole-body patient phantoms and Monte Carlo simulations to calculate organ doses originating from secondary neutrons (48–51, 110, 114, 117, 118). Considering several proton fields of varying field size, beam range, and modulation width for the treatment of tumors in the intracranial and spinal region, variations of neutron-generated dose among different organs for different treatment volumes and patient statures were studied (48, 114). To put things in perspective, assuming treatments are in the head and neck region of an adult patient, the equivalent dose from proton therapy is comparable to doses from a chest CT scan (110) or whole-body CT scan (99). However, for young patients it could be in the order of more than 20 additional CT scans (110).

18.4  Modeling Cancer Risk 18.4.1  Risk Parameters Cancer risk (i.e., the probability of a disease) is either specified as incidence risk or mortality risk. The absolute risk (AR) is defined as the rate of a disease among a population per capita per year. A relation between the incidence rate in the exposed population and the incidence rate in the unexposed population can be defined as a difference or a ratio. Relative risk (RR) is the rate of disease in the exposed groups divided by the rate in a control group. Excess relative risk (ERR) is defined as the rate of an effect in an exposed population divided by the rate of the effect in an unexposed population minus 1 (i.e., RR-1). Thus, the risk is given relative to the baseline risk. The baseline risk is the incidence observed in a group without a specific risk factor (e.g., the unirradiated reference population). Excess absolute risk (EAR) is the rate of an effect in an exposed population minus the rate of the effect in an unexposed population. In risks reported as EAR, risks are expressed as the difference between the total risk and the baseline risk. Both, ERR and EAR are used in risk modeling. Estimates based on ERR typically have less statistical uncertainty. EAR models depend on the baseline risk, that is, the area in which the person lives, the age at exposure, sex, and date of birth (9). Estimates based on EAR are often used to describe the impact of a disease on the population. Risks can be calculated as a function of attained age of the individual, age at exposure, dose received, sex index, and an index denoting population characteristics. Further, the lifetime attributable risk (LAR) provides the probability that an individual will die from (or develop) a disease (e.g., a second cancer) caused by the exposure during his or her lifetime (8, 80, 119).

Late Effects from Scattered and Secondary Radiation

571

18.4.2  Low-Dose Effects (in the OFV) Risk estimates are sometimes performed using whole-body effective doses and organ weighting factors (see above) (65). Such tissue weighting factors for the effective dose are gender- and age-averaged values. Effective doses are suited for radiation protection studies but not for risk models for second cancer, which are site specific. Risk assessments should be based on patient-specific organ doses and not on population average tissue doses (120, 121). Interpreting clinical data on second cancers is difficult, because accurate organ dose information is often missing. Furthermore, because of interpatient variability and the low frequency of second cancers, dose-response relationships from patient data are associated with large statistical uncertainties (57). To establish a reliable dose-response relationship for second cancers as a function of modality, treatment site, beam characteristics, and patient population, progressively larger epidemiological studies are required. Our knowledge (and the basis of low-dose epidemiological response models) of radiation-induced tumors is largely based on the atomic bomb survivor data (40, 41, 120–122), and models are therefore associated with considerable uncertainties (123–125). Data on solid tumor mortality among the atomic bomb survivors are consistent with linearity up to ~2.5 Sv (40, 42). Risks observed in the atomic bomb survivors were compared to risks in patients after medical exposure risks (126–128). Although it was found that the relative risk of cancer from treatment was generally less than those in comparable subsets of the bomb survivor data, a linearity of the doseresponse curve was concluded for both series (129, 130). Various dose-response relationships for carcinogenesis have been suggested (129, 131–141), and low-dose risk models have been summarized or developed by radiation protection bodies (6–8, 123). There is considerable uncertainty in the shape of the dose-response curve, and linearity may not hold for all cancers. Figure 18.9 shows the different regions of dose response. Secondary or scattered doses in the OFV are typically well below 2 Sv where a linear dose-response relationship for solid tumors is reasonable based on the available data, but the slope will most likely depend on the cancer and site. An increasing slope has been suggested as dose-effect relationship for radiation-induced leukemia (42), for example, a linear-quadratic relationship (8). At very low doses (below ~0.1 Sv), none of the epidemiological data are sufficient to predict the shape of the dose-response curve (131). Linearity is suggested at least down to about 0.1 Gy (142–144). Both the BEIR VII Committee (Biological Effects of Ionizing Radiation) (8) and the ICRP (65) recommend a linear no-threshold (LNT) model because stochastic effects are usually regarded as having no dose threshold. The validity of the LNT model has been challenged (131). It has been acknowledged that for doses below ~0.1 Gy there might be a threshold effect or a nonlinear relationship (134, 135,

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Proton Therapy Physics

Cancer risk

?

Linear increasing Plateau Bell-shaped

?

Threshold Bystander effects Hormesis ... 0.05 – 2.5 Equivalent dose [Sv]

FIGURE 18.9 Dose-response relationships for carcinogenesis showing a linear dose response in the dose range of the atomic bomb exposures of ~0.05–2.5 Sv (134) and the uncertain relationships for higher and lower doses.

145–151). A threshold in dose has been suggested for radiation-induced sarcomas (152). This is also confirmed by atomic bomb survivor data because no increased sarcoma risk is found there. A lack of evidence of carcinogenic effects at low doses could be due to a dose threshold or because these effects are too small to be detected. The situation is complex too because one often deals with population average values. The existence of a small subpopulations of individuals showing hypersensitivity would decrease the slope for cancer mortality and incidence (136). There might also be reduced radioresistance in which a small dose decreases the radiosensitivity for carcinogenesis (138, 148). Adaptive response would cause higher risk for lower doses because a small initial dose might decrease radiosensitivity. There might even be hormesis (147). Pure physics considerations might support the linearity at low doses based on the number of tracks being proportional to dose. The argument does not hold if multiple radiation-damaged cells influenced each other, and bystander effects also play a role (139, 153–157). Such effects could be relevant specifically for higher LET because bystander effects would be more pronounced if a small number of cells were traversed by particle tracks at low doses (155, 156). When estimating risks, dose-rate effects may play a role (158). Radiation therapy is mostly delivered in multiple fractions, whereas most low-dose weighting factors or response models are deduced from single irradiation. Differences in tissue repair capacities of tissues are not considered. In order to account for this effect, a dose and dose-rate effectiveness factor (DDREF) has to be applied for doses below ~0.2 Gy (62). 18.4.3  Risk Modeling Formalism in the OFV Risk (e.g., ERR) can be calculated as a function of attained age of the individual (a), age at exposure (e) (or time since exposure, t), absorbed

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Late Effects from Scattered and Secondary Radiation

dose (D), sex (s), and a parameter denoting population characteristics (8, 119). Low-dose models to calculate specific risks of cancer incidence and mortality with organ-specific parameters are given, for example, in the BEIR report (8) (there are other parameterizations by other committees as well (6, 7)):

EAR or ERR ( s, t , a , D) = ρ(D) ⋅ β s ⋅ exp( γe) ⋅ a η .

(18.6)

The BEIR committee suggests that ERR for solid cancers (except for breast and thyroid) depends on age only for exposure under age 30, replacing e by e* = (e-30)/10 (equals 0 for e > 30). For solid tumors ρ(D) is a linear function of dose. Normalizing the attained age to the reference age 60 and assuming a linear dose response leads to the following risk model for all solid cancers except thyroid and breast:

EAR or ERR ( s, a , e*, D) = D ⋅ β s ⋅ exp( γe*) ⋅ ( a / 60)η.

(18.7)

The parameter βs denotes the ERR/Sv or the EAR/104 PY Sv for a person that has been exposed to radiation at age 30 and has attained 60 years of age. The parameter γ gives the per-decade increase in age at exposure over the range 0–30 years and expresses the fact that the ERR decreases with increasing age at exposure for those exposed under age 30. For breast cancer, it was recommended that (8, 159)

ERR ( s, a, D) = D ⋅ β ⋅ ( a / 60)−2

(18.8)



EAR per 10 4 women ⋅ years = D ⋅ 9.4 ⋅ exp ( −0.05(e − 30)) ⋅ ( a / 60)η .

(18.9)

For thyroid cancer, a recommended model reads (8, 33)

ERR ( s, e , D) = D ⋅ β s ⋅ exp( γ(e − 30)).

(18.10)

Finally, the excess risk for leukemia can be defined as (8) ERR ( s, e , t , D) = D ⋅ β s ⋅ (1 + θD)exp ( γe * ⋅ δ log(t / 25) + φe * log(t / 25)) . (18.11) The LAR can be calculated by integrating ERR or EAR over the expected lifetime for all attained ages exposed at age e with dose D. Other parameters are the latent period L (e.g., 5 years for solid cancers and 2 years for leukemia), and the survival fraction (i.e., the probability at birth of reaching a specific age): a



LAR(e) =

max

∫

e +L

M(D, a , e). S( a) S(e) da ,



(18.12)

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Proton Therapy Physics

where S(a)/S(e) is the conditional probability for a person who was alive at age e to reach age a and M(D, a, e) is the excess absolute risk at the a from exposure at age e, which is defined for both EAR as well as ERR:

M (D, a , e) = EAR (D, a , e) M (D, a , e) = ERR (D, a , e) ⋅ λ cU ( a).

(18.13)

The parameter λcU(a) is the age- and gender-specific baseline (unexposed population U) cancer incidence rate at the attained age a (9). The preference for one or the other method (EAR vs. ERR) depends on whether there are differences in the baseline risks between the reference population and the considered population. The BEIR committee has recommended that LAR be estimated as a weighted average between the ERR and EAR models, except in the case of breast (ERR and EAR not combined) and thyroid (only ERR). A related parameter to LAR is REID (risk of exposure induced death), which is considered dose dependent (6, 7). 18.4.4  Results for the OFV Organ doses in the OFV in proton therapy have been simulated applying Monte Carlo simulations (Chapter 9). Based on the results, risks for developing a second malignancy in patients treated with passive and scanned proton radiation have been estimated (50, 51, 71, 114, 118, 160, 161). Wholebody computational phantoms provide the geometries to assess adult and pediatric organ doses, albeit not patient specific (114, 160, 161). It was found that young patients are subject to significantly higher risks than adult patients. The reasons are geometric differences and because of the age-dependency of risk models. Most of the calculated lifetime risks were found to be below 1% and below the baseline risks. For example, the LAR for lung and breast cancer incidences in a 4-yearold child treated for a brain tumor were 1.1% and 1.3%, respectively, and the corresponding values for an 8-year-old girl were 1.1% and 0.7%, respectively (114). Risk clearly decreases with increasing age with the risk for developing a second cancer in the thyroid, testes, and bladder reported as ≤0.3% for a 14-year-old boy. The corresponding baseline risks for thyroid, testes, and bladder were 0.4%, 0.4%, and 4%, respectively. Furthermore, LAR values were found to be higher for the deepseated tumors because of large volume exposure. The LAR values for different organs as a function of patient age are shown in Figure 18.10. The numbers can be expected to be very similar, maybe within a factor of 2, for photon treatments (161). Because the majority of neutron doses are caused by scattering devices in the treatment head, there is a big advantage of scanned proton beams over photon beams on the incidence of treatment-induced second cancers specifically for pediatric patients (45, 102). It was demonstrated that with scanned beam proton therapy there is the potential to reduce the incidence

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LAR [%]

0.6 Lung Thyroid Leukemia Esophagus

0.4

0.2

0.0

0.75

11

14

Patient age [years]

39

FIGURE 18.10 Lifetime attributable risk (LAR) for developing a second cancer after treatment of a brain tumor to 70 Gy at different ages for a male patient. The risks are averages over several treatment fields. (From Zacharatou Jarlskog et al., Phys Med Biol., 53, 693, 2008. With permission.)

of radiation-induced second cancers by a factor of 2 to 15. In another study, craniospinal irradiation of a male patient was simulated for passively scattered and scanned-beam proton treatment units, and the total lifetime risk of second cancer due exclusively to secondary radiation was 1.5% for the passively scattered treatment versus 0.8% for the scanned proton beam treatment (50). 18.4.5  Effects in the IFV Other than in the OFV, average organ doses are not meaningful in the IFV because dose-volume effects might play a role. Furthermore, mutagenesis is in competition with cell survival, causing the dose-response relationship to become nonlinear, as sterilized cells will not mutate (37, 135). In addition, tissues may respond to radiation by accelerated repopulation, contributing to tissue sparing during fractionated radiation therapy. This causes risk modeling in the IFV to be more complicated than in the OFV. Figure 18.9 shows the dose-response relationship at high doses and the potential uncertainties. An analysis of pediatric patients showed that a linear dose-response relationship best described the radiation response down to 0.1 Gy, whereas a decrease or leveling of risk was apparent beyond 10 Gy (33). On the other hand, a linear increase with dose even beyond 40 Gy was found for meningioma and glioma (28, 162). This could be because the killed cells are balanced by repopulation (163). Also, other studies have suggested a linear increase to even higher doses in second cancers after Hodgkin lymphoma or cervical cancer (134, 164, 165). Most human data show no decrease in risk but just a leveling off at higher doses. There is evidence that the risk of solid tumors might level off at 4–8 Gy (4, 166). A slight decrease after ~4 Gy has been observed for leukemia after cervical cancer (164, 167, 168). For thyroid cancer

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25

Relative risk

20 15

10 5 0

0

10

20 30 Dose [Gy]

40

50

FIGURE 18.11 Relative risks for a subsequent glioma ( (28)) and thyroid cancer ( (38)). The solid line shows a linear fit to the glioma risk data, and the dashed line represents a linear-exponential fit to the data on thyroid cancer risk.

a bell-shaped response curve with linearity up to ~25 Gy can be deduced (34, 162) with an eventual decrease of the risk with increasing dose (37). Thyroid is the only organ where this effect has been seen consistently. Figure 18.11 shows experimental data illustrating linear and bell-shaped response curves. It has been shown that second cancers are more likely in the field periphery than in the field center (23), providing evidence for the bell-shaped dose-response curves due to competing factors of cell kill and cell mutation. The reason for organ-specific differences might be differences in repopulation rates. 18.4.6  Risk Modeling Formalism for the IFV Linear fits to atomic bomb data cannot be used for IFV risk analysis, and more mechanistic interpretation is necessary. Radiation-induced cancers are rare in radiation therapy and parameterizations are thus difficult for the IFV (38, 57). Models do incorporate mechanistic considerations to guide parameter fits and radiation-induced malignancies are thus modeled considering the competing probabilities for DNA mutation and cell survival (6, 7). The survival probability can be modeled in a linear-quadratic form using α and β as the intrinsic radiosensitivities, and the probability for mutation can be parameterized by mutational radiosensitivities, γ and δ (169–175). The processes are also dependent on the kinetics of repopulation by the surviving normal and mutant cells. This can be modeled as a multistage process assuming three compartments: the nonmutated stem cells, the one-mutant stem cells (which are also the precursor cells of malignant transformation), and the probability that an individual cell population has received at least one malignant transformation in a given time interval after irradiation (170). Stem cells are subjected to a spontaneous mutation rate, μ, causing

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one-mutant cells. The expected number of malignant transformations, N, is then proportional to

N ∝ (exp[−αD − βD2 ])(1 − exp[− γD − δD2 ])(1 − exp[−µt])

(18.14)

where t is the time from conception at which the radiation dose was administered. The repopulation rate for both cell types, surviving normal stem cells and surviving one-hit mutants (two-hit mutants are assumed to lead to malignant transformation), is assumed to be the same. Example parameters are α = 0.25 Gy−1, β = 0.025 Gy−2, γ = 10−5 Gy−1, δ = 10−6 Gy−2, and μ = 10−8 month−1 (170). When analyzing high or medium dose levels organs typically receive inhomogeneous dose distributions. To consider such effects, one might use the concept of organ equivalent dose (OED), in which any dose distribution in an organ is equivalent and corresponds to the same OED if it causes the same radiation-induced cancer incidence. A risk factor is then applied to the OED (173, 176, 177). For low doses, the OED represents the average organ dose. The EAR as a function of D, a, e, and s, can be written as a product of OED and the initial slope, that is, with a risk factor based on low-dose risk models (175, 177). Parameters for OED are the organ-specific cancer incidence rate at low doses, which can be taken from the data of the atomic bomb survivors, and cell sterilization at higher doses (174). If the true dose-response curves for radiation-induced cancer were known for each organ and tissue, an OED estimate would be a perfect parameter to quantify second cancers. However, because the underlying dose-response function is not known, several models have been used. One can thus assume three dose-response relationships, linear, bell-shaped, and plateau-shaped as follows: (using free model parameters αorgan and δorgan)



1 ∑ Vi Di N i

(18.15)

1 ∑ Vi Di exp(−αorgan Di ) N i

(18.16)

OED = OED =

OED =

(

)

1 − exp[−δorgan Di ] 1 Vi . ∑ δorgan N i  

(18.17)

The total volume is denoted as N, and the summation includes all voxels, assuming that the organ volume is parameterized in a CT scan. Because there are limited data for specific organs, the original model parameters to describe the high dose response were estimated by analyzing the second cancer incidence data of patients with Hodgkin’s disease, a patient population with considerable data on second tumors because of genetic susceptibility (178).

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Note that for small doses, the formalism assumes a linear response based on an average organ dose, such as in the low-dose models, thus allowing parameters to be fitted to the atomic bomb data: OED =



1 − (1 − δorgan Di ) 1 1 Vi = ∑ Vi Di = D. ∑ δorgan N i N i

(18.18)

Tumor induction is modeled with differential equations considering the balance between cell survival, mutation, and repopulation (172). Cancer risk is defined as the ratio of the number of mutant to the number of original cells. One might also consider that carcinoma and sarcoma might have different functional dose relationships. Carcinoma induction is proportional to the sum of surviving original and repopulated cells and is expected to show a bell-shaped pattern as long as cell repopulation is small. For sarcoma induction, only repopulated cells can form tumor cells. Using the repopulation parameter R > 0, the dose per fraction dF, the total dose D, and a cell kill parameter α′, the OED can be written as follows (179): exp(− α′i Di )  1  α′i R  2 2 OEDcarcinoma = ∑ Vi Di    1 − 2 R + R exp[α′i Di ] − [1 − R] exp  − α′i R − N i 1 R    (18.19)

OEDsarcoma =



exp(− α′D ) 1 ∑ Vi α′Ri i N i i   α′i R  2 2 Di    1 − 2R + R exp[α′i Di ] − α′i RDi − [1 − R] exp − − 1 R    (18.20)  α′i = α + βDi ⋅

dF . D

(18.21)

The EAR, for example, can then be just the product of a risk parameter (from low-dose response) and the respective OED. Figure 18.12 illustrates the bell-shaped dose-response relationships for carcinoma and sarcoma. For small repopulation parameters, carcinoma induction shows a bell-shaped function of dose, whereas a plateau is reached with increasing dose if high repopulation is assumed. In contrast, sarcoma induction increases with increasing dose up to a constant value. Similar models have been proposed by others (163) and expanded by adding stochastic fluctuations of premalignant cell numbers among patient populations (180).

579

Breast cancer risk [/10000PY]

60

Rf = 99% Rf = 80%

40

Rf = 60% Rf = 40%

20

0

0

20

40 Dose [Gy]

Rf = 20% Rf = 10% Rf = 0% 60 80

Sarcoma risk [/10000PY]

Late Effects from Scattered and Secondary Radiation

2.5

Rf = 99%

2.0

Rf = 80%

1.5

Rf = 60%

1.0

Rf = 40%

0.5 0.0

0

20

40 Dose [Gy]

Rf = 20% Rf = 10% Rf = 0% 60 80

FIGURE 18.12 Calculated absolute risk for breast carcinoma (left) and for sarcoma (right) assuming different repopulation factors. The three data points on the left represent data on breast cancer after radiation therapy for Hodgkin’s disease. (From Schneider, Med Phys., 36(4), 1138, 2009. With permission.)

18.4.7  Results for IFV There are fewer modeling studies for the IFV than for the OFV. One of the reasons is the uncertainty of model parameters for the nonlinear doseresponse domain in the IFV because most IFV data from radiation therapy do not allow the deduction of a reliable dose-response curve (57). A detailed analysis of thyroid cancer in childhood cancer survivors revealed a linear dose-response relationship (with a small nonlinear contribution) with an ERR of ~1.3 per Gy for doses below 6 Gy (38). For higher doses, the analysis resulted in a relative decrease in ERR of 0.2% per unit dose squared with increasing dose. This lead to decreases in the ERR/Gy of 53% at 20 Gy and 95% at 40 Gy. The data for most organs indicate that the risk increases with dose to fairly high levels where it might eventually level off. Thus, one can assume that the risk for a second malignancy is typically higher in the IFV compared to the OFV. For prostate patients, it has been shown that about 90% of the total risk is for the colon and bladder inside the main treatment fields and that proton therapy offers an advantage over photon techniques (49). Comparisons between photon and proton therapy for IFV risk showing the advantage of proton therapy have also been done for craniospinal irradiation (50). Apparently, IMRT and proton therapy decrease the risk for second malignancies in-field when compared with 3D conformal photon therapy (175). The reason is the improved capability for shaping the dose distribution. Furthermore, because protons typically reduce the treated volume and reduce the total energy deposited in the tissue, dose to organ at risk in the IFV are typically lower compared to photon techniques (for comparable target doses). In particular for pediatric treatments it is certainly beneficial to reduce the overall treatment volume to reduce the risk for second malignancies. Even within the same modality one might influence the cancer risk. The

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choice of beam angles and the number of fields can influence the risk for a second malignancy because of different distribution of dose. When analyzing the risk for a radiation-induced cancer, treating a smaller volume to higher doses might seem beneficial compared to treating a larger volume with, on average, lower doses. However, this has to be balanced against other side effects that might deserve higher attention, for example, radiationinduced reduction in cognitive function in the case of brain dose (1).

Acknowledgments The author thanks Dr. X. George Xu, Dr. Uwe Schneider, and Jocelyn Woods for proofreading and Clemens Grassberger for help with some of the figures.

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94. Yonai S, Matsufuji N, Kanai T, Matsui Y, Matsushita K, Yamashita H, et al. Measurement of neutron ambient dose equivalent in passive carbon-ion and proton radiotherapies. Med Phys. 2008 Nov;35(11):4782–92. 95. Agosteo S, Birattari C, Caravaggio M, Silari M, Tosi G. Secondary neutron and photon dose in proton therapy. Radiother Oncol. 1998;48:293–305. 96. Binns PJ, Hough JH. Secondary dose exposures during 200 MeV proton therapy. Radiation Protect Dosim. 1997;70:441–44. 97. Clasie B, Wroe A, Kooy H, Depauw N, Flanz J, Paganetti H, et al. Assessment of out-of-field absorbed dose and equivalent dose in proton fields. Med Phys. 2010 Jan;37(1):311–21. 98. Mesoloras G, Sandison GA, Stewart RD, Farr JB, Hsi WC. Neutron scattered dose equivalent to a fetus from proton radiotherapy of the mother. Med Phys. 2006 Jul;33(7):2479–90. 99. Moyers MF, Benton ER, Ghebremedhin A, Coutrakon G. Leakage and scatter radiation from a double scattering based proton beamline. Med Phys. 2008 Jan;35(1):128–44. 100. Newhauser W, Koch N, Hummel S, Ziegler M, Titt U. Monte Carlo simulations of a nozzle for the treatment of ocular tumours with high-energy proton beams. Phys Med Biol. 2005;50:5229–49. 101. Roy SC, Sandison GA. Scattered neutron dose equivalent to a fetus from proton therapy of the mother. Radiat Phys Chem. 2004;71:997–98. 102. Schneider U, Agosteo S, Pedroni E, Besserer J. Secondary neutron dose during proton therapy using spot scanning. Int J Radiat Oncol Biol Phys. 2002;53:244–51. 103. Schneider U, Fiechtner A, Besserer J, Lomax A. Neutron dose from prostheses material during radiotherapy with protons and photons. Phys Med Biol. 2004;49:N119–N24. 104. Tayama R, Fujita Y, Tadokoro M, Fujimaki H, Sakae T, Terunuma T. Measurement of neutron dose distribution for a passive scattering nozzle at the Proton Medical Research Center (PMRC). Nucl Instrum Methods Phys Res A. 2006;564:532–36. 105. Hecksel D, Anferov V, Fitzek M, Shahnazi K. Influence of beam efficiency through the patient-specific collimator on secondary neutron dose equivalent in double scattering and uniform scanning modes of proton therapy. Med Phys. 2010 Jun;37(6):2910–17. 106. Reft CS, Runkel-Muller R, Myrianthopoulos L. In vivo and phantom measurements of the secondary photon and neutron doses for prostate patients undergoing 18 MV IMRT. Med Phys. 2006 Oct;33(10):3734–42. 107. Wroe A, Clasie B, Kooy H, Flanz J, Schulte R, Rosenfeld A. Out-of-field dose equivalents delivered by passively scattered therapeutic proton beams for clinically relevant field configurations. Int J Radiat Oncol Biol Phys. 2009 Jan 1;73(1):306–13. 108. Olsher RH, Hsu HH, Beverding A, Kleck JH, Casson WH, Vasilik DG, et al. WENDI: an improved neutron rem meter. Health Phys. 2000 Aug;79(2):170–81. 109. Polf JC, Newhauser WD, Titt U. Patient neutron dose equivalent exposures outside of the proton therapy treatment field. Radiat Proect Dosim. 2005;115(1-4):154–58. 110. Zacharatou Jarlskog C, Lee C, Bolch W, Xu XG, Paganetti H. Assessment of organ specific neutron doses in proton therapy using whole-body age-­dependent voxel phantoms. Phys Med Biol. 2008;53:693–714.

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111. Anferov V. Analytic estimates of secondary neutron dose in proton therapy. Phys Med Biol. 2010 Dec 21;55(24):7509–22. 112. Gottschalk B. Neutron dose in scattered and scanned proton beams: in regard to Eric J. Hall (Int J Radiat Oncol Biol Phys 2006;65:1–7). Int J Radiat Oncol Biol Phys. 2006 Dec 1;66(5):1594; author reply 5. 113. Perez-Andujar A, Newhauser WD, Deluca PM. Neutron production from beammodifying devices in a modern double scattering proton therapy beam delivery system. Phys Med Biol. 2009 Feb 21;54(4):993–1008. 114. Athar BS, Paganetti H. Neutron equivalent doses and associated lifetime cancer incidence risks for head & neck and spinal proton therapy. Phys Med Biol. 2009 Aug 21;54(16):4907–26. 115. Zaidi H, Xu XG. Computational anthropomorphic models of the human anatomy: the path to realistic Monte Carlo modeling in radiological sciences. Annu Rev Biomed Eng. 2007;9:471–500. 116. Xu XG, Eckerman KF. Handbook of Anatomical Models for Radiation Dosimetry (Series in Medical Physics and Biomedical Engineering). CRC Press, Taylor & Francis; ISBN-10: 1420059793, ISBN-13: 978-1420059793. 2009. 117. Fontenot J, Taddei P, Zheng Y, Mirkovic D, Jordan T, Newhauser W. Equivalent dose and effective dose from stray radiation during passively scattered proton radiotherapy for prostate cancer. Phys Med Biol. 2008 Mar 21;53(6):1677–88. 118. Taddei PJ, Mirkovic D, Fontenot JD, Giebeler A, Zheng Y, Kornguth D, et al. Stray radiation dose and second cancer risk for a pediatric patient receiving craniospinal irradiation with proton beams. Phys Med Biol. 2009 Mar 20;54(8):2259–75. 119. Kellerer AM, Nekolla EA, Walsh L. On the conversion of solid cancer excess relative risk into lifetime attributable risk. Radiat Environ Biophys. 2001 Dec;40(4):249–57. 120. Walsh L, Ruehm W, Kellerer AM. Cancer risk estimates for gamma-rays with regard to organ-specific doses. Part I: All solid cancers combined. Radiat Environ Biophys. 2004;43:145–51. 121. Walsh L, Ruehm W, Kellerer AM. Cancer risk estimates for gamma-rays with regard to organ-specific doses. Part II: Site-specific solid cancers. Radiat Environ Biophys. 2004;43:225–31. 122. Preston DL, Ron E, Tokuoka S, Funamoto S, Nishi N, Soda M, et al. Solid cancer incidence in atomic bomb survivors: 1958-1998. Radiat Res. 2007 Jul;168(1):1–64. 123. EPA UEPA. Estimating radiogenic cancer risks. Addendum: Uncertainty analysis. EPA. 1999;402-R-99-003. 124. Kry SF, Followill D, White RA, Stovall M, Kuban DA, Salehpour M. Uncertainty of calculated risk estimates for secondary malignancies after radiotherapy. Int J Radiat Oncol Biol Phys. 2007;68(4):1265–71. 125. NCRP. Uncertainties in Fatal Cancer Risk Estimates Used in Radiation Protection. National Council on Radiation Protection and Measurements Report. 1997;126. 126. Little MP, Boice JD, Jr. Comparison of breast cancer incidence in the Massachusetts tuberculosis fluoroscopy cohort and in the Japanese atomic bomb survivors. Radiat Res. 1999 Feb;151(2):218–24. 127. Little MP, Weiss HA, Boice JD, Jr., Darby SC, Day NE, Muirhead CR. Risks of leukemia in Japanese atomic bomb survivors, in women treated for cervical cancer, and in patients treated for ankylosing spondylitis. Radiat Res. 1999 Sep;152(3):280–92.

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128. Ron E. Cancer risks from medical radiation. Health Phys. 2003 Jul;85(1):47–59. 129. Little MP. A comparison of the degree of curvature in the cancer incidence doseresponse in Japanese atomic bomb survivors with that in chromosome aberrations measured in vitro. Int J Radiat Biol. 2000 Oct;76(10):1365–75. 130. Little MP. Comparison of the risks of cancer incidence and mortality following radiation therapy for benign and malignant disease with the cancer risks observed in the Japanese A-bomb survivors. Int J Radiat Biol. 2001;77:431–64. 131. Brenner DJ, Doll R, Goodhead DT, Hall EJ, Land CE, Little JB, et al. Cancer risks attributable to low doses of ionizing radiation: assessing what we really know. Proc Natl Acad Sci USA. 2003 Nov 25;100(24):13761–66. 132. Mullenders L, Atkinson M, Paretzke H, Sabatier L, Bouffler S. Assessing cancer risks of low-dose radiation. Nat Rev Cancer. 2009 Aug;9(8):596–604. 133. Heidenreich WF, Paretzke HG, Jacob P. No evidence for increased tumor rates below 200 mSv in the atomic bomb survivors data. Radiat Environ Biophys. 1997 Sep;36(3):205–207. 134. Hall EJ, Henry S. Kaplan Distinguished Scientist Award 2003: the crooked shall be made straight; dose response relationships for carcinogenesis. Int J Radiat Biol. 2004;80:327–37. 135. Upton AC. Radiation hormesis: data and interpretations. Crit Rev Toxicol. 2001 Jul;31(4-5):681–95. 136. ICRP. Genetic Susceptibility to Cancer. International Commission on Radiological Protection (Pergamon Press). 1999;79(Annals of the ICRP Volume 28/1-2). 137. Joiner MC, Marples B, Lambin P, Short SC, Turesson I. Low-dose hypersensitivity: current status and possible mechanisms. Int J Radiat Oncol Biol Phys. 2001 Feb 1;49(2):379–89. 138. Wolff S. The adaptive response in radiobiology: evolving insights and implications. Environ Health Perspect. 1998 Feb;106 Suppl 1:277–83. 139. Ballarini F, Biaggi M, Ottolenghi A, Sapora O. Cellular communication and bystander effects: a critical review for modelling low-dose radiation action. Mutat Res. 2002 Apr 25;501(1-2):1–12. 140. Tubiana M. Dose-effect relationship and estimation of the carcinogenic effects of low doses of ionizing radiation: the joint report of the Academie des Sciences (Paris) and of the Academie Nationale de Medecine. Int J Radiat Oncol Biol Phys. 2005 Oct 1;63(2):317–19. 141. Brenner DJ. Extrapolating radiation-induced cancer risks from low doses to very low doses. Health Phys. 2009 Nov;97(5):505–509. 142. Han A, Elkind MM. Transformation of mouse C3H/10T1/2 cells by single and fractionated doses of X-rays and fission-spectrum neutrons. Cancer Res. 1979 Jan;39(1):123–30. 143. Heyes GJ, Mill AJ. The neoplastic transformation potential of mammography X rays and atomic bomb spectrum radiation. Radiat Res. 2004 Aug;162(2):120–27. 144. NCRP. Evaluation of the Linear-Nonthreshold Dose-Response Model for Ionizing Radiation. National Council on Radiation Protection and Measurements Report. 2001;136. 145. Redpath JL, Lu Q, Lao X, Molloi S, Elmore E. Low doses of diagnostic energy X-rays protect against neoplastic transformation in vitro. Int J Radiat Biol. 2003 Apr;79(4):235–40.

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146. Hooker AM, Bhat M, Day TK, Lane JM, Swinburne SJ, Morleya AA, et al. The linear no-threshold model does not hold for low-dose ionizing radiation. Radiat Res. 2004;162:447–52. 147. Calabrese EJ, Baldwin LA. Hormesis: the dose-response revolution. Annu Rev Pharmacol Toxicol. 2003;43:175–97. 148. Bhattacharjee D, Ito A. Deceleration of carcinogenic potential by adaptation with low dose gamma irradiation. In Vivo. 2001 Jan-Feb;15(1):87–92. 149. Ko SJ, Liao XY, Molloi S, Elmore E, Redpath JL. Neoplastic transformation in vitro after exposure to low doses of mammographic-energy X rays: quantitative and mechanistic aspects. Radiat Res. 2004 Dec;162(6):646–54. 150. Sasaki S, Fukuda N. Dose-response relationship for induction of solid tumors in female B6C3F1 mice irradiated neonatally with a single dose of gamma rays. J Radiat Res (Tokyo). 1999 Sep;40(3):229–41. 151. Wood DH. Long-term mortality and cancer risk in irradiated rhesus monkeys. Radiat Res. 1991 May;126(2):132–40. 152. White RG, Raabe OG, Culbertson MR, Parks NJ, Samuels SJ, Rosenblatt LS. Bone sarcoma characteristics and distribution in beagles fed strontium-90. Radiat Res. 1993 Nov;136(2):178–89. 153. Nasagawa H, Little JB. Unexpected sensitivity to the induction of mutations by very low doses of alpha-particle radiation: evidence for a bystander effect. Radiat Res. 1999;152:552–57. 154. Joiner MC, Lambin P, Malaise EP, Robson T, Arrand JE, Skov KA, et al. Hypersensitivity to very-low single radiation doses: its relationship to the adaptive response and induced radioresistance. Mutat Res. 1996;358:171–83. 155. Sawant SG, Randers-Pehrson G, Geard CR, Brenner DJ, Hall EJ. The bystander effect in radiation oncogenesis: I. Transformation in C3H 10T1/2 cells in vitro can be initiated in the unirradiated neighbors of irradiated cells. Radiat Res. 2001 Mar;155(3):397–401. 156. Brenner DJ, Little JB, Sachs RK. The bystander effect in radiation oncogenesis: II. A quantitative model. Radiat Res. 2001 Mar;155(3):402–408. 157. Seymour CB, Mothersill C. Relative contribution of bystander and targeted cell killing to the low-dose region of the radiation dose-response curve. Radiat Res. 2000 May;153(5 Pt 1):508–11. 158. Gregoire O, Cleland MR. Novel approach to analyzing the carcinogenic effect of ionizing radiations. Int J Radiat Biol. 2006 Jan;82(1):13–19. 159. Preston DL, Mattsson A, Holmberg E, Shore R, Hildreth NG, Boice JD, Jr. Radiation effects on breast cancer risk: a pooled analysis of eight cohorts. Radiat Res. 2002 Aug;158(2):220–35. 160. Zacharatou Jarlskog C, Paganetti H. The risk of developing second cancer due to neutron dose in proton therapy as a function of field characteristics, organ, and patient age. Int J Radiat Oncol Biol Phys. 2008;72:228–35. 161. Athar BS, Paganetti H. Comparison of the risk for developing a second cancer due to out-of-field doses after 6-MV IMRT and proton therapy. Radiother Oncol. 2011 Jan;98(1):87–92. 162. Meadows AT, Friedman DL, Neglia JP, Mertens AC, Donaldson SS, Stovall M, et al. Second neoplasms in survivors of childhood cancer: findings from the Childhood Cancer Survivor Study cohort. J Clin Oncol. 2009 May 10;27(14):2356–62. 163. Sachs RK, Brenner DJ. Solid tumor risks after high doses of ionizing radiation. Proc Natl Acad Sci USA. 2005 Sep 13;102(37):13040–45.

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164. Boice JD, Jr., Blettner M, Kleinerman RA, Stovall M, Moloney WC, Engholm G, et al. Radiation dose and leukemia risk in patients treated for cancer of the cervix. J Natl Cancer Inst. 1987 Dec;79(6):1295–311. 165. Gilbert ES, Stovall M, Gospodarowicz M, Van Leeuwen FE, Andersson M, Glimelius B, et al. Lung cancer after treatment for Hodgkin’s disease: focus on radiation effects. Radiat Res. 2003 Feb;159(2):161–73. 166. Curtis RE, Rowlings PA, Deeg HJ, Shriner DA, Socie G, Travis LB, et al. Solid cancers after bone marrow transplantation. N Engl J Med. 1997 Mar 27;336(13):897–904. 167. Blettner M, Boice JD, Jr. Radiation dose and leukaemia risk: general relative risk techniques for dose-response models in a matched case-control study. Stat Med. 1991 Oct;10(10):1511–26. 168. Curtis RE, Boice JD, Jr., Stovall M, Bernstein L, Holowaty E, Karjalainen S, et al. Relationship of leukemia risk to radiation dose following cancer of the uterine corpus. J Natl Cancer Inst. 1994 Sep 7;86(17):1315–24. 169. Lindsay KA, Wheldon EG, Deehan C, Wheldon TE. Radiation carcinogenesis modelling for risk of treatment-related second tumours following radiotherapy. Br J Radiol. 2001 Jun;74(882):529–36. 170. Wheldon EG, Lindsay KA, Wheldon TE. The dose-response relationship for cancer incidence in a two-stage radiation carcinogenesis model incorporating cellular repopulation. Int J Radiat Biol. 2000 May;76(5):699–710. 171. Dasu A, Toma-Dasu I. Dose-effect models for risk-relationship to cell survival parameters. Acta Oncol. 2005;44(8):829–35. 172. Schneider U. Mechanistic model of radiation-induced cancer after fractionated radiotherapy using the linear-quadratic formula. Med Phys. 2009 Apr;36(4):1138–43. 173. Schneider U, Kaser-Hotz B. Radiation risk estimates after radiotherapy: application of the organ equivalent dose concept to plateau dose-response relationships. Radiat Environ Biophys. 2005 Dec;44(3):235–39. 174. Schneider U, Zwahlen D, Ross D, Kaser-Hotz B. Estimation of radiation-induced cancer from three-dimensional dose distributions: Concept of organ equivalent dose. Int J Radiat Oncol Biol Phys. 2005 Apr 1;61(5):1510–15. 175. Schneider U, Lomax A, Timmermann B. Second cancers in children treated with modern radiotherapy techniques. Radiother Oncol. 2008 Nov;89(2):135–40. 176. Schneider U, Kaser-Hotz B. A simple dose-response relationship for modeling secondary cancer incidence after radiotherapy. Z Med Phys. 2005;15(1):31–37. 177. Schneider U, Lomax A, Besserer J, Pemler P, Lombriser N, Kaser-Hotz B. The impact of dose escalation on secondary cancer risk after radiotherapy of prostate cancer. Int J Radiat Oncol Biol Phys. 2007 Jul 1;68(3):892–97. 178. Schneider U, Walsh L. Cancer risk estimates from the combined Japanese A-bomb and Hodgkin cohorts for doses relevant to radiotherapy. Radiat Environ Biophys. 2008 Apr;47(2):253–63. 179. Schneider U, Besserer J, Mack A. Hypofractionated radiotherapy has the potential for second cancer reduction. Theor Biol Med Model. 2010;7:4–11. 180. Sachs RK, Shuryak I, Brenner D, Fakir H, Hlatky L, Hahnfeldt P. Second cancers after fractionated radiotherapy: stochastic population dynamics effects. J Theor Biol. 2007 Dec 7;249(3):518–31.

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19 The Physics of Proton Biology Harald Paganetti CONTENTS 19.1 Introduction................................................................................................. 593 19.2 Mechanisms of Radiation Action............................................................. 594 19.2.1 DNA Damage.................................................................................. 594 19.2.2 Energy Deposition Events and DNA Damage........................... 595 19.2.3 Ionization Event Distribution and Lesion Complexity............. 596 19.3 Dose–Response Relationships.................................................................. 597 19.4 The Relative Biological Effectiveness.......................................................600 19.5 Rationale for the Clinical Use of 1.1 as Proton RBE...............................600 19.6 Variations of RBE........................................................................................ 602 19.6.1 LET Dependency of RBE................................................................ 602 19.6.2 Dose Dependency of RBE..............................................................606 19.6.3 Endpoint Dependency of RBE .....................................................606 19.7 Modeling Cellular Radiation Effects.......................................................608 19.8 Biophysical Models of Radiation Action on Cells.................................. 609 19.8.1 LET-Based Models..........................................................................609 19.8.2 Microdosimetric Models................................................................609 19.8.3 Lesion Interaction Models............................................................. 610 19.8.4 Lesion Induction and Repair Models........................................... 611 19.8.5 Track Structure Models.................................................................. 613 Acknowledgments............................................................................................... 617 References.............................................................................................................. 617

19.1  Introduction There is no simple relationship between dose and biological effect. Even the exact knowledge of the underlying energy deposition (i.e., the macroscopic physics) might not be sufficient to predict the effect of radiation on tissues, as is evidenced by the fact that different radiation modalities show different dose–response relationships. The reason for using dose as a clinical prescription is our lack of understanding of biological effects and the fact that we base treatments on clinical experience with specific dose levels. 593

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Some biological aspects are discussed in this chapter. A detailed discussion of subcellular mechanisms, repair pathways, and genetic effects of radiation damage and repair is beyond the scope of a book on proton therapy physics. Radiation action on living cells is a complex sequence of physical, biochemical, and physiological events.

19.2  Mechanisms of Radiation Action 19.2.1  DNA Damage Radiation interacts with tissue atoms. Ionizations lead to cellular and then to molecular effects. Radiation also causes molecules to go into excited states leading to vibrations producing heat. In fact, more than 95% of the energy in radiation therapy goes into heat. Nevertheless, the most important impact of radiation is caused by ionizations. The cell nucleus with a diameter of typically about 10 μm contains the main genetic information within the double-helical DNA macromolecules. The DNA resembles the biggest target although its diameter of about 2 nm (and a length of about 2 m) accounts for only a few percent of the total mass of the nucleus. The rest is composed of other structures, particularly water. Although all molecules in the cell are affected by ionizing radiation, there is substantial evidence that damage to the DNA molecules is the decisive lesion for mutation induction, carcinogenic transformation, and killing of most cell types. Aside from damage to other cellular structures, DNA damage is directly related to cell death. Although there are multiple copies of most molecules and those are undergoing fast turnover, only two copies exist of the DNA, and the turnover is limited. DNA is central to all cellular functions. The initial damage caused by a proton would typically be a strand break. If DNA strand breaks are in close proximity it can cause double-strand breaks (DSBs) either directly or during the strand break repair process. Only a small portion of the initial biochemical damage leads to a cellular effect because the damage is either nonsignificant or can be repaired. Damaged DNA undergoes transformations that invoke different repair mechanisms. Unrepaired DSBs lead to the dysfunction and loss of genetic material. Pieces of DNA may join to form chromosomal aberrations, which can cause cell death. The term cell death is usually used for loss of reproductive capacity, although this definition might not be relevant for all cell types and tissues. For some cell types, apoptosis or programmed cell death may also be initiated by damage to the cell membrane. Although cell death via necrosis increases exponentially with increasing dose, induction of apoptosis saturates with increasing dose.

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19.2.2  Energy Deposition Events and DNA Damage If an electron originating from an ionization event has enough energy to cause further ionizations, it is called a δ-electron. For protons with energy between ~0.5 and ~100 MeV, ~70% of the energy lost is transferred to and then transported by secondary electrons, ~25% is needed to overcome their binding potential, and the residual 5% produces neutral excited species (1). Each photon or proton track is associated with δ-electrons of widely different energies. Therefore, the spatial pattern of energy deposition is complex. There are ionizations and excitations that can be considered independently as well as clusters of ionizations and excitations caused by track-ends of lowenergy δ-electrons. Ionizations in water are responsible for the type of damage that leads to chemical reactions threatening the DNA via highly reactive radicals (indirect effects). This has to occur within a few nanometers of the DNA, that is, within the diffusion distance of the radicals. In addition, radiation can cause lethal damage from the direct deposition of energy (direct effects) in the DNA. For low-LET (linear energy transfer) radiation, effects are caused mainly via δ-electrons creating free radicals. Direct hits become more pronounced at higher LET. Figure 19.1 illustrates different interaction channels. The number of energy depositions per cell per Gray is quite substantial. Assuming a 100-keV electron, there will be more than ~500 energy deposition events with energies larger than 10 eV in a 6-nm2 target but less than 10 with energies larger than 150 eV (2). Table 19.1 shows the approximate number of events in a mammalian cell following different radiation fields after a dose of 1 Gy (3, 4). Interestingly, the number of ionizations per cell nucleus is about the same. Even the initial yield of DSBs shows little variation with ionization density. Importantly, the number of residual breaks at 8 h after cellular repair substantially differs. The same number of initial DSBs gives rise to a substantially larger number of chromosome aberrations after high-LET ~ 2 mm direct

indirect

OH*

H H

O

~ 2 nm FIGURE 19.1 Direct and indirect (via diffusion of free radicals) radiation effects on the DNA. The dashed lines show two potential particle paths leading to the two interaction types. The insert illustrates the size of a proton track with ionization events and δ-electrons (white tracks).

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TABLE 19.1 Average Yield of Damage in a Single Mammalian Cell after 1 Gy Delivered by Photons (low-LET) or Low-Energy α Particles (high-LET) Radiation

Low-LET

High-LET

Tracks in nucleus Ionizations in nucleus Ionizations in DNA Base damage DNA single-strand break DNA double-strand breaks (initially) DNA double-strand breaks (after 8 h) Chromosome aberrations Complex aberrations Lethal lesions Cells inactivated

1000 105 1500 104 700–1000 18–60 6 0.3 10% 0.2–0.8 10–50%

2 105 1500 104 300–600 70 30 2.5 45% 1.3–3.9 70–95%

The assumed nucleus has a diameter of 8 μm, and the energy deposition per ionization is set to 25 eV. Source: Adapted from Goodhead, Can J Phys., 68 ,872, 1990; and Nikjoo et al., Int J Radiat Biol., 73, 355, 1998.

versus low-LET irradiation. Furthermore, higher-LET radiation increases the frequency of complex aberrations. 19.2.3  Ionization Event Distribution and Lesion Complexity The number of initial DSBs is not directly proportional to cellular damage. The number of DSBs per cells typically increases with dose linearly (Figure 19.2). Even if two different modalities, for example, photons and protons, cause the same number of DNA DSBs per unit dose, the distribution of the DSBs can differ substantially. It is not so much the type of DSBs but the spatial distribution of DNA lesions within the cell that determines radiation effects (5). The key to understanding radiation effects lies in the spatial distribution of energy deposition events and the complex lesions this may cause. The spatial distribution of lesions might be random for low-LET radiation but follows more closely specific particle tracks at high-LET values (6). With increasing LET more DSBs are predicted within dimensions of several base pairs (7). Clustering of radiation damage is assumed to be responsible for the effectiveness of high-LET radiation (7, 8). Lesion complexity is not restricted to DSB but can also involve single-strand breaks. It can involve more than two strand breaks (9) or damage enhanced by damaged bases. Thus, lesions from protons might be more complex than those from photons (10). This complexity increases with LET due to higher energy delivered in direct hits (5, 11–13) together with an LET dependence of the DSB repair kinetics (14–16). The resulting cluster of strand breaks that are more concentrated in space and the associated damage is believed to render the lesions less amenable

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10000

DSBs per cell

1000 100 10 1 0.1 0.01 0.001

0.01

0.1 1 Dose (Gy)

10

100

FIGURE 19.2 DSB induction in MRC-5 cells showing a rate of approximately 35 DSBs per cell per Gray. (From Rothkamm and Loebrich, Proc Natl Acad Sci USA, 100, 5057, 2003. With permission.)

to repair, or, rather, to competent repair (17). Furthermore, clustered strand breaks increase the likelihood of mis-joining, which can cause chromosome aberrations. The importance of understanding lesion complexities and repair mechanisms in order to understand radiation effects is illustrated by the fact that the difference between protons and photons with respect to DSB induction as a function of dose is smaller than the one for cell reproductive death or chromosomal aberrations (18). Cell kill and cell mutation show different dependencies on dose and energy deposition pattern. Because repair depends on the spatial distribution of lesions (19), one interesting consequence might be that the difference in radiation sensitivity among different cell lines might be, at least in part, due to different spatial orientation of the DNA.

19.3  Dose–Response Relationships If we assume a single particle crossing a radiosensitive volume and no variation in energy deposition characteristics, Poisson statistics define the mean number of effective hits per unit dose. The probability of finding a nucleus with ω lethal events if an average of Ω lethal events per nucleus is produced in the whole population is



P(ωΩ) =

Ωω exp(− Ω). ω!

(19.1)

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Because only cells without lethal events will survive, the survival probability as a function of absorbed dose, D, with N0 being the initial number of cells and N being the number of unaffected cells, is given as



N (D) = P(0, Ω ) = exp ( −Ω( D) ) . N0

(19.2)

The response of a biological system to dose is typically visualized in a doseresponse curve, for example, cell survival as a function of dose. Cell survival curves represent the number of cells that have lost the ability for unlimited proliferation. The assumption that there are individual single targets requiring a single hit (i.e., that it requires one hit by a particle to inactivate a sensitive area) would result in a straight line on the logarithmic dose-response plot. However, the dose-response relationship typically results in a sigmoidal curve. A linear-quadratic parameterization is the simplest mathematical formulation to fit most survival curves (20, 21):



N (D) = exp ( − αD − βD2 ) . N0

(19.3)

Accordingly, a biological effect can be defined as (with either the dose D delivered at once or in n fractions of d):

(

)

E(D) = αD + βD2 = n αd + βd 2 .

(19.4)

The linear quadratic form of the cell survival curve could be due to dual lesion interactions (e.g., two particles from two tracks, leading to a quadratic term in dose) or because of competing effects in lesion induction linear with dose and the dose-dependent depletion of repair enzymes. The likelihood of radiation lesion from two tracks occurring at a short distance from each other is quite small within the dimensions of the DNA molecule. Consequently, biophysical models that include repair have been more successful in interpreting experimental results (see Section 19.7). Figure 19.3 shows two dose-response curves. The curvature, or shoulder, of a survival curve can be interpreted based on lesion repair capacity or lesion induction mechanisms, that is, by the α/β ratio. For a given end point, the dose-response curves from proton radiation are steeper than the ones from photon radiation, indicating perhaps that the likelihood for repair of lesions is decreasing. If the proton energy is decreasing, that is, increasing LET, the response curve becomes steeper (reduction of the width of the shoulder of the response curve) up to a limit after which it may be reversed (see Section 19.6.1). Specifically, α typically increases with increasing LET, whereas β is not significantly affected (22–25).

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1

N/N0

0.1

0.01

0.001

0

1

2

3 4 Dose (Gy)

5

6

FIGURE 19.3 Example of two dose-response curves. The solid line might resemble the response after photon irradiation, and the long dashed line might be caused by low-energy proton irradiation. The relative biological effectiveness (RBE) at 10% survival would be ~2.55/1.3 = 1.96, whereas at 1% survival it would be ~4.15/2.4 = 1.73 (short dashed lines).

A more general form of the linear-quadratic equation also takes into account the dose rate and time-dependent repair. It can be written including the Lea-Catcheside dose protraction factor, G (26):

N (D) = exp ( − αD − βGD2 ) . N0

(19.5)

The dose-response relationship is not simply related to killing a fraction of a given number of cells. The linear-quadratic equation is only an approximation to a more general description using a number of sensitive sites in a cell nucleus, which in contrast to the pure linear-quadratic formulation has an exponential asymptote for high doses (27, 28). The linear-quadratic formalism is typically only valid roughly in the dose region from ~1 to ~10 Gy (depending on the end point), and when fitting α and β to a response curve, one has to keep in mind that the result may depend on the dose range considered (29, 30). Although the linear-quadratic function is the most common in radiation therapy, dose–response curves can also be described with other mathematical equations, for example, the multitarget/single-hit equation with the parameters D0 (intrinsic radiosensitivity) and n. The parameter n is the extrapolation number representing the ability to accumulate and repair sublethal damage: n



  D  N = 1 −  1 − exp −   . N0  D0   

(19.6)

When interpreted mechanistically, the multitarget formalism assumes that from a collection of targets in the cell nucleus, n have to be hit at least k times each to inactivate the cell (k is set equal to 1 in the equation above).

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19.4  The Relative Biological Effectiveness Protons are more biologically effective than photons, that is, a lower dose is required in order to cause the same biological effect. The relative biological effectiveness (RBE) of protons is defined as the dose of a reference radiation, Dx, divided by the proton dose, Dp, to achieve the same biological effect (see Figure 19.3): RBE(endpoint) =

Dx . Dp

(19.7)



The RBE adjusted dose is defined as the product of the physical dose and the respective RBE. The prescribed dose to the target, dose constraints to critical structures, and fractionation schemes are largely based on clinical experience gained mostly by treating patients with photon beams. For consistency in the clinic and in order to benefit from the large pool of clinical results obtained with photon beams, prescription doses are defined as photon doses. Proton therapy patients receive a 10% lower prescribed dose than would be prescribed using photons, thus assuming an RBE of 1.1. Before 2008 proton doses were given in Cobalt Gray Equivalent (CGE), and then it was changed to reporting DRBE as Gy(RBE) (31). Because the RBE is defined for a given level of effect, one can easily deduce the RBE for a given proton dose as a function of the proton, p, and reference, x, radiation parameters from the linear-quadratic dose-response relationship:



(

)

RBE Dp , αx , β x , α p , β p =

(

)

α2x + 4β x Dp α p + β p Dp − αx 2 β x Dp

.

(19.8)

Note that for treatment-planning considerations not only the total dose but also fractionation needs to be taken into account. Fractionation effects (32, 33) are beyond the scope of this chapter and are, by definition, not included in the RBE formalism.

19.5  Rationale for the Clinical Use of 1.1 as Proton RBE Proton therapy is based on the use of a single RBE. The value of 1.1 is mainly based on animal experiments performed in the early days of proton therapy (34–37). There are obvious advantages of using a generic RBE. Converting photon doses into proton doses for clinical trials is straightforward. Furthermore, clinical dosimetry is based on homogeneous dose distributions in the target.

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On the other hand, a generic value disregards the dependencies of the RBE on various physical and biological properties (e.g., proton beam energy, depth of penetration, biological endpoint, dose per fraction, position in the spread-out Bragg Peak [SOBP], and particular tissue). It is well-known that the RBE is not a constant, but there are no clinical data indicating that the use of a generic RBE of 1.1 is unreasonable (i.e., that it leads to unexpected side effects). On the other hand, clinical data cannot confirm that the RBE of 1.1 is correct because not only the effect but also the dose distributions differ between photon and proton irradiations. As shown in Figure 19.4 for in vivo and in vitro data, measured proton RBE values show significant variations of the RBE (38). The measured RBE values using colony formation as the measure of cell survival in vitro indicate a substantial spread between the diverse cell lines (38). The average value at mid-SOBP over all dose levels is about 1.2, ranging from 0.9 to 2.1. The average RBE value at mid-SOBP in vivo is about 1.1, ranging from 0.7 to 1.6 (38). The majority of RBE studies have been done with in vitro systems and V79 cells inhibiting a low α/β ratio, whereas most of the in vivo studies were performed in early-reacting tissues with a high α/β ratio. Importantly, the magnitude of RBE variation with physical or biological parameters is usually small relative to our abilities to determine RBE values. The required number of animals to measure a 5% RBE difference (1.10 vs. 1.15) for one endpoint can be several hundred (38). To implement RBE variations in treatment planning, we need to understand the relationships between LET, dose, and biological endpoint. Systematic quantitative statements regarding therapeutic situations are still difficult because of the experimental uncertainties, the specific experimental arrangements used, and the different biological endpoints chosen in the experiments. At present, there seems to be too much uncertainty in the RBE value for any human tissue, for example, to propose RBE values specific for tissue, dose/fraction, and proton energy. 2.5

2.5

in vitro

2.0 RBE

RBE

2.0 1.5 1.0 0.5

in vivo

1.5 1.0

1

Dose (Gy)

10

0.5

1

Dose (Gy)

10

FIGURE 19.4 Experimental proton RBE values (relative to 60Co) as a function of dose/fraction for cell inactivation measured in vitro (left) and in vivo (right). (From Paganetti et al., Int J Radiat, Oncol, Biol Phys., 53, 407, 2003. With permission.)

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19.6  Variations of RBE 19.6.1  LET Dependency of RBE The LET is the energy transferred to the absorbing medium per unit track length of the particle. Note that the region of maximum energy transfer is not occurring at the Bragg peak but downstream of the Bragg peak (Figure 19.5). The reason for the Bragg peak is a combination of LET and decreasing proton fluence. Biologically, the increase in LET can cause an increase in both the amount of damage and its complexity. Both can influence the ability of the cellular system to repair itself, either because of the frequency or the severity of damage. When describing energy loss on a cellular level, the LET concept is only a crude approximation because the track structure and micro- or even nanodosimetric effects play a role. The LET is a macroscopic rather than microscopic parameter and deals with energy loss per unit path length rather than energy loss in subcellular volumes. At a given LET protons are in fact more effective than carbon ions (5, 25, 39). This is because protons have smaller track radii (as defined by the range of δ-electrons), implying higher ionization density in the submicrometer range, ultimately leading to more complex and potentially clustered DSBs (40). Radiation is more effective per unit dose when the energy deposition is more concentrated in space. Figure 19.6 shows how the dose is distributed in a cell. Because of the huge number of tracks and ionization events to deliver 1 Gy of low LET photon irradiation, the distribution is basically homogeneous. For a given particle (e.g., a proton) it becomes more and more heterogeneous as the energy deposition per path length increases. 16

100% Dose [arbitrary units]

LET [keV/µm]

14 12 10 8 6 4 2 0

0

50

100 Depth [mm]

150

200

FIGURE 19.5 Dose (dotted line; right axis scale) and dose-averaged LET (left axis scale) as a function of depth in a water phantom for a 160-MeV beam. The dashed line shows the total dose-averaged LET (primary and secondary particles), and the solid line shows the dose-averaged LET for the primary protons only.

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100 80 60 40 20 0

0.1

1 10 Maximum dose [Gy]

100

FIGURE 19.6 Dose distribution within a cell after photon and proton irradiation. The graph shows the integral dose distribution for 5-MeV protons at a macroscopic dose of 3 Gy (solid line), 5 Gy (longdashed line), and 7 Gy (short-dashed line). Also shown are the limits for infinitesimal low-LET for 3, 5, and 7 Gy (dashed-dotted). (From Paganetti, Med Phys., 32, 2548, 2005. With permission.)

Considering one particle type only, the RBE increases with increasing LET up to a certain maximum (3). If the LET is further increased, far fewer tracks are required to deposit the same dose. This leads to saturation of the effect in small regions and eventually to a decrease of RBE with increasing LET. For protons, the maximum RBE occurs at extremely low proton energies where the contribution to the dose in a clinical scenario is negligible. Thus, we can safely assume that RBE increases with LET, with the slope depending on the biological endpoint. Low-energy protons can have high RBE values (24, 41–50). RBE values for cell survival for near-mono-energetic proton beams of <8.7 MeV are presented in Figure 19.7. These low-energy protons contribute 5

RBE

4 3 2 1 1

Proton energy [MeV]

10

FIGURE 19.7 Experimental RBE values (relative to 60Co; various dose levels) as a function of proton energy for cell inactivation measured in vitro for near mono-energetic protons. Open circles refer to human tumor cell lines at 2 Gy. (From Paganetti et al., Int J Radiat, Oncol, Biol Phys., 53, 407, 2003. With permission.)

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typically less than ≈1% to the total dose within an SOBP but illustrate the LET dependency nicely. Because of protons slowing down, the LET increases, resulting in an increasing RBE with depth in an SOBP (23, 51–64). The results of a study using a 70-MeV 2.5-cm SOBP beam with a high-precision cell sorter assay system are shown in Figure 19.8 (64). The RBE clearly increases with increasing depth. One might expect, on average, an increase in RBE of ≈5% at 4 mm and ≈10% at 2 mm from the distal edge, relative to the mid-SOBP RBE (38). Although difficult to measure in vivo, an increase of RBE with depth has been seen using mouse thorax and gut. The increase in LET at the end of range (i.e., at the Bragg peak and beyond) is more pronounced in pristine Bragg curves than in SOBPs because of the contribution of several pristine peaks and the mix of proton energies (63, 65). a

RBE

1.6 80% Survival 50% Survival 3% Survival

1.4 1.2

LET (keV/µm)

1.0

b

8 6

Doseaveraged LET

4 2

Relative dose

0

c

1.0

Spread-out Bragg peak Calculated Bragg peak Measured Bragg peak

0.8 0.6 0.4 0.2 0.0

0

5

10

15 20 25 30 Depth (mm of H2O)

35

40

45

FIGURE 19.8 (a) Proton RBE for different cell survival levels of V79 Chinese hamster cells measured in an SOBP. (b) Dose-averaged LET as a function of depth in the SOBP. (c) Depth–dose distribution at position of cell samples ( ). (From Wouters et al., Radiat Res., 146, 159, 1996. With permission.)

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Furthermore, there can be additional dilution in the patient because of frequent interfaces between different materials in the beam path and significant scatter in the bone. At the trailing edge of the distal most Bragg peak of the SOBP, the dose falls very rapidly with increasing depth. The rise in LET and RBE results in an extension of the biologically effective range by 1-2 mm (23, 51, 57–59, 61, 64, 66). Although there is a greater absolute RBE effect for lower-energy beams, this shift is smaller because of the sharper falloff (58). The clinical consequence of the increasing RBE and the uncertainty of the distal edge position of the Bragg peak is the avoidance of beams that place the distal edge close to critical structures. LET distributions in a patient geometry can be calculated with analytical methods (67), using interpolations based on Monte Carlo calculations in homogeneous media (68) or using Monte Carlo simulations in a patient CT geometry (see Chapter 9) (69). For the dose-averaged LET (LETd), the LET is averaged in such a way that the contribution of each particle is weighted by the dose it deposits. This concept is valid for proton beams where the number of particle tracks crossing a subcellular structure is quite large (70). However, one should keep in mind that, for high-LET ion beams, the number of tracks per subcellular target may be much smaller and the track averaged LET might become more meaningful. This illustrates the limitations of the LET concept when, at low fluence, the track structure becomes increasingly important (71). Figure 19.5 shows distributions of dose and LETd in a water tank, whereas Figure 19.9 illustrates the distributions in a patient. LETd values in patient geometries can be more than 10 keV/μm in the distal falloff, but only between 1.5 and 4 keV/μm in the target, using typical beam arrangements (69). 6 5

100%

4 3 2 1

FIGURE 19.9 (See color insert.) Dose distribution and distribution of dose-averaged LET (LETd) for an intensity-modulated proton therapy (IMPT) treatment plan. The contour for the GTV is shown in blue. Right: dose in percent of prescribed dose. Left: LETd distribution in keV/μm. The LET distribution is a potential measure of biological effectiveness. See (69) for more details.

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19.6.2  Dose Dependency of RBE Because of the more pronounced shoulder in the x-ray survival curve compared to the proton survival curve (Figure 19.3), the RBE depends on dose; for example, the RBE is higher at a cell survival level of 80% than at 3% (64). Both in vitro and in vivo data indicate a statistically significant increase in RBE for lower doses per fraction (38). Specifically, there is experimental evidence that RBE increases with decreasing dose for cell survival (51, 52, 62, 64, 72) and for induction of dicentrics (73). The RBE increases more rapidly with decreasing dose for late-responding tissues (low α/β) compared to early-responding tissues (high α/β) (74). No dose dependency is seen for cells that inhibit a linear dose-response curve. Figure 19.10 shows the RBE as a function of dose for the inactivation V79 cells in vitro. Most experimental RBE studies in vivo have used large doses for which an RBE effect may be expected to be minimal. 19.6.3  Endpoint Dependency of RBE The RBE is defined for a given level of effect. There is a difference between the radiation response of normal and malignant cells due to differences in repair mechanisms and cell repopulation. Furthermore, there is greater resistance to radiation in regions of low oxygen that are often found in tumors, hindering the creation of free radicals (Figure 19.1). At the same time, there is an increased repair capacity in the presence of oxygen because the damage from free radicals can be fixed in the presence of oxygen. The latter plays a role in high-LET radiation therapy with an increased likelihood of direct actions influencing the oxygen-enhancement ratio (75). Many different endpoints can be scored based on radiation damage, for example, 2.0

RBE

1.8 1.6 1.4 Total Proximal Distal Distal edge

1.2 1.0

0

2

4

6

8

10

12

Proton dose [Gy] FIGURE 19.10 Proton RBE as a function of dose for cell survival levels of V79 Chinese hamster cells measured at different positions in an SOBP. (From Wouters et al., Radiat Res., 146, 159, 1996. With permission.)

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inactivation (cell survival) and chromosomal aberrations or mutations. For assessing the biological effectiveness in the target, one is mainly interested in the RBE for cell death. Other effects are also important, in particular when considering organs at risk that might not receive sufficient dose to cause significant cell inactivation. RBE values for cell death and mutation have been compared, and most studies find that the RBE values are comparable. For example, the RBE for mutation at the HGPRT locus at various proton energies was found to be approximately equal compared to cell killing the LET for protons at the maximum mutation induction in the range of 25–30 keV/µm (76, 77). The dependency of the RBE on the α/β ratio has been studied using experimental data (74) and theoretical models (29). RBE for late damage seems to be higher than for early damage (78). Figure 19.11 shows theoretical RBE values plotted as a function of the tissues’ α/β. A strong tendency toward an increased RBE in cells exhibiting smaller α/β ratios is apparent at the lower dose levels. Thus, the biggest variation in RBE can be expected in lateresponding normal tissues. This in turn predicts an advantage of proton therapy when treating, for example, prostate carcinoma (79), but it might also increase the risk for side effects for other treatment sites if the spinal cord, another tissue with a low α/β ratio, has to be partially irradiated to achieve sufficient tumor coverage. Differences seen between in vivo and in vitro (Figure 19.4) are most likely due to the different endpoints used in the experiments (i.e., the larger shoulder seen in the survival curves for the endpoints used in vitro). In vitro studies have predominantly used Chinese hamster ovary and especially V79 cells, which exhibit large shoulders on their x-ray response curve and low α/β ratios. Most in vitro experiments use as their endpoint the killing of single cells of one cell population (colony formation). On the other hand, most in vivo RBE studies have used early-reacting tissues having a high 2.4 2.2 RBE

2.0 1.8 1.6 1.4 1.2 1.0

0

2

4

6 8 α/β [Gy]

10

12

14

FIGURE 19.11 Calculated RBE values as a function of α/β for 2 Gy ( ) and 6 Gy ( ). RBE values were determined in the middle of the SOBP or averaged over the entire SOBP. (From Paganetti et al., Int J Radiat Biol., 76, 985, 2000. With permission.)

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α/β ratio. The in vivo response reflects the more complex expression of the integrated radiation damage to several tissue systems and various biological processes (e.g., mutation). Figure 19.7 shows the RBE measured in vitro for low-energy protons on human tumor cell and V79 Chinese hamster cell data. In the studies with low-energy beams, the data on human cells (41, 46) are significantly lower than the RBE values determined for hamster cells (24, 42, 48, 49, 80, 81).

19.7  Modeling Cellular Radiation Effects The frequencies of energy deposition by protons in small subcellular targets have been studied extensively (82–86), for example, using Monte Carlo (see Chapter 9). Subsequently, there are chemical processes, biochemical processes, and finally, a macroscopic cellular response leading to a molecular response. Of particular interest is the impact of radiation damage on the DNA macromolecule and subsequent cellular response. At the DNA level, the energy deposition events are extremely nonuniform, depending on the properties of the incident ionizing particles. Even a complete understanding of the energy deposition events may give only limited insight into the biological consequences because of the different types of direct and indirect reactions that can lead to radiation-induced effects and the complicated repair phenomena. Most experimental data only give a macroscopic view. Biophysical models relate the biological effect of ionizing radiation to the physical properties of the incident radiation field. Modeling radiation action mechanistically is difficult because the radiation field can be complex with primary and secondary particles and because the biological target (i.e., the cell nucleus containing the DNA molecule) is highly structured. Mechanistic approaches to DNA damage and early chemistry have made much progress in describing the initial events produced by radiation (87), but no truly mechanistic model exists for describing biological endpoints such as cell killing (88). Most models are in fact mechanistic when considering the underlying physics but take a phenomenological approach toward the biology. Some of the model assumptions, in particular the ones on hypothetical cellular subtargets, are rather unrealistic. Furthermore, the definitions of lesions or sublesions are often a mathematical necessity rather than a description of true biological phenomena. The knowledge about subcellular physics certainly exceeds the knowledge about subcellular or molecular biological mechanisms. Biological model parameters are typically obtained from cell survival experiments because models are typically based on the description of the shoulder in the dose-response curve caused by the interaction of sublesions

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and/or by repair kinetics (89, 90). Some assume a nonlinear increase of lesions or certain kinds of repair saturation where the shape of the survival curve is determined by a dose-dependent rate of repair. The following section gives a brief, but not comprehensive, overview of some of the models.

19.8  Biophysical Models of Radiation Action on Cells 19.8.1  LET-Based Models The LET is a macroscopic parameter and does not take into account the track structure. Nevertheless, LET-based models, although entirely phenomenological, can be a valuable approximation because they can be based on only a few parameters. To calculate dose-averaged LET distributions, analytical functions (67) or Monte Carlo calculations (69) can be used. The biological part is described by the linear quadratic dose-response curve. Unfortunately, not many α and β values for relevant tissues in vivo are known. Most experimental data in vitro are based on V79 (low α/β ratio, i.e., ~2 Gy) and SQ20B and C3H10T1/2 cells (high α/β ratio, i.e., ~10 Gy). One solution is to use a linear relationship between LET and the α value, for example, of the following form:

α = α 0 + λLETd .



(19.9)

One might assume that β is independent of LET (63, 91–93), which is motivated by experimental data (22, 23, 25). By knowing α and β from photon data and as a function of LET, one can thus predict the cell survival curve and the RBE. For mixed radiation fields (e.g., for broad proton energy distribution) dose-averaged means of α and √β have to be applied. A related phenomenological approach is to combine measured RBE values from various low-energy proton beams with the proton energy distribution as a function of location in the irradiated volume (94). 19.8.2  Microdosimetric Models In the framework of microdosimetry a radiation field is characterized by energy deposition in a small subcellular volume, that is, by the energy imparted, z. Dose is related to the probability density function of z in a set of cellular targets. Another important parameter is the frequency distribution of the energy deposited, y. It is the energy deposited in a volume divided by the mean chord length and is related to the macroscopic quantity of LET. Note that LET is defined for a track segment, whereas the lineal energy y considers energy deposition in a volume. The microdosimetric

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quantities, energy imparted and lineal energy, are both measureable in small proportional counters with low-density gas mimicking micrometer volumes (see Chapter 7). Microdosimetric models are purely phenomenological. The biological effect is described by experimentally determined response functions (56, 72, 95–97). A response function describes a cumulative probability that a subcellular target structure will respond to a specific target-averaged ionization density (96). A microdosimetry spectrum (e.g., the measured dose distribution in lineal energy d(y)) can be convolved with a biological response function r(y) to obtain biological effectiveness as a function of y (59, 96–99):

RBE( y ) = ∫ r( y )d( y )dy.



(19.10)

The response functions can be obtained experimentally by measuring biological effect as a function of y. The concept finds application in radiation protection (100). The initial formalism of the model was valid only for single-event distributions, that is, interactions of a single particle track with the sample volume. This limits the concept to low doses and low dose rates. The formalism can also be extended to include multiple events. Although phenomenological, the model is convenient because both the biological part (i.e., dose-response curves) and the physical part (i.e., microdosimetric energy loss spectra) are measurable (53, 56, 72, 101). This, for example, makes the model suitable for intercomparison studies of relative effect between proton therapy installations (53, 59, 99). 19.8.3  Lesion Interaction Models Lesion interaction models, for example, the dual radiation action model (DRA) (102), represent a step further toward mechanistic description of radiation action. The assumption is that nonlethal sublesions are produced proportional to the energy absorbed in a radiosensitive volume, z. Lesion production is then proportional to z2. This theory is linked to microdosimetry because the radiosensitive volume can be associated with a microdosimetric volume and the energy imparted in it, z1D (i.e., the dose-mean specific energy for a single event). The model results in linear-quadratic dose-response relationships of the following form (with a constant k):



(

)

N = exp − k  z1D D + D2  . N0

(19.11)

Initially, the model assumed that a pair of sublesions could interact with constant probability if within a distance of ~0.4 μm. This lead to RBE values exceeding those seen experimentally specifically at low doses and for

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high-LET radiation. Furthermore, lesions were seen experimentally that could not be related to long-range sublesion interactions. Consequently, the model was refined by introducing a sublesion interaction probability that depends on the distance between sublesions (103, 104). Thus, the generalized DRA uses a distance model, whereas the original approach was a site model. A shortcoming of the concept is the fact that the interaction of two sublesions is extremely unlikely at typical dose levels because of the low probability of two independent particle tracks causing a single-strand break in close enough proximity to form a DSB. It is more likely that a single track causes clustered damage. For high-LET values, the probability of multiple ionizations or excitation in close proximity is increased (105). For protons below 10 MeV, there is a high probability of finding two δ-electrons causing independent lesions close to each other. In contrast, for high-energy protons (160 MeV; low LET), the probability of finding two energy deposition events within 2 nm is almost zero. Related to the theory of DRA is the stochastic track structure–dependent approach (106, 107). It also contains a proximity concept where the probability of misrepair increases with decreasing distance of sublesions. 19.8.4  Lesion Induction and Repair Models The lethal-potentially lethal (LPL) model (108) is based on lesions that are either repairable or nonrepairable. Nonrepairable lesions are responsible for the linear part of the dose-response curve, whereas repairable lesions include repair and binary misrepair. Different effects are caused by the amount of energy deposited locally. Lesions that cannot be repaired (lethal lesions) are formed proportional to dose and a parameter ηL. Repairable, or potentially lethal, lesions are formed proportional to dose and a parameter ηPL. These lesions are categorized into two groups: a slow- and a fast-repairing component. The slowly repairing lesions (repair rate εPL) can either turn lethal (fixed) or interact with another potentially lethal lesions to form a lethal lesion (rate 2ε2PL; binary misrepair). The resulting dose-response curve for cell survival becomes



  N η D = exp ( − [ ηL + ηPL ] D) ×  1 + PL 1 − exp {−ε PL tr }  N0 ε PL ε 2 PL  

εPL ε2 PL

. (19.12)

The time tr is the time after irradiation and it determines the repair rate. The model converges to the linear-quadratic formulation at low doses. Note that, unlike in the DRA model, individual lesions can be lethal without the need of sublesion interaction. This is accomplished by fixation. Related to the LPL model is the repair-misrepair (RMR) model, which assumes that there are linear repair processes and quadratic misrepair

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processes (109, 110). Further, the saturable repair model assumes that repair becomes saturated with increasing dose (111). This can be either because the complexity or number of lesions increases or because the supply of repair enzymes is limited. The saturable repair approach assumes that repair capability depends on the total number of lesions, the time for repair, and the availability of repair enzymes. This is different from other approaches including repair (e.g., the LPL model) where repair capability solely depends on the damage concentration. Saturable repair models do explain the curvature of survival curves without the need for multitrack action. The increasing RBE with LET is due to more efficient production of less repairable lesions. The final slope of the survival curve is a measure of the number of critical lesions produced before repair. Another ansatz is the two-lesion kinetic model, which provides a direct link between the biochemical processing of DSBs and cell survival (112). All DSBs are subdivided into simple and complex DSBs, each with a unique repair characteristic. It can be transformed into linear-quadratic formalism for therapeutic doses and dose rates (113). The microdosimetric-kinetic model (MKM) (114–118) uses principles of the DRA, the LPL model, and the RMR model. It also uses microdosimetric concepts via the dose mean lineal energy, yD. It is assumed that the sensitivity of cells to low-LET radiation is largely determined by their vulnerability to the formation of lethal unrepairable lesions from single potentially lethal lesions (PLL) but not due to forming them from pairwise combination of two PLL. As in other models, differences in radiation action are due to differences in the energy deposition characteristics. MKM predicts the β value in the linear-quadratic equation to be independent of LET and results in RBE values to increase with decreasing α/β. The cell nucleus is divided into subvolumes, called domains, and each particle track deposits dose in one or several domains. A domain can be thought of as a sphere of unit density. The size of a domain is a unique property of a cell type, and the DNA content may vary from domain to domain. The dose absorbed in a domain is z, the energy imparted. The specific energy of a domain is the sum of the contributions from each track. The MKM model assumes a linear-quadratic dose-response relationship in each domain with two types of lesions: lethal (proportional to z) and repairable. The diameter of a domain is inversely related to the rate of repair of a PLL. The maximum travel distance of a PLL is limited by the domain, that is, there is a restriction in the distance of PLL interactions (note the relation to DRA). The domains are just a mathematical concept to define the proximity of two lesions in order to have a chance of connecting. A PLL may be repaired, or it may combine with another PLL in the same domain to form an unrepairable lesion. In addition, the PLL may turn into a lethal, unrepairable lesion. The MKM model, as it is based on subcellular domains, deals with yD instead of LET, and it assumes a direct relationship between a dose-weighted z, the energy imparted, and cell survival.

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Let Dd be the absorbed dose in one of the p domains within the nucleus. Then, the average number of lethal lesions, per domain is given as

N = α 0 Dd + βDd2 .

(19.13)



A parameter α can be defined as

α = α0 + βz1∗D .

(19.14)

The number of lethal lesions depends on the average number of lethal lesions that form per cell per Gray from conversion of a single PLL and on the average number of lethal lesions created per cell per Gray from combination of pairs of PLL created from passage of a single charged particle through or near the nucleus. Here, z1d* is the saturation-corrected dose-mean specific energy of a domain. The actual model parameters are thus α0 and the radius of the domain (e.g., ~0.3 μm). Another approach combining some of the RMR and LPL concepts is the repair-misrepair-fixation (RMF) model (119). It is a kinetic reaction-rate model and relates DSB induction and processing to cell death. It links radiosensitivity parameters in the linear-quadratic equation to DSB induction and repair and explicitly accounts for unrejoinable DSB, misrepaired DSB, and exchanges formed through intra- and intertrack DSB interactions. The ­linear-quadratic parameters are parameterized as follows: α = (1 − fR )Σ + θfR Σ + z F (η / λ)( γ − θ)( f R Σ) 2

β = (η / [2λ])(γ − θ)( f R Σ) 2 .



(19.15)

Here f R denotes the fraction of potentially rejoinable DSBs, λ the rate of DSB repair, η the rate of binary misrepair, Σ the expected number of DSBs per Gray per cell, θ the probability of a DSB lethally misrepaired/fixed, and γ the probability of a lethal exchange-type aberration. The three terms adding to α stand for the unrejoinable and lethal damage, the lethal misrepair and fixation, and the intratrack DSB interaction, respectively. The β term describes intertrack DSB interaction. Note the microdosimetric parameter zF, the frequency-mean specific energy per radiation event and that zF × f R × Σ gives the DSBs per track per cell. 19.8.5  Track Structure Models Track structure models are based on the physical details of a particle track, including its secondary particles. Because the main goal is to calculate relative biological effects (i.e., RBE values), biological phenomena are treated in a purely phenomenological way, as relative effects. Track structure theory ignores the actual mechanisms of energy deposition and repair mechanisms,

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for example, whether the curvature of the response curve has its origin in the interaction of sublesions or if it is due to some mechanism like dose-­ dependent repair processes. The key assumption is that the difference in biological efficiency, when comparing photons with protons, is caused by different microscopic dose deposition patterns (i.e., track structure). Radiation is more effective per unit dose when the energy deposition is more concentrated in space. Track structure theory (120–123) assumes a simplified biological target and a simplified particle track. The target is assumed to be an infinitely thin disc to ensure that there is no LET variation within the target (track segment condition). A proton track is characterized by its radial dose distribution originating from δ-electrons emitted in ionization events. The track’s δ-electron halo (i.e., the dose as a function of distance to the track center) is approximated by a smooth radial distribution. One can think of each particle track as an amorphous track with a certain diameter (124). Various models and parameterizations were published to calculate this radial deposited energy (120, 125–128). Generally, the dose deposited as a function of the distance, r, to the ion path can be written as a function of 1/r2 up to a limit determined by the maximal radial penetration of δ-rays. Track structure theory involves some simplification. The track volume for protons is mostly empty with only a few δ-ray events on the scale of the cell nucleus size. The stochastic nature of particle-induced events is not taken into account when applying a continuous radial dose distribution defining the track shape. The higher the mean free path of the ion, the more important will be statistical fluctuations such as the stochastic δ-ray emission (129–131). For equal absorbed dose, the microscopic response due to δ-electrons from protons is assumed to be identical to that due to δ-electrons from photons. Based on this assumption, the knowledge of both the response of a medium to photons and the spatial distribution of the dose yield the spatial distribution of response around the path of a particle. The efficiencies of different types of radiation result solely from different dose deposition patterns. In the initial track structure model approach, the biological effect is calculated from the overlap of the track with the target, considering local energy depositions in subtargets (120–123). The subtarget concept is similar to the MKM model. The saturation value of the action cross section of the cell nucleus, σ0, is not necessarily equal to the geometrical size of the target. A set of cellular subtargets have to be activated or inactivated in order to achieve a given effect. The sensitive target radius, a0, is characterized by a dimensionless variable κ. The radius of the subtargets is calculated using D0 (intrinsic radiosensitivity in the multitarget/single-hit formalism) and κ. Each biological endpoint is characterized by a set of four radiosensitivity parameters: n, D0, σ0, and κ (132). The parameters can be obtained by a fit on a set of response curves for the considered endpoint measured in different radiation fields (122, 133, 134). Photon dose-response curve data are needed to obtain the parameters n and D0.

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Two modes of interaction are considered: single-track action (called ionkill) and multitrack action (called γ-kill). Differences in biological effect between two radiation modalities are due to different probabilities for these two reaction channels. Ion-kill is described by the single-hit/single-target relationship for cell response. Thus, in the case of cell inactivation, it is possible to inactivate a biological target by a single particle track. It usually dominates at low fluence and high-LET. The initial slope of the dose-response curve is attributed to the ion-kill mode because, at low doses, particles are so far apart that it is unlikely that their δ-rays overlap in the nucleus. If the cell is not inactivated in this mode, the remaining dose can still lead to an inactivation due to the overlapping of several particle tracks. The γ-kill is defined by a multitarget/single-hit equation where a set of subtargets has to be inactivated. The term γ-kill underlines the analogy to photon inactivation. The γ-kill mode is responsible for the shouldered response curve. Because there is usually a mixture of the ion-kill and γ-kill components, the cell inactivation is a product of single-target/single-hit and multitarget/single-hit components (120, 135). Protons, due to their generally low LET, are usually limited to ion-kill probabilities much lower than 1 (136). With increasing LET, the action mode passes from predominantly γ-kill to predominantly ion-kill. When the LET is further increased, the action cross section increases over σ0, and the socalled track-width region is reached. The radiation action is now due to longrange δ-rays, which pass the target although the ion does not. The dose is now deposited almost completely by ion-kill. The central part of the track has saturated the biological effect, and the width of the track determines the probability of biological effects. At high LET the action cross section decreases due to a decreasing track radius from low-energy δ-rays (137). Within this concept, one integrates the dose deposited in the subtarget over the radial dose distribution. Next, the effect produced by this average dose is calculated, and the effects are integrated over impact parameters. A dose-response relationship can be written as



  D N dE   σ  = exp  − σD 1−  × 1 − 1 − exp − N0 dx   σ0   D0  

  

n

 .  

(19.16)

To calculate the response to a mixed radiation field, a calculation for each energy and particle type must be done (122, 138–140). It has been demonstrated that for n = 2, as well as in the case of low dose and low-LET, the LPL model and the track structure model converge and can be converted into a linear-quadratic formula (138). The track structure approach was implemented in a different fashion in the form of the local effect model (LEM) (141, 142). Compared to the original track structure model, the unrealistic concept of subtargets was initially dropped. The whole cell nucleus is assumed to be the critical target for which

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local effects are averaged, rather than averaging local doses in subtargets. The biological target, that is, the cell nucleus, is assumed to be a thin disc covering an area Anucl. Each track is described as the path of the primary ion and its associated δ-rays. If the dose is not averaged over subvolumes, the 1/r2-dependent radial dose distribution shows infinite values for the local dose at r = 0. Because in this model approach local effects have to be determined, a cutoff for small radii must be introduced and a normalization constant adjusted, so that an integral overall track radii will yield the unrestricted LET. A linear-quadratic dose response is assumed. However, it is a poor approximation for high doses as encountered locally in a subcellular target. Consequently, a modified formulation of the linear-quadratic equation is used to parameterize the photon dose-response curve where a parameter Dt denotes the transition point from the shouldered low-dose region to an exponential tail for high doses, thus ensuring that there is an exponential asymptote at high doses. The biological input parameters are the geometrical cross section (i.e., the size of the cell nucleus) and the photon dose-response curve with the parameters α, β, and Dt. The diameter of the cell nucleus can be determined microscopically. The parameter Dt is difficult to measure because values in the range of several hundreds or thousands of Gray can occur. Therefore, the transition point between the linear-quadratic and the exponential shape, Dt, must often be an estimated endpoint dependent on the predicted ion response curves. Because there are no subtargets, the response of the biological target is determined by the responses due to local dose deposition events (i.e., pointlike targets). The concept of track structure is that, for a proton radiation field, one can derive the mean number of lethal events by integrating the survival over the cell nucleus volume assuming local photon dose response. Based on a photon survival parameterization, the mean number of lethal events produced per cell can be calculated and the effect be determined based on Poisson distribution of the mean. Several tracks can contribute to the local dose at a specific position inside the nucleus so that the effect is based on the total deposited dose. The superposition of dose from different tracks leads to an enhanced efficiency for the production of lethal events. The average number of lethal events does not increase linearly with the particle fluence, and this leads to a shouldered response curve. The relative enhancement is highest when small doses are superimposed, so it is mostly the outer parts of the track that contribute to the shoulder. Shouldered dose-response curves after charged particle irradiation can only be expected if the track diameters and particle fluences are sufficiently large that they obtain a significant fraction of energy deposition by superposition of local doses from several tracks. Dose-response curves can be determined by Monte Carlo simulation of the stochastic process of irradiation. For cell inactivation, the total number

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of lethal events is determined, and the survival probability is calculated according to hits    N = exp  −Y  Anucl , ∑ Dlocal (rj ), Φ(rj , t j , Anucl  . N0 j=0   

(



)

(19.17)

The average number of lethal events, Y, is a function of the number of lethal particle hits, the nuclear area and the local dose caused by the radial dose distribution, Dlocal (Φ describes the overlap between particle track and cell nucleus). Every simulated track deposits a certain local dose in a small, ideally infinitesimal, voxel, and the considered number of tracks depends on the macroscopic dose to be delivered to the cell nucleus. The two track structure approaches described above have been compared (71), as have the LEM and the MKM model (143). There are quite a few commonalities. By introducing subvolumes to the LEM (via MKM) a high dose cutoff in the track center can be avoided. In the MKM, the cell survival curve for photons determines the local dose response in a subvolume, and the summation of the effect in all subvolumes determines the cell survival probability. The LEM has been modified several times to improve the agreement with experimental data (144, 145). For example, one modification takes into account cluster effects at high local doses leading to greater damage at the track center (144). Additionally, the radial dose distribution can be modified to take into account the radical diffusion length in mammalian cells. The most recent version includes a more mechanistic description of the spatial distribution of DSBs (146). Because a full model calculation can be time consuming, specifically in a clinical setting, approximations to the model have been introduced (141, 142, 147, 148).

Acknowledgments The author thanks Dr. Leo Gerweck, Dr. Alejandro Carabe Fernandez, and Jocelyn Woods for proofreading.

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100. Zaider M, Brenner DJ. On the microdosimetric definition of quality factors. Radiation Research. 1985;103:302–16. 101. Cosgrove VP, Delacroix S, Green S, Mazal A, Scott MC. Microdosimetric studies on the ORSAY proton synchrocyclotron at 73 and 200 MeV. Radiation Protection Dosimetry. 1997;70:493–96. 102. Kellerer AM, Rossi HH. The theory of dual radiation action. Current Topics in Radation Research. 1974;Q 8:S17–S67. 103. Kellerer AM, Rossi HH. A generalized formulation of dual radiation action. Radiation Research. 1978;75:471–88. 104. Zaider M, Rossi HH. On the application of microdosimetry to radiobiology. Radiation Research. 1988 Jan;113(1):15-24. 105. Gonzalez-Munoz G, Tilly N, Fernandez-Varea JM, Ahnesjo A. Monte Carlo simulation and analysis of proton energy-deposition patterns in the Bragg peak. Physics in Medicine and Biology. 2008 Jun 7;53(11):2857–75. 106. Brenner DJ. Track structure, lesion development, and cell survival. Radiation Research. 1990(124):S29–S37. 107. Sachs RK, Chen AM, Brenner DJ. Review: proximity effects in the production of chromosome aberrations by ionizing radiation. International Journal of Radiation Biology. 1997 Jan;71(1):1–19. 108. Curtis SB. Lethal and potentially lethal lesions induced by radiation—a unified repair model. Radiation Research. 1986;106:252–70. 109. Tobias CA. The repair-misrepair model in radiobiology: comparison to other models. Radiation Research. 1985;104:s77–s95. 110. Tobias CA, Blakely EA, Ngo FQH, Yang TCH. The repair-misrepair model of cell survival. In: Radiation Biology and Cancer Research (Meyn, RE and Withers, HR, eds.), Raven, New York. 1980:195–230. 111. Goodhead DT. Saturable repair models of radiation action in mammalian cells. Radiation Research. 1985;104:S58–S67. 112. Stewart RD. Two-lesion kinetic model of double-strand break rejoining and cell killing. Radiation Research. 2001;156:365–78. 113. Guerrero M, Stewart RD, Wang JZ, Li XA. Equivalence of the linear-quadratic and two-lesion kinetic models. Physics in Medicine and Biology. 2002;47:3197–209. 114. Hawkins RB. A statistical theory of cell killing by radiation of varying linear energy transfer. Radiation Research. 1994;140:366–74. 115. Hawkins RB. A microdosimetric-kinetic theory of the dependence of the RBE for cell death on LET. Medical Physics. 1998;25:1157–70. 116. Hawkins RB. A microdosimetric-kinetic model for the effect of non-Poisson distribution of lethal lesions on the variation of RBE with LET. Radiation Research. 2003 Jul;160(1):61–69. 117. Hawkins RB. The relationship between the sensitivity of cells to high-energy photons and the RBE of particle radiation used in radiotherapy. Radiation Research. 2009 Dec;172(6):761–76. 118. Hawkins RB. A microdosimetric-kinetic model of cell death from exposure to ionizing radiation of any LET, with experimental and clinical applications. International Journal of Radiation Biology. 1996 Jun;69(6):739–55. 119. Carlson DJ, Stewart RD, Semenenko VA, Sandison GA. Combined use of Monte Carlo DNA damage simulations and deterministic repair models to examine putative mechanisms of cell killing. Radiation Research. 2008 Apr;169(4):447–59.

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120. Butts JJ, Katz R. Theory of RBE for heavy ion bombardment of dry enzymes and viruses. Radiation Research. 1967;30:855–71. 121. Katz R, Ackerson B, Homayoonfar M, Sharma SC. Inactivation of cells by heavy ion bombardment. Radiation Research. 1971;47:402–25. 122. Katz R, Sharma SC. Response of cells to fast neutrons, stopped pions, and heavy ion beams. Nuclear Instruments and Methods. 1973;111:93–116. 123. Katz R, Sharma SC. Heavy particles in therapy: an application of track theory. Physics in Medicine and Biology. 1974;19:413–35. 124. Chen J, Kellerer AM. Calculation of radial dose distributions for heavy ions by a new analytical approach. Radiation Protection Dosimetry. 1997;70:55–58. 125. Chen J, Kellerer AM, Rossi HH. Radially restricted linear energy transfer for high-energy protons: a new analytical approach. Radiation and Environmental Biophysics. 1994;33:181-7. 126. Cucinotta FA, Katz R, Wilson JW. Radial distribution of electron spectra from high-energy ions. Radiation and Environmental Biophysics. 1998;37:259–65. 127. Kiefer J, Straaten H. A model of ion track structure based on classical collision dynamics. Physics in Medicine and Biology. 1986;31:1201–1209. 128. Rudd ME. User-friendly model for the energy distribution of electrons from proton or electron collisions. Nuclear Tracks in Radiation Measurements (Int J Radiat Apl Instrum Part D). 1989;16:213–18. 129. Cucinotta FA, Nikjoo H, Goodhead DT. Model for radial dependence of frequency distributions for energy imparted in nanometer volumes from HZE particles. Radiation Research. 2000;153:459–68. 130. Hamm RN, Turner JE, Wright HA, Ritchie RH. Calculated ionization distributions in small volumes in liquid water irradiated by protons. Radiation Research. 1984;97:16–24. 131. Schmollack JU, Klaumuenzer SL, Kiefer J. Stochastic radial dose distributions and track structure theory. Radiation Research. 2000;153:469–78. 132. Katz R, Sharma SC, Homayoonfar M. The structure of particle tracks. In: Topics in Radiation Dosimetry, Suppl. 1 (Attix, F.H., ed.), Academic Press. 1972: 317–83. 133. Roth RA, Sharma SC, Katz R. Systematic evaluation of cellular radiosensitivity parameters. Physics in Medicine and Biology. 1976;21:491–503. 134. Waligorski MPR. Track structure analysis of survival of two lymphoma L5178Y cell strains of different radiation sensitivity. Radiation Protection Dosimetry. 1994;52:207–10. 135. Barendsen GW. Damage to the reproductive capacity of human cells in tissue culture by ionizing radiations of different linear energy transfer. In: The Initial Effects of Ionizing Radiations on Cells (Harris, RJC, ed.), Academic Press, New York. 1961:183–94. 136. Barkas MJ, Berger M. Studies in penetration of charged particles in matter. NAS NRC Publication 1133 Nuclear Science Series Report. 1963;39. 137. Katz R, Dunn DE, Sinclair GL. Thindown in radiobiology. Radiation Protection Dosimetry. 1985;13:281–4. 138. Curtis SB. The Katz cell-survival model and beams of heavy charged particles. Nuclear Tracks in Radiation Measurements (Int J Radiat Appl Instrum Part D). 1989;16:97–103. 139. Katz R. Relative effectiveness of mixed radiation fields. Radiation Research. 1993;133:390.

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140. Katz R, Fullerton BG, Roth RA, Sharma SC. Simplified RBE-dose calculations for mixed radiation fields. Health Physics. 1976;30:148–50. 141. Krämer M, Jäkel O, Haberer T, Kraft G, Schardt D, Weber U. Treatment planning for heavy ion radiotherapy: physical beam model and dose optimization. Physics in Medicine and Biology. 2000;45:3299–317. 142. Scholz M, Kraft G. Calculation of heavy ion inactivation probabilities based on track structure, X-ray sensitivity and target size. Radiation Protection Dosimetry. 1994;52:29–33. 143. Kase Y, Kanai T, Matsufuji N, Furusawa Y, Elsasser T, Scholz M. Biophysical calculation of cell survival probabilities using amorphous track structure models for heavy-ion irradiation. Physics in Medicine and Biology. 2008 Jan 7;53(1):37–59. 144. Elsasser T, Kramer M, Scholz M. Accuracy of the local effect model for the prediction of biologic effects of carbon ion beams in vitro and in vivo. Int J Radiat Oncol Biol Phys. 2008 Jul 1;71(3):866–72. 145. Elsasser T, Scholz M. Cluster effects within the local effect model. Radiation Research. 2007 Mar;167(3):319–29. 146. Elsasser T, Weyrather WK, Friedrich T, Durante M, Iancu G, Kramer M, et al. Quantification of the relative biological effectiveness for ion beam radiotherapy: direct experimental comparison of proton and carbon ion beams and a novel approach for treatment planning. International Journal of Radiation Oncology, Biology, Physics. 2010 Nov 15;78(4):1177–83. 147. Scholz M, Kellerer AM, Kraft-Weyrather W, Kraft G. Computation of cell survival in heavy ion beams for therapy. The model and its approximation. Radiation and Environmental Biophysics. 1997;36:59–66. 148. Kramer M, Scholz M. Rapid calculation of biological effects in ion radiotherapy. Physics in Medicine and Biology. 2006 Apr 21;51(8):1959–70. 149. Rothkamm K, Loebrich M. Evidence for a lack of DNA double-strand break repair in human cells exposed to very low x-ray doses. Proceedings of the National Academy of Sciences. 2003;100:5057–62.

20 Fully Exploiting the Benefits of Protons: Using Risk Models for Normal Tissue Complications in Treatment Optimization Peter van Luijk and Marco Schippers CONTENTS 20.1 Introduction................................................................................................. 627 20.2 Radiotherapy: Patient Characterization for Individualized Tailoring of Treatment Technology.......................................................... 628 20.3 The Development of Radiation-Induced Normal Tissue Damage...... 631 20.4 Methodology of Model Development...................................................... 632 20.4.1 Choice of Endpoint......................................................................... 632 20.4.2 Data Gathering................................................................................634 20.4.3 Fitting a Model to Binary Data.....................................................634 20.4.4 Testing Model Validity................................................................... 635 20.4.5 Cross-Validation.............................................................................. 638 20.5 Available Models for the Risk of Normal Tissue Damage.................... 639 20.5.1 The Sigmoid Curve: The Shape of the Population Distribution of the Tolerance......................................................... 639 20.5.2 Logistic Regression Analysis: Identifying Predictive Factors....... 640 20.5.3 Lyman-Kutcher-Burman (LKB) Model........................................ 641 20.5.4 Functional Subunit-Based Models...............................................643 20.5.5 Including Clinical and Patient Characteristics: Logistic Regression Models..........................................................................645 20.6 Developments and Future Directions......................................................646 20.7 Applicability to Proton Therapy............................................................... 649 Acknowledgments............................................................................................... 650 References..............................................................................................................650

20.1  Introduction For many cancers radiotherapy is a common and effective treatment aiming at sterilizing tumor cells using radiation. At present, roughly 45–50% of all patients receive radiotherapy at some stage of their treatment. For most cancers, 627

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however, normal tissues are inevitably coirradiated. This often leads to toxicity and a reduction of the quality of life (QoL) of the patient. For some tumors, such as lung cancer, the dose that can be administered safely to the tumor and consequently the efficacy of the treatment are limited by the risk of severe toxicity. Because the risk of toxicity depends on radiation dose and the amount of irradiated normal tissue, technological developments such as proton therapy are aimed at minimizing the dose and amount of normal tissue that is coirradiated. Protons indisputably have a superior physical dose distribution compared to classically used photons, because they lose most of their energy in a small region called the Bragg peak that can be positioned in the target volume (see Chapter 2 for details on the depth–dose distribution of protons). Optimal use of proton therapy, however, requires the (1) selection of patient populations for which use of protons may offer advantages, (2) comparison to alternative treatment techniques, and (3) individualized optimization of the selected technique (e.g., using optimization techniques described in Chapter 15). Each of these optimizations requires the ability to quantify the quality of a treatment (plan) by a figure-of-merit related to tumor control and normal tissue toxicity. Therefore an important prerequisite of optimized use of proton therapy is the availability of accurate models for the relation between the dose distribution and the risk of complications. In all current evaluation methods the physical quantity “dose” plays a major role. This is partly due to the fact that this quantity can be calculated, adjusted, measured, and compared with great accuracy. However, one should keep in mind that it is the biological or clinical effect (tumor control or the occurrence of a complication) that determines the treatment outcome, and not the dose; “dose” is only a surrogate for what is clinically important (1). In this chapter we will describe the attempts that are currently being made to determine the relationship(s) between dose and toxicity. Because relatively little data are available on complications occurring after proton therapy, at present this relation can only be estimated from data obtained after treatment with photons. However, the shapes of dose distributions that can be achieved using protons differ considerably from those obtained using photon-based techniques (see also Chapters 10 and 11). As such, extrapolating photon-based experience to proton therapy by using normal tissue complication probability (NTCP) models fitted to photon data is not trivial. In this chapter an overview of various aspects of development and use of risk models for the prediction of responses to proton therapy as well as their limitations will be given.

20.2 Radiotherapy: Patient Characterization for Individualized Tailoring of Treatment Technology Different types and stages of tumor are treated using different treatment modalities such as fractionated photon therapy using a linear accelerator

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(linac), single fraction stereotactic radiotherapy, proton therapy, or brachytherapy using implanted radiation sources, all with the aim to maximize the probability of curing the patient while limiting toxicity to normal tissues. The choice of treatment modality is based on the clinical characteristics of the patient as well as the radiobiological characteristics of the tumor and surrounding normal tissues. As such the choice for proton therapy is based on for example, differences in expected risks of normal tissue complications. Therefore optimized selection of a treatment modality and specifically the choice for proton therapy is a very important field for the application of risk models for normal tissue damage. Each treatment modality possesses many parameters that can be used to optimize its application. For example, in external radiotherapy (linac-based photon therapy, proton therapy) the choice of number and shape of the beams and their angles with respect to the patient facilitate optimization of the dose to the tumor and normal tissues. Again based on the general location of the tumor and adjacent normal tissues, class solutions (treatment techniques) are developed for specific groups of patients. The development and optimization of these treatment techniques therefore represent a second level of treatment optimization where risk models for normal tissue damage are used. Though these treatment techniques can serve as starting points for whole classes of patients, variability in patient anatomy necessitates individualized tailoring of this technique to each patient (treatment plan optimization). Factors determining the final treatment plan include the size, shape, and position of the tumor and the exact anatomy of adjacent organs. In this final optimization step imaging plays a pivotal role. The most-used imaging modality in radiotherapy is x-ray computed tomography (CT) scanning. In addition imaging modalities such as positron emission tomography (PET), single photon-emission CT (SPECT), or magnetic resonance imaging (MRI) are used to facilitate the identification of the most active parts of the tumor (e.g., 18FDG PET), most functional parts of the lung (99mTc SPECT) or to improve the visibility of different brain regions (MRI). As an example, Figure 20.1A shows the CT scan of a patient with a lung tumor. To distinguish better between normal structures within the lung and extensions of the tumor, an 18FDG PET scan was made and superimposed on the CT scan. The available images can be imported in a treatment-planning system that contains a dose model of the treatment machine. Based on the CT and PET scan, the tumor and adjacent critical organs (e.g., the lung) are contoured. By varying treatment parameters such as beam angles, weights, and shapes, the treatment plan can be optimized (see also Chapters 10, 11, and 15). Figure 20.1B shows an example of the beam angles used in this patient. Based on the dose model, the treatment plan, and the patient geometry, the dose distribution in the patient can be calculated (Figure 20.1C). Direct comparison of three-dimensional (3D) dose distributions of alternative treatment plans is very inconvenient. Therefore the present practice is to summarize the 3D dose distribution in a dose-volume histogram. For each

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FIGURE 20.1 (See color insert.) Tailoring modern radiotherapy technology to the patient requires characterization of the patient using imaging (A). The anatomy of the patient is characterized using a CT scan (gray scale). In addition to better distinguish between normal and tumor tissue 18FDGPET scanning was used (color scale). The gross tumor volume is identified (green contour) and expanded with a margin to account for microscopic extensions, patient positioning, and tumor motion uncertainties to yield the planning target volume (red contour). Moreover, the critical organs are contoured (e.g., white contour for the lung). Subsequently in a treatment-planning system a treatment technique is applied to the patient (B) and the resulting dose distribution is calculated (color scale, C). Next dose-volume histograms (DVHs) are constructed of dose deposited in the target volume and critical organs (D). In practice these differential DVHs are converted in cumulative DVHs, giving the volume receiving more than a specific dose as a function of that dose (E). Based on these dose-volume histograms, the technique may be further adapted to the patient.

(relative) dose level, this histogram gives the volume that receives that dose (Figure 20.1D). In practice the cumulative dose-volume histogram (DVH), giving the volume receiving more than a certain dose as a function of that dose, is reported by treatment-planning systems (Figure 20.1E). Even though a DVH discards a lot of information compared with the 3D dose distribution, at present this DVH is the starting point for the derivation of figures-of-merit, based on which the treatment plan can be optimized. Classically, individual DVH points, the mean dose or generalized forms of the mean dose are used

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for this. However, because the relation of these figures-of-merit to clinical outcome is not trivial, large efforts have been made to develop and use risk models explicitly describing normal tissue damage instead.

20.3 The Development of RadiationInduced Normal Tissue Damage To be able to fully appreciate the complexity of events that risk models need to describe, a brief overview of the different events that lead from dose deposition to tissue damage and possibly clinical complications will be given. In the presence of oxygen, photon irradiation leads to the formation of reactive oxygen species. These induce sparse DNA lesions such as singleand double-strand breaks dispersed through the cell nucleus. In comparison with photon irradiation, particle beams act more directly on the DNA and produce dense ionization tracks that cause clustered DNA damage which are, especially in the Bragg peak region, more difficult to repair for a cell (see Chapter 19 for details.) Cell death is primarily determined by nonrepairable double-strand breaks. Normal tissue damage, however, also depends strongly on other stress responses. Besides death, in normal tissue cells DNA-damage may also lead to differentiation or proliferation of specific cells, cell-cycle arrest, initiating immune responses, changed metabolism, collagen and extracellular matrix deposition, and other fibrotic reactions, in response to activation of cytokines and upregulation of profibrotic genes. How these local effects are translated into clinical complications, however, strongly depends on organ or even endpoint-specific mechanisms; for example, in the parotid gland, late loss of function is mostly due to a loss of repopulating primitive cells, whereas in the lung, late loss of function is due to excessive deposition of extracellular matrix material. Moreover, whether damage to tissue within the organ actually leads to a complication may depend on dose to other organs. Examples of these are dose to the heart, increasing the risk and severity of loss of pulmonary function after lung irradiation (2, 3) and the risk of patient-rated xerostomia (dry-mouth) depending on dose to the parotid gland as well as on dose to the submandibular gland (4). Moreover, the relationship between DVH parameters and complication risk may also influenced by other factors. For example, the relationship between dose and complication risk after irradiation for prostate cancer depends on whether or not abdominal surgery has been performed (5). As such each endpoint depends on a unique chain of events leading from initial dose deposition and local damage to the final clinical endpoint. Therefore NTCP models describing these endpoints need to be tailored to the organ and endpoint studied.

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20.4  Methodology of Model Development For the application of new techniques, obtaining an NTCP estimate from an NTCP model is in fact extrapolating from current knowledge (the data). This extrapolation, however, heavily depends on the assumptions of the NTCP model. As such it is critical to realize that the estimates obtained from the model are as good as the data and the assumptions on which it was built. Therefore in this section various stages of model development, such as the collection of data, describing the data with a model, and testing the applicability of this model, are given. 20.4.1  Choice of Endpoint Because the application of NTCP models is to optimize the treatment with respect to normal tissue toxicity, the exact type of toxicity (or endpoint) to be described by the model has to be chosen carefully. Roughly three classes of endpoints can be distinguished. First, toxicity can be determined objectively in terms deterioration of organ function or changes in tissue, visualized by imaging. This type of  endpoint has the advantage that it depends on direct measurements of changes in organ function (e.g., lung capacity, saliva production), and therefore it allows an objective determination of radiation effects. Moreover, because this type of measurement can also be performed in animal models, modeling this type of endpoint can benefit from mechanistic insight obtained from radiobiology studies. For most of these endpoints, however, it is unclear what the clinical impact is: although loss of 75% of parotid gland saliva production or density changes in the lung visible on CT clearly demonstrates damage to the parotid gland and lung, respectively, by itself, it does not establish a clinical impact that can be weighed against toxicity in other organs or tumor control. Second, toxicity can be reported in terms of a clinical complication. As an example the Common Terminology Criteria for Adverse Events (CTCAE v4.0) defines for each complication a grade between 1 and 5, where 1 indicates toxicity that remains asymptomatic or results in mild symptoms not requiring intervention and 5 indicates death related to the complication. Though using this system complications can be classified according to clinical impact, this inherently also introduces some subjectivity; for example, radiation pneumonitis is classified as a grade 2 based on the need to administer steroids. Whether or not steroids are prescribed may, however, vary between physicians. Moreover, the observed clinical complication may originate from damage and/or functional problems in multiple organs (4). As such, accurate prediction of clinical complications requires a good insight into the doses to which organs potentially contribute to the clinical symptoms. Consequently, modeling this type of endpoint requires the inclusion of a large number of

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dosimetric predictors and a large dataset with many events to support the model. Finally, because the ultimate aim of (the optimization of) the radiotherapy treatment is to cure the patient while preserving or improving the QoL of the cancer patient, the impact of a treatment on QoL can also be used as an endpoint. QoL is generally measured using questionnaires (e.g., EORTC QLQ-C30 (6)). The results of a number of studies clearly showed an inverse relationship between the presence and severity of radiation-induced side effects and the more general dimensions of QoL. Similar to scoring of clinical symptoms, changes in QoL, may result from radiation effects in many organs as well as from the clinical status of the patient and/or comorbid diseases; for example, in head and neck cancer, the clinical complication xerostomia is the most frequently reported late side effect, which is also considered by patients to affect their QoL. However, in a recent study, radiation-induced swallowing dysfunction appeared to be more important with regard to the effect on QoL compared to xerostomia (7). Thus, changes in QoL may result from multiple clinical complications that in turn may result from dose to multiple organs. As such including dosimetric information on all organs that may be involved in the reduction of QoL requires an enormous amount of data. Moreover, the QoL could ignore clinically relevant toxicity that has limited impact on the QoL. When basing treatment optimization of QoL, these toxicities would not be taken into account. In conclusion, choosing between these classes of endpoints is making a trade-off between specificity and relevance to the patient (8). The optimization of a treatment will usually involve multiple endpoints. Normal tissue damage has to be weighed against the risk of not curing the patient. Moreover, for many disease sites the patient is at risk for developing more than one type of toxicity. Simultaneous optimization of a treatment with respect to multiple endpoints requires that comparable figures-of-merit are used for each separately. A solution to this is to specify which amount of function loss, what grade of clinical complication, or what loss of health-related QoL is considered clinically relevant. Based on criteria such as loss of 75% of parotid saliva production, a grade 2 or higher radiation pneumonitis, or loss of more than 10 points in QoL, these endpoints can be converted to a binary endpoint that specifies whether or not the complication occurred. Now the treatment can be optimized with respect to these binary endpoints, using tumor control probability and NTCP models. Though probabilities are suitable to compare nonequivalent types of endpoints, care should be taken to use binary endpoints that specify equally severe complications. Optimizing the occurrence of a grade 1 (asymptomatic) radiation pneumonitis against the probability of tumor control would compromise a lethal complication (not achieving tumor control) too much in favor of an asymptomatic complication.

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20.4.2  Data Gathering Because a model is in essence a summary of previously made observations, the quality of the data used for the development of the model is critical to its applicability. As such when collecting data to facilitate the development of NTCP models to be used in treatment optimization with respect to some clinical endpoint, it is important that the data collected at least contains the candidate predictors that can be expected to be related to this endpoint. Because many clinical endpoints (e.g., swallowing disorders, xerostomia, and radiation pneumonitis) are multiorgan endpoints, it is imperative that a dataset used for their predictive modeling includes clinical and dosimetric parameters of all organs involved. Moreover, though 3D dose distributions are generally reduced to dose-volume histograms, from the endpoint’s perspective dose-volume histogram points may not be the most sensible choice. In addition, because the risk of many complications depends on a combination of dosimetric and other clinical, treatment, or demographic factors, such as the addition of concurrent chemotherapy to radiation and age, it is imperative to collect these parameters and include them in the analysis as candidate predictors. Because models built on such a multitude of predictive factors require an amount of data that is generally beyond the capacity of individual centers, data gathering requires extensive collaborations such as the U.S. QUANTEC collaboration (9). Finally, because a model in principle summarizes the data used to construct it, the quality of a model critically depends on the quality of these data. As such the quality of a model is influenced strongly by the accuracy by which endpoints are scored, consistency in organ delineation, and the accuracy of the estimated dose distribution. 20.4.3  Fitting a Model to Binary Data After the data has been collected, a model has to be selected to describe them. For models with a fixed set of predictors and parameters such as the Lyman-Kutcher-Burman (LKB) model, critical-element and critical-volume models, or logistic regression models with a known set of predictors (see the next section for descriptions), parameter values can be determined by fitting the model to the data. Because the model describes a process with binary outcome (the occurrence or absence of a complication), the most appropriate fitting method is the maximum-likelihood fit (10). In this approach the model parameters are selected for which the model prediction maximizes the probability that the experimental data would be observed. This in general corresponds to maximizing

L ( m ) = ∑ ei ⋅ ln ( NTCPi ( m) ) + (1 − ei ) ⋅ ln ( 1 − NTCPi ( m) ). i

(20.1)

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L indicates the logarithm of the likelihood, ei indicates the outcome (0 or 1) for patient i, and NTCPi(m) indicates the estimate of the NTCP for the para­ meter set m. For testing the consistency between model and data (see below in this section) patients need to be grouped based on similarity of treatment with respect to the predictors in the model. The likelihood function to be optimized then becomes

L ( m ) = ∑ ri ⋅ ln ( NTCPi ( m) ) + (ni − ri ) ⋅ ln ( 1 − NTCPi ( m) ).

(20.2)

i

Here ni and ri indicate the number of patients and the number of complications in group i, respectively. As an example Figure 20.2A shows the incidence of a reduction to 25% saliva production compared to the pretreatment level in patients treated in the head-and-neck region (11). Using the maximum-likelihood method given by Equation 20.2, a logistic model (see Equations 20.6 and 20.7) was fitted to these data (curves).

20.4.4  Testing Model Validity Though fitting a model to data will always produce a set of parameters that makes the model correspond to the data as well as possible, this does not imply that the model accurately describes the data. Different ways to assess the quality of the model put emphasis on different aspects such as correspondence between model and data or the ability to correctly distinguish between responding and nonresponding patients. As a first measure of how well the data are described by the model, the likelihood L(m) (Equation 20.1 or 20.2) can be used. Although higher values of L(m) indicate a better fit of the model to the data, by itself it does not provide a means to determine whether the model predictions are consistent to the data and can be used for a specific task. Derived from the likelihood, various information criteria have been developed. These criteria also depend on the number of model parameters and as such provide a means to determine whether the addition of a new parameter in a model can be justified by the improvement in the likelihood. Examples of these are Akaike’s or the Bayesian information criteria (AIC/BIC):

AIC = 2 ⋅ k − 2 ⋅ L

(20.3)



BIC = k ⋅ ln ( n) − 2 ⋅ L.

(20.4)

Here k indicates the number of model parameters and L the natural logarithm of the likelihood obtained from the maximum likelihood fit. By comparing Equations 20.3 and 20.4, the difference between the BIC and the AIC can be seen to be in the penalization of the addition of a model parameter. In the BIC this penalty depends on the logarithm of the number of samples, which leads to more conservative models, for datasets larger than six samples.

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FIGURE 20.2 Overview of methods and their use in an example. Data on reduction >75% of parotid gland saliva production at 6 weeks and 1 year (11) are modeled using the mean parotid gland dose in a logistic model (Equation 20.6). The model is fitted to two-thirds of the data using the maximum likelihood method (Equation 20.2, A). (B) The expected distribution of the deviance, determined by fitting to 10 5 alternative outcomes that were obtained using a Monte Carlo technique (Section 20.4.4). The dotted line indicates the deviance obtained in the real study. Based on these, the probability of finding larger deviances is 45%. As such the differences between model and data are not significant (p = 0.45), and the model is not rejected by the data. To determine to what extent the model distinguishes between responders and nonresponders, an ROC analysis was performed (C). For internal cross-validation the fitted model shown in A was compared to the unused one-third of the data (validation dataset, D). New Monte Carlo datasets were generated to determine the deviance distribution for the validation data (E). The difference between the model fitted in (A) and the validation data, however, is significant. (F)  ROC analysis showing that the performance of the model in the validation data is lower than in the training set.

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Many other statistical methods exist to quantify correspondence between model and data and to what extent the model separates patients with complications from patients without complications. The most elementary test of the model is whether ranking of patients according to their predicted risk corresponds to ranking them according to the incidence of the complication. To this end, Spearman’s rank correlation coefficient can be used (12). Though a high correlation coefficient indicates that the model can be used to optimize the plan based on this model, it also does not test whether the probabilities are quantitatively correct. Treatment optimization based on risks of multiple endpoints (e.g., tumor control, xerostomia, and dysphagia), however, requires quantitatively correct NTCP values. Biases in the individual models would inadvertently influence plan selection (13). Therefore, in addition to testing the ability of a model to rank plans with respect to a specific endpoint, also checking the accuracy of the NTCP values obtained from the model is desired. For large datasets with normally distributed uncertainties generally the χ2 test is used to test whether differences between model and data are larger than expected based on the statistical properties of the data. A similar method suitable for smaller datasets and binary outcome data is based on the likelihood given by Equation 20.1 or 20.2 (10). The data themselves are used as the best possible model, also called “the full model” (14). Subsequently it is tested whether the likelihood of the fitted model has significantly deteriorated compared with that of the full model. The expected distribution of the difference between model and data is determined using a Monte Carlo method. The likelihood of obtaining the data if the model NTCP values are given by the data themselves can be obtained by substituting NTCPi = ri/ni in Equation 20.2 to yield



r L0 = ∑ ri ⋅ ln  i i  ni

  ri   + ( ni − rr ) ln  1 −  . ni   

(20.5)

Now it can be tested whether the decrease of L(m) with respect to L0 significantly exceeds the amount expected based on the statistical noise in the data. Usually in this analysis the deviance, given by −2 ∙ (L(m) − L0), is used since for large datasets the distribution of the deviance resembles the χ2 distribution (14). However, the probability distribution of the deviance has to be known so that one can set a maximum decrease of the fitted models deviance with respect to the full model at which the model is considered to significantly deviate from the data. This distribution can be determined based on alternative study outcomes obtained using the fitted model and a Monte Carlo technique (10). In this approach for each data point the NTCP is calculated using the fitted model. Subsequently for each patient included in this data point a random number between 0 and 1 is drawn and compared to the NTCP. If the random number is lower than the NTCP, for the simulated outcome the

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patient is scored as showing the complication. Using this procedure a large number of alternate datasets that could have occurred given that the fitted NTCP model is obtained. Subsequently L0 can be recalculated and the NTCP model refitted for each of these datasets. This results in a large number of alternate values of the deviance and their distribution. Finally, from this distribution it can be determined which fraction of the fits to the Monte Carlo datasets resulted in a larger deviance than the fit to the experimental data. Because larger values indicate a larger difference between model and data, a small fraction (e.g., <5%) indicates that the difference between model and actual outcome is unlikely (e.g., probability <5%) to occur based on the statistical spread in the data, which is a good reason to reject the model. Figure 20.2B shows the deviance distribution for the model fit shown in Figure 20.2A. The difference between the model and data is not significant. Besides testing whether the fitted model actually corresponds to the data, it is important to assess its ability to distinguish between responding and nonresponding patients. This aspect of performance, called discrimination, can be characterized by the Receiver Operating Characteristic (ROC) curve (15). The ROC plot is a plot of true positive vs. false positive rates for all possible NTCP threshold values (see e.g., Figure 20.2C). For a random prediction (lowest performance) the area under this curve is 0.5. For better performing models this area increases up to a maximum of 1. 20.4.5  Cross-Validation The fact that a model was developed based on a dataset does not automatic­ ally imply that it is capable of predicting normal tissue toxicity in a new group of patients receiving the same type of treatment, let alone that its results can be extrapolated to other treatment modalities. Testing the ability of a model to predict the response in new patients can be done by cross-validation. Two stages of cross-validation can be distinguished. Internal cross-validation can be performed to test the predictive power within the patient population and treatment type the model was developed in. In internal cross-validation the dataset is split into a “training set” used to develop (i.e., determine predictive factors and/or fit model parameters) the model and a “validation set” to test the model performance in an independent set of data. In fact for the model fits shown in Figure 20.2A, only two-thirds of the available data was used as a training set. Every third patient was saved for a cross-validation. Figure 20.2D shows the original model curves copied from panel A, together with the cross-validation data. Here it can be seen that, though the model follows the data, it appears to underestimate the risk at higher dose levels. Similar to Figure 20.2B, the significance of the difference between model and data can be tested. Because the deviance depends on L0 and thus on the dataset, the deviance distribution has to be redetermined by generating alternative outcomes and calculating the deviance using Equation 20.1 or 20.2, and the model must be fitted to the training set. The resulting distribution is shown

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in Figure 20.2E. The difference between the model and the cross-validation datasets is indeed significant. As also expected, the performance of the model assessed by the ROC curve is reduced (Figure 20.2F). One should be aware that this approach to cross-validation may be sensitive to the specific selection of development and cross-validation datasets. This sensitivity can be reduced by using bootstrapping. In bootstrapping multiple validation sets are sampled by randomly selecting patients from the original dataset (12). The ability of the model developed in the original dataset to predict the outcomes in the bootstrapping datasets can now be assessed by the previously described methods, such as the ROC curve or Spearman’s correlation. A successful internal cross-validation does not imply that it is accurate beyond the domain specified by the dataset on which it was based (e.g., other new treatment techniques or modalities). Therefore, any extrapolation to other patient populations or treatment techniques/modalities should be regarded as a hypothesis that needs to be tested prospectively in a new dataset that was obtained in this new patient population or using the new treatment technique. To this end again the previously described methods (see “testing model validity” section) can be applied to test consistency or performance of the model in new datasets. This procedure is called external cross-validation.

20.5  Available Models for the Risk of Normal Tissue Damage For a long time efforts have been made to create predictive models for the benefit of treatment optimization. Only during the past two decades evolution of treatment techniques and technology made the systematic collection of dose distribution and response data, and consequently the development of models describing their relation, possible. In the following subsections a selection of these models will be described. In addition, in Table 20.1 a summary of these models, their properties, and typical applications is given. 20.5.1 The Sigmoid Curve: The Shape of the Population Distribution of the Tolerance Already in 1924 in the field of toxicology it was recognized that the dose dependence of “poisoning can be described by an S-shaped curve, and that such a curve is properly conceived as an expression of the variation, either in sensitiveness or in resistance, of organisms, tissues or cells toward a given poison” (16). Though radiation can be regarded similar to poison, the normal tissues are generally not receiving a uniform dose. Therefore one of the challenges in NTCP modeling is to recognize what predictive factor, derived

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TABLE 20.1 Overview of Models and Their Properties Model Logistic regression Lyman-KutcherBurman (LKB)

Critical element Critical volume

Relative seriality

Extended multivariate logistic regression modeling framework

Parameters

Remarks

Depending on model composition

Classical epidemiology approach n    volume effect (Figure 20.3) Most generally used specialized D50(1) tolerance to whole-organ NTCP model at present irradiation m    relative slope P(1, D) Dose–response to Designed for so-called “serial whole-organ irradiation organs” Tolerance dose and slope of Designed for so-called “parallel dose-response curve of the organs” function subunit vr  functional reserve σr  population spread of vr P(1, D) Dose–response curve to Designed for mixed behavior. whole-organ irradiation Parameter s describes the s     relative seriality extent to which the organ parameter behaves serially or parallel. Depending on model composition Approach rather than a model. Most versatile allowing combining different types of predictive factors

from the dose distribution applied to the patient, best characterizes the variation of the resistance to the treatment (population tolerance distribution). 20.5.2  Logistic Regression Analysis: Identifying Predictive Factors Classically the description of the relation between (candidate) predictive factors and outcome are the domain of the epidemiologist. Though in this field many possible modeling techniques are available, logistic regression analysis is still one of the most commonly used tools. The logistic regression model is given by

NTCP =

1 . 1 + e−z

(20.6)

Here z is the predictive factor representing the stimulus of which the population tolerance distribution can be used to predict outcome. This predictive factor z can be a single variable (e.g., mean dose) or a function of multiple predictive variables. Though any type of function is possible, usually a linear function such as

z = β 0 + β1 ⋅ x1 + β 2 ⋅ x2 + …

(20.7)

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is used. In Equation 20.7 the parameters βi represent regression coefficients and xi the corresponding predictive variables, such as points from the dosevolume histogram, mean dose, or clinical parameters such as pretreatment pulmonary function. Though Equation 20.7 shows a linear function of independent predictive factors, each of these factors may depend on (combinations of) dose, volume, or clinical factors via a nonlinear function. The advantages of this type of model are the wide availability of methods for fitting it to data in statistics software packages and its intrinsic capability of combining a very heterogenic set of predictive factors, such as dose-related and patient factors. 20.5.3  Lyman-Kutcher-Burman (LKB) Model In the clinical physics field efforts have been made to create mathematical formalisms that summarize 3D dose distributions in a single predictive factor. Because mechanisms underlying normal tissue damage vary by organ and even type of toxicity within the organ, the optimal strategy by which the 3D dose distribution is reduced to a single predictive factor is organ dependent. One of the first and still the most-often used model in this class is the LKB model (17). In this model the nonuniform dose distribution is reduced to a uniform dose distribution that is assumed to be equivalently effective as the original nonuniform one. To this end the relative contribution of each subvolume of the organ to the uniformly irradiated volume is assumed to be proportional to a power function of its relative dose: 1



1

 D n  D n 1 veff = ∑  i  ⋅ vi = ∑  i  . N i  Dmax  i  Dmax 

(20.8)

Here Di indicates the dose in relative subvolume of size vi in the original, nonuniform dose distribution. If equally sized subvolumes (e.g., voxels in the 3D dose distribution) are used, the second formulation can be used. Here N indicates the number of subvolumes. Depending on the value of para­ meter n subvolumes contribute only to the effective volume if they contain a dose close to the maximum dose (n→0), proportionally to the relative dose (n = 1), or already starting at a low dose (n >> 1). Irradiation of a volume veff to a dose Dmax is assumed to result in the same clinical outcome as irradiation with the original dose distribution. Furthermore the parameter D50, also called the tolerance dose, is assumed to depend on the effective irradiated volume and the tolerance to irradiation of the whole organ D50(1) following a power law:



D50 ( v ) =

D50 (1) . veffn

(20.9)

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Finally, by assuming that this D50(v) is normally distributed over the population with a relative uncertainty (i.e., standard deviation) m, the NTCP is given by  D − D50 ( v )  NTCP = Φ  max   m ⋅ D50 ( v ) 



(20.10)

where Φ represents the cumulative normal distribution and is given by x

y2

− 1 Φ ( x) = ⋅ ∫ e 2 ⋅ dy . 2 π −∞



(20.11)

Altogether, by specifying the parameter n, organ-specific behavior can be introduced (see Figure 20.3). For small values of n the tolerance dose will hardly depend on irradiated volume and the NTCP is determined mostly by the Dmax of the dose distribution. For n = 1, however, the contribution of all subvolumes to the effective volume is proportional to dose and changes in irradiated volume will result in a proportional change in tolerance dose. At large values of n (>>1) any subvolume receiving even a low dose contributes fully to the effective volume. The tolerance dose, however, rises steeply if part of the organ is spared. Because this type of volume dependence might arise if subvolumes of the organ function independently and only a small functional subvolume is required for the organ to perform its function, this type of behavior is often characterized as “parallel,” as opposed to “serial” behavior occurring for n << 1, where damaging even the smallest subvolume renders the organ dysfunctional.

n=5

n=10

n=2 D50(v)

n=1 n=0.5 n=0.05

D50(1) 0

0.2

0.4 0.6 Relative volume

0.8

1

FIGURE 20.3 Dependence of the relation between the tolerance dose and irradiated volume on the value of parameter n of the Lyman model. For small values of n, the tolerance dose hardly depends on irradiated volume, in contrast to large values of n leading to a strong volume dependency.

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At present treatment optimization is still most-often performed based on dose metrics such as DVH points and mean dose, rather than NTCP models. One of the figures-of-merit often used in such dose-based optimization is the generalized equivalent uniform dose (gEUD) (18): 1



 1 a gEUD =  ∑ Dia  N i 

(20.12)

where N represents the number of equivalently sized subvolumes in the organ at risk and a is a free parameter. The formulation of the EUD is very similar to the effective volume of the LKB model. In fact by substituting a = 1/n in Equation 21.12, the LKB model can be reformulated in terms of the gEUD:



 gEUD − D50 ( 1)  NTCP = Φ    m ⋅ D50 ( 1) 

(20.13)

showing that the gEUD is in fact equivalent to the dosimetric predictor underlying the LKB model. 20.5.4  Functional Subunit-Based Models The serial and parallel types of behavior were modeled explicitly in a class of models assuming that organs consist of independent substructures, called functional subunits, and that the organ response is determined by the organization and response of these functional subunits to radiation (19). Initially three of these models have been developed, assuming a serial (critical-­ element model [20]), parallel (critical-volume model [21]), or a mixed (relative seriality [22]) organization. All three models start with the assumption that the risk of failure of this substructure (p) as a function of dose is given by a sigmoid curve. Many formulations (e.g., logistic, Poisson, and cumulative normal distribution) for this type of curve are available. As such the logistic regression model of Equation 20.6 could be used with dose as a predictive factor. Alternatively it could be assumed that the tolerance dose of functional subunits is distributed according to the normal distribution. In this case the dose-response curve is given by the cumulative normal distribution (see Equation 20.11). Finally, the Poisson distribution that describes the number of rare events (e.g., a lethal hit to a cell) occurring in a large sample size (e.g., all dose deposition events in the cell) could be used. Although the underlying assumptions differ, it is important to note that for all practical applications these models perform similarly. The critical-element model is based on the assumption that damage to any subvolume of the organ will result in failure of the entire organ (20). Because the probability of preserving function in subvolume i is given by

1 − p ( Di )

(20.14)

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and the probability of preserving function in all subvolumes is obtained by multiplication over all subvolumes, the risk of organ failure is given by

NTCP = 1 − ∏ ( 1 − p ( Di ) )

(20.15)

i

where Di indicates the dose in FSU i. Similar to the Lyman model, also the critical element model can be expressed in terms of the response to wholeorgan irradiation:



(

(

NTCP = 1 − ∏ 1 − P 1, Dj j

))

vj



(20.16)

where P(1, Dj ) equals the NTCP after irradiation of the whole organ to a dose Dj and (Dj, vj ) represents the dose-volume histogram. In contrast, the critical-volume model is based on the assumption that the organ possesses some spare capacity. Organ failure is assumed to occur only if the damaged fraction of the organ exceeds this spare capacity. Therefore, to estimate the NTCP, first an estimate of the damaged volume has to be obtained: N



vd = ∑ vi ⋅ p ( Di )

(20.17)

i=1

where vi indicates the relative volume of subvolume i and N is the total number of subvolumes. Assuming a normal distribution for the spare capacity, the risk of the damaged volume exceeding the spare capacity is then given by



 v − vr  NTCP = Φ  d   σr 

(20.18)

where vr and σr indicate the spare capacity and its population spread, respectively. A model that combines both types of behaviors and allows the type of response (i.e., the degree of seriality) to be determined by a fit parameter is the relative seriality model: 1



s  s NTCP = 1 − ∏ ( 1 − pFSU ( Di ))  i  

(20.19)

where the parameter s determines whether the volume dependency of the tolerance dose follows a parallel (s << 1) or serial (s = 1) behavior (Figure 20.4).

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1

A)

Critical element/volume model

NTCP

0.8 0.6

Critical element Critical volume

0.4 0.2 0

1

Dose (a.u) B)

Relative seriality model

NTCP

0.8 0.6

Serial (s = 1) Parallel (s = 0.05)

0.4 0.2 0

Dose (a.u)

FIGURE 20.4 Behavior of FSU-based models illustrated by dose-response curves expected after irradiation of 100%, 67%, and 33% of the organ. The curves of the critical-element model and the relative seriality model in its serial limit demonstrate the characteristic small effect of irradiated volume on tolerance dose for low risk levels. In contrast the critical volume model and the relative seriality model in its parallel regime show a strong dependence of tolerance dose on irradiated volume for all risk levels.

Similar to the LKB and critical-element models also the relative seriality model can be expressed in the response after whole-organ irradiation:



 NTCP = 1 − ∏ 1 − P s 1, D j j 

(

(

1

))

vj

s  . 

(20.20)

During the last decade the number of available models has increased enormously. Most of these recent models, however, share the most critical assumptions of the aforementioned models, and until now their benefit over the previously described ones has not been demonstrated experimentally. 20.5.5 Including Clinical and Patient Characteristics: Logistic Regression Models The LKB, critical element, critical volume, and relative seriality models are exclusively based on the entire dose distribution. Their formulation does

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not generally facilitate the inclusion of clinical parameters (e.g., addition of chemo or pre-existing morbidity), which would improve the accuracy of NTCP models. Alternatively, however, this can be achieved using a multivariate logistic regression model in which, for example, the damaged volume for the critical-volume model, or the effective volume and dose for the LKB model are used as predictors. Establishing the optimal combination of predictors resulting in the most accurate prediction of normal tissue toxicity is, however, not trivial. El Naqa et al. (12) gave an overview of methods that can be used to achieve this using a multivariate modeling approach combined with methods to test model robustness and prevent overfitting. The development of such a model involves (1) determining which parameter combinations result in a good description of the data, (2) determining the number of parameters that can be supported by the data without overfitting, and (3) determining the robustness of parameter selection. First, determining combinations of candidate predictors that result in an accurate description of the data by testing all possible combinations is not feasible, especially if large numbers of candidates are considered. Therefore, two possible alternative approaches are sequentially adding the candidate that most improves the performance of the model or starting with all candidates and sequentially leaving out the one that leads to the least deterioration of model performance. Both approaches will result in a series of models with a number of predictors ranging from a single parameter to all candidate predictors. Subsequently the optimal model order needs to be determined. To this end various criteria, such as the AIC or BIC (Equations 20.3 and 20.4), can be used. Finally the stability of the selection of predictive factors can be assessed by performing this procedure on alternative datasets, for example, sampling by bootstrapping. For each bootstrap dataset the selection of predictive factors as described above can be repeated, and for each factor the number of times it is selected can be determined, giving an indication of which factors are generally selected, independent of statistical fluctuations in the data. Because in many studies it was demonstrated that accurate prediction of normal tissue damage requires combining clinical and dosimetric factors, optimized multivariate modeling is a promising approach to NTCP modeling.

20.6  Developments and Future Directions NTCP model development was initially inspired by improvements in radiotherapy technology allowing sparing of normal tissues. Because both clinical data relating 3D dose distributions to clinical outcome and the knowledge of mechanisms underlying the irradiated-volume dependence of the risk

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of toxicity were sparse, the models described in the previous section were based on abstract assumptions. To test the validity of these assumptions to allow improvement of the accuracy of NTCP models, many radiobiological studies have been performed, leading to new insights in the development of normal tissue damage and providing directions for improving and developing predictive NTCP models. All previously described models share a set of assumptions. First, the risk of damaging a subvolume (or functional subunit) is assumed to depend on dose to that subvolume alone. As such, damage in the tissue is assumed to be independent of events occurring elsewhere. Second, the radiation response of all subvolumes is assumed to be identical. Third, it is assumed that organ failure is the result of inactivation of a single type of target. To test these assumptions, during the past two decades numerous studies have been performed on the lung, parotid gland, and spinal cord. Already in the 1990s it was demonstrated in the mouse lung that the response of the lung to irradiation of the apex differed from that after irradiation of the base (23), indicating that the either the functional consequence of dose may vary with the location at which it is deposited within the organ. Similarly, experiments in the rat spinal cord demonstrated that laterally located white matter is more radiosensitive than centrally located white matter (24), leading to large regional differences in tolerance dose for paralysis. Finally, also in the rat parotid gland the response to irradiation of the cranial parts of the gland differed from irradiation of the caudal parts of the glands (25). All together these results demonstrate that, in contrast to current model assumptions, the response of organs to irradiation is not uniform. Moreover, in the rat spinal cord the tolerance dose for irradiation of 8-mm cord length was found to be only 56% of the tolerance to a split-field dose distribution consisting of two segments of 4 mm (26), demonstrating irradiated volume is not generally the determinant of toxicity. In addition, the tolerance of the spinal cord to irradiation of a small subvolume (shower) was strongly reduced by a subtolerance dose (e.g., 20% of ED50) administered to a larger, surrounding volume (bath) (26) (Figure 20.5A). Interestingly, this bath-andshower effect was also observed in the rat parotid gland, showing that this is not an isolated finding, unique to the spinal cord (27) (Figure 20.5B). In addition, it has been long recognized that the response of the lung is not limited to its irradiated parts (28). Taken together these observations demonstrate that the occurrence of tissue damage does not only depend on local dose. In fact, in the rat lung it was demonstrated that radiation-induced loss of pulmonary tissue strongly depended on the dose administered to the heart, showing that in fact the response of an organ may depend on the dose distribution in other organs (2). Though the exact mechanisms underlying these nonlocal effects are not fully characterized, taken together these observations all demonstrate that the functional response of an organ to irradiation is not trivially related to local dose. Moreover, even though this was demonstrated by looking at

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A) 100

Spinal cord

ED50 (Gy)

80 60 40 20

Loss of saliva production (%)

0

60 50

0

5

10 Bath dose (Gy)

15

20

B) Parotid gland

40 30 20 10 0

0

2

4 6 Bath dose (Gy)

8

10

FIGURE 20.5 The effect of irradiation of a small subvolume can be strongly modulated by coirradiation of larger volumes to a low dose. (A) The tolerance dose for irradiation of a 2-mm section of the cervical spinal cord of the rat in the center of a 20-mm section irradiated to a low dose (bath dose). Though the tolerance dose for irradiation of 20 mm of the spinal cord is 19.7 Gy, a dose of only 4 Gy already reduces the tolerance dose in the 2-mm section from 87.5 to 56 Gy. Similarly the reduction of the rat parotid saliva production after irradiation of the caudal 50% of the parotid gland to 50 Gy was increased by ~15-30% when adding a bath dose to the cranial 50%. (After van Luijk et al., Int J Radiat Oncol Phys., 73(4), 1002, 2009; van Luijk et al., Int J Radiat Oncol Phys., 61(3), 892, 2009; and Bijl et al., 64(4), 1204, 2006.)

organ-specific effects, mostly in animal models, the fact that nonlocal effects were observed in virtually any organ that was studied suggests that these nonlocal effects are likely to be the rule rather than an exception. More importantly, these effects have been shown to have a strong impact on tolerance doses and responses. This indicates that accounting for these effects in NTCP models will greatly enhance their accuracy. Improvement of NTCP models by choosing predictors based on these nonlocal mechanisms requires an approach that is more organ-specific than has been done so far. Because inclusion of full mathematical descriptions of biological mechanisms would likely lead to overly complex models with too many parameters, an epidemiological approach (i.e., logistic regression

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analysis) that uses the biological mechanisms to select candidate predictors may be preferable over mechanistic modeling approaches that were used classically. Moreover, to allow testing of candidate predictors in a clinical setting, the data gathering needs to be expanded from the widespread practice of collecting dose-volume histograms to actually storing 3D dose distributions to allow the extraction of these biology-based candidate predictors.

20.7  Applicability to Proton Therapy The development of NTCP models was inspired by the development of new techniques that allowed dose reductions in the normal tissues surrounding the target volume and the question of how to optimally put this new technology to use. As an example the introduction of advanced techniques such as proton therapy provided the clinic with an unprecedented control over the dose distribution. However, the most generally used dosimetric predictors, such as dose-volume histogram points and mean organ dose, were selected exclusively from available clinical data, which were mostly obtained in photon-based treatments. In such an analysis, only predictors showing both impact on outcome and strong variability in the dataset are selected. Because of this variability criterion, however, this does not necessarily yield those parameters that best describe the biological processes underlying the toxicity with respect to which the treatment is to be optimized. Consequently, optimization of novel treatment techniques using a thus-selected predictor is not necessarily minimizing toxicity. Moreover, new treatment modalities, such as particle therapy, allow controlling more and other characteristics of the dose distribution than was possible with the modalities that the models were based on. As such when optimizing these new modalities based on a model solely based on data obtained in old treatment techniques, unique properties of the new treatment modality are not used to their full potential. Thus, when using NTCP models developed in photon-based datasets for the optimization of proton therapy treatment it is important to realize that these models may not optimize unique features of proton therapy and NTCP estimates will be biased. As such the NTCP model can only be used routinely for proton therapy after prospective testing against actual data on the effect of proton therapy. These issues might be avoided by using independent mechanistic information obtained in preclinical studies, because this may allow the identification of predictive factors describing the underlying biological processes, independent of the extent to which their effect was the most prominent effect in existing photon-based data. As such using these biology-based factors for treatment optimization is expected to better optimize for the biological effect and use new treatment modalities such as proton therapy to their full potential.

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Acknowledgments The authors thank Dr. R. P. Coppes, Dr. C. Schilstra, and Dr. J. A. Langendijk for critically reading the manuscript. Moreover, they also thank numerous colleagues in the field for the fruitful discussions that contributed to the insights presented in this chapter.

References









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13. Langer M, Morrill SS, Lane R. A test of the claim that plan rankings are determined by relative complication and tumor-control probabilities, Int. J. Radiat. Oncol. Biol.Phys., 1998; 41(2):451–57. 14. Collet D. Modelling binary data, London: Chapman and Hall, 1991. 15. Lind PA, Marks LB, Hollis D, et al. Receiver operating characteristic curves to assess predictors of radiation-induced symptomatic lung injury, Int. J. Radiat. Oncol. Biol. Phys., 2002; 54(2):340–47. 16. Shackell LF, Williamson W, Deitchman MM, Katzman GM, Kleinman BS. The relation of dosage to effect, J. Pharmacol. Exp. Ther., 1924; 24(1):53–65. 17. Lyman JT. Complication Probability as Assessed from Dose Volume Histograms, Radiat. Res., 1985; 104(2):S13–S19. 18. Wu Q, Mohan R, Niemierko A. IMRT optimization based on the generalized equivalent uniform dose (EUD), Engineering in Medicine and Biology Society, 2000. Proceedings of the 22nd Annual International Conference of the IEEE, 2000; 710. 19. Withers HR, Taylor JM, Maciejewski B. Treatment volume and tissue tolerance, Int. J. Radiat. Oncol. Biol. Phys., 1988; 14(4):751–59. 20. Niemierko A, Goitein M. Calculation of normal tissue complication probability and dose-volume histogram reduction schemes for tissues with a critical element architecture, Radiother. Oncol., 1991; 20(3):166–76. 21. Niemierko A, Goitein M. Modeling of normal tissue response to radiation: the critical volume model, Int. J. Radiat. Oncol. Biol. Phys., 1993; 25(1):135–45. 22. Kallman P, Agren A, Brahme A. Tumour and normal tissue responses to fractionated non-uniform dose delivery, Int. J. Radiat. Biol., 1992; 62(2):249–62. 23. Travis EL, Liao ZX, Tucker SL. Spatial heterogeneity of the volume effect for radiation pneumonitis in mouse lung, Int. J. Radiat. Oncol. Biol. Phys., no. 03603016; 1997; 38(5):1045–54. 24. Bijl HP, van Luijk P, Coppes RP, Schippers JM, Konings AW, van Der Kogel AJ. Regional differences in radiosensitivity across the rat cervical spinal cord, Int. J. Radiat. Oncol. Biol. Phys., 2005; 61(2):543–51. 25. Konings AW, Cotteleer F, Faber H, van Luijk P, Meertens H, Coppes RP. Volume effects and region-dependent radiosensitivity of the parotid gland, Int. J. Radiat. Oncol. Biol. Phys., 2005; 62(4):1090–95. 26. Bijl HP, van Luijk P, Coppes RP, Schippers JM, Konings AW, van der Kogel AJ. Unexpected changes of rat cervical spinal cord tolerance caused by inhomogeneous dose distributions, Int. J. Radiat. Oncol. Biol. Phys., 2003; 57(1):274–81. 27. van Luijk P, Faber H, Schippers JM, et al. Bath and shower effects in the rat parotid gland explain increased relative risk of parotid gland dysfunction after intensity-modulated radiotherapy, Int. J. Radiat. Oncol. Biol. Phys., 2009; 74(4):1002–1005. 28. Morgan GW, Breit SN. Radiation and the lung: a reevaluation of the mechanisms mediating pulmonary injury, Int. J. Radiat. Oncol. Biol. Phys., no. 03603016; 1995: 31(2):361–69. 29. van Luijk P, Bijl HP, Konings AW, van der Kogel AJ, Schippers JM. Data on dosevolume effects in the rat spinal cord do not support existing NTCP models, Int. J. Radiat. Oncol. Biol. Phys., 2005; 61(3):pp. 892–900. 30. Bijl HP, van Luijk P, Coppes RP, Schippers JM, Konings AW, van der Kogel AJ. Influence of adjacent low-dose fields on tolerance to high doses of protons in rat cervical spinal cord, Int. J. Radiat. Oncol. Biol. Phys., 2006; 64(4):1204–10.

[cm]Y

100% = 35.5875 cGy

11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 –1.0 –2.0 –3.0 –4.0 –5.0 –6.0 –7.0 –8.0 –9.0 –10.0 –11.0

10 50 96 98 100 102 105

–10.0 –8.0 –6.0 –4.0 –2.0 0.0 2.0 4.0 6.0 8.0 10.0

B

[cm]X

A

20 40 60 80

20

40

60

FIGURE 6.8 position (x, y) 15 10

sigmaX y (cm)

5 0

–5 dose

–10 –15 –15 –10 –5

0 5 x (cm)

10

sigmaY

FIGURE 6.21

100

5 10 15 20 25 30 35 Dose [Gy] CTV

10

Nominal 1MU repainted 1MU skipped

% Volume 

60

60

40

40

20

20 0 30

80 % Volume 

80

100

20 30 40 Dose [Gy] Spinal cord

32

34 36 38 40 Dose (Gv) 

42

0 20

FIGURE 6.23

22

24 26 28 30 Dose (Gv) 

32

15

2000 1800 1600 1400 1200 1000 800 600 400 200 0

Depth [cm.H2O]

100 60 40 20 –5

0 Y [cm]

5

80 60 40 20 –5

0 Y [cm]

5

10

2 4 6 8 10 12 14 16

120 100 80 60 40 20 0 20 10 Depth 5 0–10 –5 0 [cm.H2O] Y [cm]

30 20 10 0 –10 –20

–10

10

–5

0 Y [cm]

5

10

40

Relative dose [%]

Relative dose [%]

120 100 80 60 40 20 0 20 10 Depth 5 0–10 –5 0 [cm.H2O] Y [cm]

100

–10

10

Difference eclipse - measurement

120

Relative dose [%]

–10

80

Eclipse 2 4 6 8 10 12 14 16

Depth [cm.H2O]

120

Depth [cm.H2O]

Measurement 2 4 6 8 10 12 14 16

20 0

–20

10

–40 20 10 Depth [cm.H2O]

0–10 –5

5 0 Y [cm]

10

FIGURE 8.10 105 % 95 % 50 % 20 %

Through Through beam

Target Volume

d) Patch Volume Through beam

a) 105 % 95 % 50 % 20 %

Patch

e)

Patch beam

Target Volume

b) 105 % 95 % 50 % 20 %

f)

Patch beam

Patch Volume

g)

c)

FIGURE 10.6 Disp. Width: +29.7 mm Center: (+3.1, +9.1)

Disp. Width: +36.8 mm Center: (-2.2, +6.7)

Dose % 100 90 70 50 30 10

2 2

3 1 mm

a)

1

1 mm

Scale: 5.389 : 1

b)

FIGURE 10.8

3

14

Scale: 4.345 : 1

2250 2200 2000 1000 2

Left

Right

Anterior

1 3

3

b)

a)

Posterior

c) 450 400 200 100

1100 1000 900 400

1100 1000 900 400

Pa tch

ro

Pa tch

tch

Th

Pa

h

ug ro

Th

ch

t Pa

ug

h

Through

d)

f)

e) 100

5200 5000 4750 3000 2000

GTV

90

Volume (%)

80 70

Spinal Cord

60 50 40 30 10 0

g)

0

Brainstem

h)

50 0 10 00 15 00 20 00 25 00 30 00 35 00 40 00 45 00 50 00 55 00 60 00

20

Dose (cGy * RBE)

FIGURE 10.9

a)

95% 50% 20% b)

95% 50% 20% c)

95% 50% 20% d)

95% 50% 20%

e)

95% 50% 20% f)

95% 50% 20% g)

95% 50% 20% h)

95% 50% 20%

FIGURE 10.10

Dose % 104 90 80 70 60 50 40 30 0 FIGURE 11.1

a

c

e

% 112

b

% 100

95

40

90

25

80

18

70

12

60

9

50

7

30

5

0

% 100

d

0 % 106

40

95

25

90

18

80

12

70

9

60

7

50

5

30

0

% 100

f

0 % 112

40

95

25

90

18

80

12

70

9

60

7

50

5

30

0

0

FIGURE 11.2

% 100

a

40

40

25

25

18

18

12

12

9

9

7

7

5

5

0

0 % 112

% 112

c

% 100

b

d

95

95

90

90

80

80

70

70

60

60

50

50

30

30

0

0

FIGURE 11.6

F3 F1

F4 Combined distributon

FIGURE 11.7

Dose % 107 90 80 70 60 50 40 30 0

F2

F3

F4 Combined distributon

F1

Dose % 122 90 80 70 60 50 40 30 0

F2

FIGURE 11.8

Dose % 117

26% 24%

b

Dose % 123

110

110

90

90

80

80

70

70

60

60

50

50

30

30

0

0

c

22% 20%

IMRT - 5 Fields IMRT - 9 Fields IMPT - 3 Fields IMPT - 5 Fields IMPT - 9 Fields

18% 16% 14% 12% 10%

20 .0 % 25 .0 % 30 .0 % 35 .0 % 40 .0 % 45 .0 % 50 .0 % 55 .0 %

D105-D95 (PTV at level of parotids)

a

Mean bilateral parotid dose FIGURE 11.9

a

IMPHNT_CTO_TO

b

c

IMPHNT_CTO_TO

IMPHNT_CTO_TO

2500 spots per field

150 spots per field

120 spots per field

d

e

f FIGURE 11.10

a

c

%

%

108

b

% 131

105

105

95

95

90

90

80

80

70

70

50

50

30

30

0

0 % 121

110

d

105

105

95

95

90

90

80

80

70

70

50

50

30

30

0

0

FIGURE 11.13

% 109

a

D2 = 106% D98 = 99%

% 109

b

105

105

99

99

90

90

80

80

70

70

50

50 D2 = 106% D98 = 97%

30 0

30 0

FIGURE 11.14

SFUD plan

Dose distribution

a

Composite error-bar

c

IMPT plan % 106

b

% 123

105

105

95

95

90

90

80

80

70

70

50

50

30

30

0 Diff-% 43

d

0 Diff-% 43

20

20

16

16

13

13

10

10

7

7

4

4

1

1

FIGURE 11.15

a

% 107

b

95

90

90

80

80

70

70

60

60

50

50

30

30

0

c

% 114

d

0 % 114

95

95

90

90

80

80

70

70

60

60

50

50

30

30

0

e

% 107

95

% 110

f

0 % 110

95

95

90

90

80

80

70

70

60

60

50

50

30 0

30 0

FIGURE 11.17 a

c

e

%

%

%

110

b

% 110

95

95

90

90

80

80

70

70

60

60

50

50

30

30

0 116

d

0 % 116

95

95

90

90

80

80

70

70

60

60

50

50

30

30

0 110

f

0 % 110

95

95

90

90

80

80

70

70

60

60

50

50

30

30

0

0

FIGURE 11.18

10 30 50 70 90 95 100 102

1 3 5 7 9 9.5 10

FIGURE 12.9

1 Gy(RBE) 3 Gy(RBE) 5 Gy(RBE) 7 Gy(RBE) 9 Gy(RBE) 11 Gy(RBE) 13 Gy(RBE) 15 Gy(RBE) 17 Gy(RBE)

FIGURE 12.10

6 cm.H2O Measurement

–10 –5

100 80 60 40 20 0 5 Y [cm]

100

120

Depth [cm.H2O)

2 4 6 8 10 12 14

10

Depth 8.7 cm

120

5 cm Relative dose [%]

3 cm.H2O

80 60 40

Eclipse (raw) Eclipse (convolved) Measurement (diode)

20 0 –10 FIGURE 13.3

–5

0 Y [cm]

5

10

Dose volume histogram

Norm. volume

(b) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Lower 95% Upper bound bound

0

1000 2000 3000 4000 5000 6000 Dose (cGy)

(c) 100

Case 1 Case 2

80 60 40

(a)

20 0

0

1 2 3 4 5 6 7 Dose uncertainty (%)

FIGURE 13.7

a)

b)

c) FIGURE 14.2

S R

(mm-WEL) 15

L I T 0%

T 10%

T 20%

T 30%

T 40%

7.5

0 T 50%

T 60%

T 70%

T 80%

T 90%

FIGURE 14.4

(a)

(c)

(b)

Stationary, CTV (d)

T = 4s, ϕ = 0°

Stationary, ITVR 100

(e)

80

50% 95%

Stationary

(f )

Volume [%]

105%

60 40 20

T = 4s, ϕ = 90°

T = 4s, ϕ = 90°, 90% extr.

0

T = 4s, ϕ = 0°

T = 4s, ϕ = 90°

T = 4s, ϕ = 90°, 90% etr. 75 80 85 90 95 100 105 110 115 Dose [%]

FIGURE 14.5

1 rescan

No motion

4 rescans

8 rescans

6 rescans

max: 103.2% 100.0% 90.0% 80.0% 70.0% 60.0% 50.0% 40.0% 30.0%

a)

b)

c)

d) FIGURE 14.6

e)

20.0% 10.0% 0.0%

A

B

20

30

40

Dose [%] 50

60

70

80

D

90

100

E

100

80

80

Volume [%]

100

Spinal cord

60

F

100

60

40

20 0

G

20 20

40

60

Dose [%]

80

100

0 0

Liver

40

H

20 20

40

60

80

100

0 0

Dose [%]

A

I

20

40

60

Dose [%]

FIGURE 15.2

B

C

Target

80

Stomach

60

40

0

C

D

E FIGURE 15.3

80

100

Target Dose Homogeneity

OAR Sparing FIGURE 15.5

A

B FIGURE 15.7 Physical MC PET

mGy –1500–1000–500 0

500 1000 1500

Dose

MC PET + washout

Bq/ml –200

0

200

Activity (2.5 GyE)

PET/CT Meas.

Bq/ml –150 –100 –50

0

50

100 150

Activity (32.5 GyE)

Port-1

Relative activity normalized at I.C. [%/100]

Planned dose

–100

FIGURE 16.10

Bq/ml –150 –100 –50

0

50 100 150

Day 1 Day 4 Day 7 Day 13

–50

0 Depth [mm]

50

100

5961.3

268.3

(Counts/cGy)

PET with washout

(Counts/cGy)

PG

(%)

100

Dose

0

0

0

FIGURE 16.12

a)

b)

c)

Normalised signal intensity

0.25 0.2

0.15 0.1

0.05

50 GyRBE 40 30 20 10 Beam direction

0

–0.05 –0.1 0

5

10 15 20 25 30 35 40 45 50 Radiation dose (GyRBE)

0 12 3 cm 36 GyRBE

FIGURE 16.14

6 5 4 3 2 1

FIGURE 19.9

100%

Dose calculation

Planning

B)

Volume (% per Gy)

C)

Imaging

Volume (%)

A)

30

D)

Dose-volume histogram (DVH) PTV

Myleum

Lung

Heart

20 10 0 100

0 E)

20 40 Cummulative DVH

60

0

20

60

50 0

FIGURE 20.1

40

Physics

SerieS editorS: John G WebSter, Slavik tabakov, kWan-hoonG nG

PROTON THERAPY PHYSICS Proton Therapy Physics goes beyond current books on proton therapy to provide an in-depth overview of the physics aspects of this radiation therapy modality, eliminating the need to dig through information scattered in the medical physics literature. After tracing the history of proton therapy, the book summarizes the atomic and nuclear physics background necessary for understanding proton interactions with tissue. It describes the physics of proton accelerators, the parameters of clinical proton beams, and the mechanisms to generate a conformal dose distribution in a patient. The text then covers detector systems and measuring techniques for reference dosimetry, outlines basic quality assurance and commissioning guidelines, and gives examples of Monte Carlo simulations in proton therapy. The book moves on to discussions of treatment planning for single- and multiple-field uniform doses, dose calculation concepts and algorithms, and precision and uncertainties for nonmoving and moving targets. It also examines computerized treatment plan optimization, methods for in vivo dose or beam range verification, the safety of patients and operating personnel, and the biological implications of using protons from a physics perspective. The final chapter illustrates the use of risk models for common tissue complications in treatment optimization. Along with exploring quality assurance issues and biological considerations, this practical guide collects the latest clinical studies on the use of protons in treatment planning and radiation monitoring. Suitable for both newcomers in medical physics and more seasoned specialists in radiation oncology, the book helps readers understand the uncertainties and limitations of precisely shaped dose distribution.

K11646 ISBN: 978-1-4398-3644-6

90000

9 781439 836446