Medical Image Computing and Computer-Assisted Intervention -- MICCAI 2010: 13th International Conference, Beijing, China, September 20-24, 2010, ... Vision, Pattern Recognition, and Graphics)

Lecture Notes in Computer Science Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen

Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Alfred Kobsa University of California, Irvine, CA, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen TU Dortmund University, Germany Madhu Sudan Microsoft Research, Cambridge, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max Planck Institute for Informatics, Saarbruecken, Germany

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Tianzi Jiang Nassir Navab Josien P.W. Pluim Max A. Viergever (Eds.)

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2010 13th International Conference Beijing, China, September 20-24, 2010 Proceedings, Part II

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Volume Editors Tianzi Jiang The Chinese Academy of Sciences, Institute of Automation Beijing 100080, P. R. China E-mail: [email protected] Nassir Navab Technische Universität München, Institut für Informatik I16 Boltzmannstr. 3, 85748 Garching, Germany E-mail: [email protected] Josien P.W. Pluim Max A. Viergever University Medical Center Utrecht, QS.459 Heidelberglaan 100, 3584 CX Utrecht, The Netherlands E-mail: [email protected], [email protected]

Library of Congress Control Number: 2010933822 CR Subject Classification (1998): I.4, I.5, I.2.10, I.3.5, J.3, I.6 LNCS Sublibrary: SL 6 – Image Processing, Computer Vision, Pattern Recognition, and Graphics ISSN ISBN-10 ISBN-13

0302-9743 3-642-15744-0 Springer Berlin Heidelberg New York 978-3-642-15744-8 Springer Berlin Heidelberg New York

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. springer.com © Springer-Verlag Berlin Heidelberg 2010 Printed in Germany Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper 06/3180

Preface

The 13th International Conference on Medical Image Computing and ComputerAssisted Intervention, MICCAI 2010, was held in Beijing, China from 20-24 September, 2010. The venue was the China National Convention Center (CNCC), China’s largest and newest conference center with excellent facilities and a prime location in the heart of the Olympic Green, adjacent to characteristic constructions like the Bird’s Nest (National Stadium) and the Water Cube (National Aquatics Center). MICCAI is the foremost international scientific event in the field of medical image computing and computer-assisted interventions. The annual conference has a high scientific standard by virtue of the threshold for acceptance, and accordingly MICCAI has built up a track record of attracting leading scientists, engineers and clinicians from a wide range of technical and biomedical disciplines. This year, we received 786 submissions, well in line with the previous two conferences in New York and London. Three program chairs and a program committee of 31 scientists, all with a recognized standing in the field of the conference, were responsible for the selection of the papers. The review process was set up such that each paper was considered by the three program chairs, two program committee members, and a minimum of three external reviewers. The review process was double-blind, so the reviewers did not know the identity of the authors of the submission. After a careful evaluation procedure, in which all controversial and gray area papers were discussed individually, we arrived at a total of 251 accepted papers for MICCAI 2010, of which 45 were selected for podium presentation and 206 for poster presentation. The acceptance percentage (32%) was in keeping with that of previous MICCAI conferences. All 251 papers are included in the three MICCAI 2010 LNCS volumes. We are greatly indebted to the reviewers and to the members of the program committee for their invaluable efforts in critically assessing and evaluating the submissions in a very short time frame. The annual MICCAI event has, in addition to its main conference, a rising number of satellite tutorials and workshops, organized on the day before and the day after the main conference. This year’s call for submission for tutorials and workshops led to a record number of proposals, of which a significant fraction had to be rejected because of space and time limitations. The final program hosted eight tutorials, which together gave a comprehensive overview of many areas of the field, and provided rich educational material especially aimed at PhD students and postdoctoral researchers. The 15 workshops gave - mostly younger - researchers the opportunity to present their work, often in an early stage of their investigations, so that they could obtain useful feedback from more experienced scientists in the field. The

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workshop subjects highlighted topics that were not all fully covered in the main conference, and thus added to the diversity of the MICCAI program. In particular, several workshops offered so-called challenges in which researchers were in competition to best segment or register a set of clinical images with ground truth provided by medical experts. We are grateful to the tutorial and workshop committees, in particular to the chairs Dinggang Shen and Bram van Ginneken, for making these satellite events a success. Highlights of the conference were the two keynote lectures. Professor Alan C. Evans of the McConnell Brain Imaging Centre, Montreal Neurological Institute, McGill University, Montreal, Canada described recent activity in brain network modeling with an emphasis on anatomical correlation analysis in his presentation “Network Analysis of Cortical Anatomy”. Professor Guang-Zhong Yang of the Royal Society/Wolfson Medical Image Computing Laboratory, Imperial College, London, UK outlined key clinical challenges and research opportunities in developing minimally invasive surgery systems in his presentation “Snake and Lobster - A Feast for MICCAI?”. MICCAI 2010 would not have been feasible without the efforts of many people behind the scenes. We are particularly indebted to the local organizing committee in Beijing, consisting of Nianming Zuo, Yong Liu, Ming Song, Bing Liu, Bizhen Hong, Shaomei Wang, and Gangqin Zhang, all of the Institute of Automation of the Chinese Academy of Sciences, for their excellent work before and during the conference, and to Jacqueline Wermers for her outstanding assistance with the editorial work in compiling the three Springer LNCS books that contain the proceedings of this conference. We are obliged to the Board of the MICCAI Society for the opportunity to organize this prestigious conference, and to many of the Society Board and Staff members for valuable and continuous advice and support through all phases of the preparation. A special word of thanks goes to our sponsors, who generously provided financial support of the conference as a whole, or of specific activities. This greatly helped us with the overall organization of the meeting, as well as allowed us to award prizes for best papers in various categories and travel stipends to an appreciable number of student participants. It was our great pleasure to welcome the attendees to Beijing for this exciting MICCAI 2010 conference and its satellite tutorials and workshops. The 14th International Conference on Medical Image Computing and Computer-Assisted Intervention will be held in Toronto, Canada, from 15-21 September 2011. We look forward to seeing you there. September 2010

Tianzi Jiang Nassir Navab Josien Pluim Max Viergever

Organization

General Chair and Co-chairs Tianzi Jiang Alan Colchester James Duncan

Institute of Automation, CAS, China University of Kent, UK Yale University, USA

Program Chair and Co-chairs Max Viergever Nassir Navab Josien Pluim

Utrecht University and UMC Utrecht, The Netherlands Technische Universit¨ at M¨ unchen, Germany University Medical Center Utrecht, The Netherlands

Workshop Chair and Co-chairs Bram van Ginneken Yong Fan Polina Golland Tim Salcudean

Radboud University Nijmegen, The Netherlands Institute of Automation, CAS, China Massachusetts Institute of Technology, USA University of British Columbia, Canada

Tutorial Chair and Co-chairs Dinggang Shen Alejandro Frangi G´ abor Sz´ekely

University of North Carolina, USA Universitat Pompeu Fabra, Spain ETH Z¨ urich, Switzerland

MICCAI Society, Board of Directors Nicholas Ayache Kevin Cleary James Duncan (President) Gabor Fichtinger Polina Golland Tianzi Jiang Nassir Navab Alison Noble S´ebastien Ourselin Ichiro Sakuma Sandy Wells Guang-Zhong Yang

INRIA Sophia Antipolis, France Georgetown University, USA Yale University, USA Queen’s University, Canada Massachusetts Institute of Technology, USA Institute of Automation, CAS, China Technische Universit¨ at M¨ unchen, Germany University of Oxford, UK University College London, UK University of Tokyo, Japan Harvard Medical School, USA Imperial College London, UK

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Organization

Program Committee Christian Barillot Albert Chung Gabor Fichtinger Alejandro Frangi Jim Gee Bram van Ginneken Polina Golland David Hawkes Xiaoping Hu Hongen Liao Huafeng Liu Cristian Lorenz Frederik Maes Anne Martel Kensaku Mori Mads Nielsen Poul Nielsen Wiro Niessen Xiaochuan Pan Franjo Pernuˇs Terry Peters Daniel Rueckert Tim Salcudean Yoshinobu Sato Dinggang Shen Pengcheng Shi G´ abor Sz´ekely Jocelyne Troccaz Simon Warfield Carl-Fredrik Westin Guang-Zhong Yang

IRISA Rennes, France Hong Kong UST, China Queen’s University, Canada Universitat Pompeu Fabra, Spain University of Pennsylvania, USA Radboud University Nijmegen, The Netherlands Massachusetts Institute of Technology, USA University College London, UK Emory University, USA University of Tokyo, Japan Zhejiang University, China Philips Research Lab Hamburg, Germany University of Leuven, Belgium University of Toronto, Canada Nagoya University, Japan University of Copenhagen, Denmark University of Auckland, New Zealand Erasmus MC Rotterdam, The Netherlands University of Chicago, USA University of Ljubljana, Slovenia Robarts Research Institute, Canada Imperial College London, UK University of British Columbia, Canada Osaka University, Japan University of North Carolina, USA Rochester Institute of Technology, USA ETH Z¨ urich, Switzerland TIMC-IMAG, Grenoble, France Harvard University, USA Harvard University, USA Imperial College London, UK

Local Organizing Committee Nianming Zuo Yong Liu Ming Song Bing Liu Bizhen Hong Shaomei Wang Gangqin Zhang Jacqueline Wermers

Institute of Automation, Chinese Academy of Sciences, China

UMC Utrecht, The Netherlands

Organization

Reviewers Abolmaesumi, Purang Abugharbieh, Rafeef Acar, Burak Aja-Fern´ andez, Santiago Akselrod-Ballin, Ayelet Alexander, Andrew Alexander, Daniel Aljabar, Paul Alomari, Raja Alvino, Christopher An, Jungha Angelini, Elsa Anor, Tomer Arbel, Tal Arridge, Simon Ashburner, John Astley, Sue Atkinson, David Audette, Michel Avants, Brian Awate, Suyash Babalola, Kolawole Bach Cuadra, Meritxell Baillet, Sylvain Banks, Scott Barratt, Dean Batchelor, Philip Baumann, Michael Bazin, Pierre-Louis Beckmann, Christian Beg, Mirza Faisal Beichel, Reinhard Berger, Marie-Odile Bergtholdt, Martin Berman, Jeffrey Betke, Margrit Bhalerao, Abhir Bhotika, Rahul Bian, Junguo Birkfellner, Wolfgang Birn, Rasmus Bischof, Horst Boctor, Emad Boisvert, Jonathan

Bosch, Johan Bouix, Sylvain Boukerroui, Djamal Bourgeat, Pierrick Brady, Mike Bricault, Ivan Brun, Caroline Buelow, Thomas Bullitt, Elizabeth Burschka, Darius Butakoff, Constantine Cahill, Nathan Cai, Yiyu Camara, Oscar Cardenes, Ruben Cates, Joshua Cattin, Philippe Chakravarty, Mallar Chen, Elvis Chen, Sheng Chen, Wei Chen, Yunmei Chen, Zhiqiang Cheriet, Farida Chinzei, Kiyoyuki Chou, Yiyu Christensen, Gary Chung, Moo Cinquin, Philippe Ciuciu, Philippe Claridge, Ela Clarysse, Patrick Cleary, Kevin Clerc, Maureen Colchester, Alan Collins, Louis Colliot, Olivier Comaniciu, Dorin Commowick, Olivier Cook, Philip Cootes, Tim Cotin, St´ephane Coulon, Olivier Coup´e, Pierrick

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Organization

Craddock, Cameron Crozier, Stuart Crum, William Darkner, Sune Dauguet, Julien Dawant, Benoit De Bruijne, Marleen De Buck, Stijn De Craene, Mathieu Deguchi, Daisuke Dehghan, Ehsan Deligianni, Fani Demirci, Stefanie Deriche, Rachid Descoteaux, Maxime Desphande, Gopikrishna Desvignes, Michel Dey, Joyoni Dijkstra, Jouke DiMaio, Simon Doignon, Christophe Douiri, Abdel Drangova, Maria Du, Yiping Duan, Qi Duchesne, Simon Duncan, James Dupont, Pierre Ebrahimi, Mehran Ecabert, Olivier Eggers, Georg Ehrhardt, Jan El-Baz, Ayman Ellis, Randy Enescu, Monica Fabry, Thomas Fahrig, Rebecca Fan, Yong Farag, Aly Fenster, Aaron Feragen, Aasa Ferrari, Ricardo Feuerstein, Marco Figl, Michael Fillard, Pierre

Fischer, Bernd Fitzpatrick, Michael Fleig, Oliver Florack, Luc Fouard, Celine Freysinger, Wolfgang Fuernstahl, Philipp Funka-Lea, Gareth Gan, Rui Ganz, Melanie Gao, Fei Gee, Andrew Gerig, Guido Gessat, Michael Gholipour, Ali Gibaud, Bernard Gladilin, Evgeny Glocker, Ben Goksel, Orcun Gonzalez Ballester, Miguel Angel Gooding, Mark Goodlett, Casey Gooya, Ali Gorbunova, Vladlena Grady, Leo Graham, Jim Grau, Vicente Groher, Martin Gu, Lixu Guehring, Jens Guetter, Christoph Haake, Anne Hager, Gregory Hahn, Horst Hamarneh, Ghassan Han, Xiao Hanson, Dennis Harders, Matthias Hastreiter, Peter Hata, Nobuhiko Haynor, David He, Yong Heimann, Tobias Hellier, Pierre Heng, Pheng Ann

Organization

Hermosillo, Gerardo Higgins, William Hipwell, John Ho, Hon Pong Hoffmann, Kenneth Hogeweg, Laurens Holmes, David Holz, Dirk Hoogendoorn, Corn´e Hornegger, Joachim Howe, Robert Hu, Mingxing Hu, Zhenghui Huang, Heng Huang, Qi-xing Huang, Xiaolei Huo, Xiaoming Hyde, Damon Ingalhalikar, Madhura Iˇsgum, Ivana Jain, Ameet Janke, Andrew Jannin, Pierre Jin, Mingwu Jomier, Julien Joshi, Anand Joshi, Sarang Kabus, Sven Kadah, Yasser Kadir, Timor Kadoury, Samuel Kamen, Ali Kang, Dong-Goo Karemore, Gopal Karssemeijer, Nico Kaus, Michael Kazanzides, Peter Keeve, Erwin Kerrien, Erwan Kervrann, Charles Kikinis, Ron Kim, Boklye Kindlmann, Gordon King, Andrew Kirchberg, Klaus

Kitasaka, Takayuki Klein, Arno Klein, Stefan Klinder, Tobias Kontos, Despina Krissian, Karl Kruggel, Frithjof Kutter, Oliver Kybic, Jan Lai, Shang-Hong Laine, Andrew Landman, Bennett Langs, Georg Larrabide, Ignacio Larsen, Rasmus Lassen, Bianca Law, Max Lazar, Mariana Lee, Junghoon Leemans, Alexander Lei, Hao Lekadir, Karim Lelieveldt, Boudewijn Leow, Alex Lepore, Natasha Lerch, Jason Lesage, David Li, Chunming Li, Ming Li, Quanzheng Li, Shuo Liang, Jianming Liao, Rui Liao, Shu Likar, Boˇstjan Lin, Xiang Lindseth, Frank Linguraru, Marius George Linte, Cristian Litt, Harold Liu, Alan Liu, Tianming Liu, Yong Lo, Pechin Loeckx, Dirk

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Organization

Loew, Murray Lu, Le Luan, Kuan Luboz, Vincent Luo, Yishan Ma, Burton Madabhushi, Anant Maeder, Anthony Magee, Derek Maier-Hein, Lena Mainprize, James Malandain, Gregoire Manduca, Armando Mangin, Jean-Fran¸cois Mao, Hongda Mao, Hui Markelj, Primoˇz Mart´ı, Robert Martin-Fernandez, Marcos Masamune, Ken Masutani, Yoshitaka Mazza, Edoardo McClelland, Jamie McCulloch, Andrew McGregor, Robert Metaxas, Dimitris Metz, Coert Meyer, Chuck Miller, James Milles, Julien Mohamed, Ashraf Moireau, Philippe Mollemans, Wouter Mungwe, Stanley Murgasova, Maria Murphy, Keelin Mylonas, George Naish, Michael Nakamoto, Masahiko Nash, Martyn Nedjati-Gilani, Shahrum Nichols, Thomas Nicolau, Stephane Niemeijer, Meindert Niethammer, Marc

Nimura, Yukitaka Noble, Alison No¨el, Peter Nolte, Lutz Noonan, David Oda, Masahiro O’Donnell, Lauren O’Donnell, Thomas Ogier, Arnaud Oguz, Ipek Olabarriaga, Silvia Olmos, Salvador Olszewski, Mark Orkisz, Maciej Otake, Yoshito Ourselin, S´ebastien Ozarslan, Evren Pang, Wai-Man Pantazis, Dimitrios Papadopoulo, Th´eo Paragios, Nikos Pasternak, Ofer Patriciu, Alexandru Pavani, Sri Kaushik Payan, Yohan Peitgen, Heinz-Otto Pennec, Xavier Penney, Graeme Petersen, Kersten Petr, Jan Peyrat, Jean-Marc Pham, Dzung Pichon, Eric Pike, Bruce Pitiot, Alain Pizarro, Luis Pohl, Kilian Maria Poignet, Philippe Prager, Richard Prastawa, Marcel Prause, Guido Prima, Sylvain Prince, Jerry Promayon, Emmanuel Qi, Jinyi

Organization

Qian, Xiaoning Radeva, Petia Rajagopal, Vijayaraghavan Rajpoot, Nasir Rangarajan, Anand Rasche, Volker Reichl, Tobias Reinhardt, Joseph Rexilius, Jan Reyes, Mauricio Rhode, Kawal Ribbens, Annemie Ridgway, Gerard Rittscher, Jens Rivaz, Hassan Riviere, Cameron Robb, Richard Robinson, Emma Rohlfing, Torsten Rohling, Robert Rohr, Karl Rougon, Nicolas Rousseau, Fran¸cois Russakoff, Daniel Sabuncu, Mert Rory Sachse, Frank Sakuma, Ichiro Salvado, Olivier Samani, Abbas Sanchez, Clara Savadjiev, Peter Schaap, Michiel Scherrer, Benoit Schnabel, Julia Schweikard, Achim Sebastian, Rafa Sermesant, Maxime Shams, Ramtin Shechter, Guy Shi, Yonggang Shi, Yundi Shimizu, Akinobu Siddiqi, Kaleem Sidky, Emil Siewerdsen, Jeffrey

Simaan, Nabil Skrinjar, Oskar Slagmolen, Pieter Sled, John Smal, Ihor Smeets, Dirk Smelyanskiy, Mikhail So, Wai King Sommer, Stefan Song, Xubo Sonka, Milan Sørensen, Lauge Spillmann, Jonas Sporring, Jon Staal, Joes Staib, Lawrence Staring, Marius Stewart, James Stoyanov, Danail Studholme, Colin Styner, Martin Suarez, Ralph Subramanian, Navneeth Sukno, Federico Summers, Ronald Suzuki, Kenji Szczerba, Dominik Szilagyi, Laszlo Tanner, Christine Tao, Xiaodong Tasdizen, Tolga Taylor, Chris Taylor, Russell Taylor, Zeike Tek, Huseyin Ter Haar Romeny, Bart Th´evenaz, Philippe Thiran, Jean-Philippe Thiriet, Marc Thirion, Bertrand Todd Pokropek, Andrew Toews, Matthew Tomaˇzeviˇc, Dejan Tosun, Duygu Trist´ an-Vega, Antonio

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Organization

Tsechpenakis, Gavriil Tustison, Nicholas Tutar, Ismail Twining, Carole Unal, Gozde Vaillant, Regis Van Leemput, Koen Van Rikxoort, Eva Van Stralen, Marijn Van Walsum, Theo Vannier, Michael Vemuri, Baba Venkataraman, Archana Vercauteren, Tom Verma, Ragini Vidal, Pierre Paul Vik, Torbj¨ orn Vilanova, Anna Villard, Pierre-Frederic Von Berg, Jens Voros, Sandrine Vos, Frans Vosburgh, Kirby Vrooman, Henri Vrtovec, Tomaˇz Wachinger, Christian Wang, Defeng Wang, Fei Wang, Junchen Wang, Linwei Wang, Yalin Wang, Yongmei Michelle Ward, Aaron Watton, Paul Weber, Stefan Weese, J¨ urgen Wein, Wolfgang Weisenfeld, Neil Wells, William West, Jay Whitaker, Ross

Wiemker, Rafael Wimmer, Andreas Wolf, Ivo Wolz, Robin Wong, Ken Woolrich, Mark Wu, Ed Wu, Guorong Wu, John Jue Xia, Dan Xu, Jianwu Xu, Qianyi Xue, Zhong Yan, Pingkun Yang, Hua Yap, Pew-Thian Yeo, Thomas Yezzi, Anthony Yoo, Terry Yoshida, Hiro Young, Alistair Yu, Weichuan Yushkevich, Paul Zang, Yufeng Zhang, Heye Zhang, Hui Zhang, Yong Zhao, Fuqiang Zheng, Bo Zheng, Guoyan Zheng, Yefeng Zhou, Luping Zhou, Kevin Zhou, Xiang Zhou, Yu Zhu, Hongtu Zhu, Yun Zikic, Darko Z¨ollei, Lilla Zuo, Nianming Zwiggelaar, Reyer

Organization

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Awards Presented at the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2009, London MICCAI Society Enduring Impact Award The Enduring Impact Award is the highest award of the Medical Image Computing and Computer-Assisted Intervention Society. It is a career award for continued excellence in the MICCAI research field. The 2009 Enduring Impact Award was presented to Ron Kikinis, Harvard Medical School, USA. MICCAI Society Fellowships MICCAI Fellowships are bestowed annually on a small number of senior members of the Society in recognition of substantial scientific contributions to the MICCAI research field and service to the MICCAI community. The first fellowships were presented in 2009, to Nicholas Ayache (INRIA Sophia-Antipolis, France) Alan Colchester (University of Kent, UK) Takeyoshi Dohi (University of Tokyo, Japan) Guido Gerig (University of Utah, USA) David Hawkes (University College London, UK) Karl Heinz H¨ ohne (University of Hamburg, Germany) Ron Kikinis (Harvard Medical School, USA) Terry Peters (Robarts Research Institute, Canada) Richard Robb (Mayo Clinic, USA) Chris Taylor (University of Manchester, UK) Russ Taylor (Johns Hopkins University, USA) Max Viergever (University Medical Center Utrecht, The Netherlands). MedIA-MICCAI Prize The 2009 MedIA-MICCAI Prize for the best paper in the special MICCAI issue of Medical Image Analysis, sponsored by Elsevier, was awarded to Vicky Wang (University of Auckland, New Zealand) for the article “Modelling passive diastolic mechanics with quantitative MRI of cardiac structure and function”, authored by Vicky Y. Wang, Hoi I. Lam, Daniel B. Ennis, Brett R. Cowan, Alistair A. Young, and Martyn P. Nash. Best Paper in Navigation The prize for the best paper in the MICCAI 2009 conference in the area of navigation, sponsored by Medtronic, was awarded to Wolfgang Wein (Siemens Corporate Research, Princeton, USA) for the article: “Towards guidance of electrophysiological procedures with realtime 3D intracardiac echocardiography fusion to C-arm CT”, authored by Wolfgang Wein, Estelle Camus, Matthias John, Mamadou Diallo, Christophe Duong, Amin Al-Ahmad, Rebecca Fahrig, Ali Khamene, and Chenyang Xu.

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Organization

Best Paper in Computer-Assisted Intervention Systems and Medical Robotics The prize for the best paper in the MICCAI 2009 conference in the area of computer-assisted intervention systems and medical robotics, sponsored by Intuitive Surgical, was awarded to Marcin Balicki (Johns Hopkins University, USA) for the article “Single fiber optical coherence tomography microsurgical instruments for computer and robot-assisted retinal surgery”, authored by Marcin Balicki, Jae-Ho Han, Iulian Iordachita, Peter Gehlbach, James Handa, Russell Taylor, Jin Kang. MICCAI Young Scientist Awards The Young Scientist Awards are stimulation prizes awarded to the best first authors of MICCAI contributions in distinct subject areas. The nominees had to be a full-time student at a recognized university at - or within the two years before - the time of submission. The 2009 MICCAI Young Scientist Awards were presented to Tammy Riklin Raviv (MIT, USA), for the article “Joint segmentation of image ensembles via latent atlases” Christopher Rohkohl (Friedrich-Alexander University, Germany), for the article “‘Interventional 4-D motion estimation and reconstruction of cardiac vasculature without motion” Peter Savadjiev (Harvard Medical School, USA), for the article “Local white matter geometry indices from diffusion tensor gradients” Lejing Wang (TU Munich, Germany), for the article “Parallax-free long bone X-ray image stitching” Yiyi Wei (INRIA Lille, France; LIAMA CASIA, China), for the article “Toward real-time simulation of blood-coil interaction during aneurysm embolization”.

Table of Contents – Part II

Ultrasound Imaging Temporal Diffeomorphic Free-Form Deformation for Strain Quantification in 3D-US Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mathieu De Craene, Gemma Piella, Nicolas Duchateau, Etel Silva, Adelina Doltra, Hang Gao, Jan D’hooge, Oscar Camara, Josep Brugada, Marta Sitges, and Alejandro F. Frangi Tracked Ultrasound Elastography (TrUE) . . . . . . . . . . . . . . . . . . . . . . . . . . . Pezhman Foroughi, Hassan Rivaz, Ioana N. Fleming, Gregory D. Hager, and Emad M. Boctor Evaluation of Inter-session 3D-TRUS to 3D-TRUS Image Registration for Repeat Prostate Biopsies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vaishali V. Karnik, Aaron Fenster, Jeff Bax, Lori Gardi, Igor Gyacskov, Jacques Montreuil, Cesare Romagnoli, and Aaron D. Ward Manifold Learning for Image-Based Breathing Gating with Application to 4D Ultrasound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Christian Wachinger, Mehmet Yigitsoy, and Nassir Navab Measurement of the Skin-Liver Capsule Distance on Ultrasound RF Data for 1D Transient Elastography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . St´ephane Audi`ere, Maurice Charbit, Elsa D. Angelini, Jennifer Oudry, and Laurent Sandrin Incremental Shape Statistics Learning for Prostate Tracking in TRUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pingkun Yan and Jochen Kruecker Fast and Accurate Ultrasonography for Visceral Fat Measurement . . . . . . You Zhou, Norihiro Koizumi, Naoto Kubota, Takaharu Asano, Kazuhito Yuhashi, Takashi Mochizuki, Takashi Kadowaki, Ichiro Sakuma, and Hongen Liao Real-Time Gating of IVUS Sequences Based on Motion Blur Analysis: Method and Quantitative Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Carlo Gatta, Simone Balocco, Francesco Ciompi, Rayyan Hemetsberger, Oriol Rodriguez Leor, and Petia Radeva

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Table of Contents – Part II

Registration of a Statistical Shape Model of the Lumbar Spine to 3D Ultrasound Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Siavash Khallaghi, Parvin Mousavi, Ren Hui Gong, Sean Gill, Jonathan Boisvert, Gabor Fichtinger, David Pichora, Dan Borschneck, and Purang Abolmaesumi Automatic Prostate Segmentation Using Fused Ultrasound B-Mode and Elastography Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Sara Mahdavi, Mehdi Moradi, William J. Morris, and Septimiu E. Salcudean

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Neuroimage Analysis ODF Maxima Extraction in Spherical Harmonic Representation via Analytical Search Space Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Iman Aganj, Christophe Lenglet, and Guillermo Sapiro An Anthropomorphic Polyvinyl Alcohol Triple-Modality Brain Phantom Based on Colin27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sean Jy-Shyang Chen, Pierre Hellier, Jean-Yves Gauvrit, Maud Marchal, Xavier Morandi, and D. Louis Collins Statistical Analysis of Structural Brain Connectivity . . . . . . . . . . . . . . . . . Renske de Boer, Michiel Schaap, Fedde van der Lijn, Henri A. Vrooman, Marius de Groot, Meike W. Vernooij, M. Arfan Ikram, Evert F.S. van Velsen, Aad van der Lugt, Monique M.B. Breteler, and Wiro J. Niessen Maximum A Posteriori Estimation of Isotropic High-Resolution Volumetric MRI from Orthogonal Thick-Slice Scans . . . . . . . . . . . . . . . . . . Ali Gholipour, Judy A. Estroff, Mustafa Sahin, Sanjay P. Prabhu, and Simon K. Warfield Change Detection in Diffusion MRI Using Multivariate Statistical Testing on Tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Antoine Grigis, Vincent Noblet, F´elix Renard, Fabrice Heitz, Jean-Paul Armspach, and Lucien Rumbach Increasing Power to Predict Mild Cognitive Impairment Conversion to Alzheimer’s Disease Using Hippocampal Atrophy Rate and Statistical Shape Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kelvin K. Leung, Kai-Kai Shen, Josephine Barnes, Gerard R. Ridgway, Matthew J. Clarkson, Jurgen Fripp, Olivier Salvado, Fabrice Meriaudeau, Nick C. Fox, Pierrick Bourgeat, and S´ebastien Ourselin

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Table of Contents – Part II

Consistent 4D Cortical Thickness Measurement for Longitudinal Neuroimaging Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yang Li, Yaping Wang, Zhong Xue, Feng Shi, Weili Lin, Dinggang Shen, and The Alzheimer’s Disease Neuroimaging Initiative Fiber-Centered Analysis of Brain Connectivities Using DTI and Resting State FMRI Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jinglei Lv, Lei Guo, Xintao Hu, Tuo Zhang, Kaiming Li, Degang Zhang, Jianfei Yang, and Tianming Liu A Generative Model for Brain Tumor Segmentation in Multi-Modal Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bjoern H. Menze, Koen Van Leemput, Danial Lashkari, Marc-Andr´e Weber, Nicholas Ayache, and Polina Golland Spatio-temporal Analysis of Brain MRI Images Using Hidden Markov Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ying Wang, Susan M. Resnick, and Christos Davatzikos Estimating Local Surface Complexity Maps Using Spherical Harmonic Reconstructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rachel Aine Yotter, Paul M. Thompson, Igor Nenadic, and Christian Gaser Brain Morphometry by Probabilistic Latent Semantic Analysis . . . . . . . . U. Castellani, A. Perina, V. Murino, M. Bellani, G. Rambaldelli, M. Tansella, and P. Brambilla Joint Factor and Kinetic Analysis of Dynamic FDOPA PET Scans of Brain Cancer Patients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. Dowson, P. Bourgeat, S. Rose, M. Daglish, J. Smith, M. Fay, A. Coulthard, C. Winter, D. MacFarlane, P. Thomas, S. Crozier, and O. Salvado

XIX

133

143

151

160

169

177

185

Early Detection of Emphysema Progression . . . . . . . . . . . . . . . . . . . . . . . . . Vladlena Gorbunova, Sander S.A.M. Jacobs, Pechin Lo, Asger Dirksen, Mads Nielsen, Alireza Bab-Hadiashar, and Marleen de Bruijne

193

Unsupervised Learning of Brain States from fMRI Data . . . . . . . . . . . . . . . ´ M´ F. Janoos, R. Machiraju, S. Sammet, M.V. Knopp, and I.A. orocz

201

Geometrical Consistent 3D Tracing of Neuronal Processes in ssTEM Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Verena Kaynig, Thomas J. Fuchs, and Joachim M. Buhmann

209

XX

Table of Contents – Part II

Analysis of the Striato-Thalamo-Cortical Connectivity on the Cortical Surface to Infer Biomarkers of Huntington’s Disease . . . . . . . . . . . . . . . . . . Linda Marrakchi-Kacem, Christine Delmaire, Alan Tucholka, Pauline Roca, Pamela Guevara, Fabrice Poupon, J´erˆ ome Yelnik, Alexandra Durr, Jean-Fran¸cois Mangin, St´ephane Lehericy, and Cyril Poupon The Fiber Laterality Histogram: A New Way to Measure White Matter Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lauren J. O’Donnell, Carl-Fredrik Westin, Isaiah Norton, Stephen Whalen, Laura Rigolo, Ruth Propper, and Alexandra J. Golby A Geometry-Based Particle Filtering Approach to White Matter Tractography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Peter Savadjiev, Yogesh Rathi, James G. Malcolm, Martha E. Shenton, and Carl-Fredrik Westin Accurate Definition of Brain Regions Position through the Functional Landmark Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bertrand Thirion, Ga¨el Varoquaux, and Jean-Baptiste Poline A Comparison of the Cingulum Tract in ALS-B Patients and Controls Using Kernel Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sander van Noorden, Matthan Caan, Maaike van der Graaff, Lucas van Vliet, and Frans Vos Optimally-Discriminative Voxel-Based Analysis . . . . . . . . . . . . . . . . . . . . . . Tianhao Zhang and Christos Davatzikos Hippocampal Shape Classification Using Redundancy Constrained Feature Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Luping Zhou, Lei Wang, Chunhua Shen, and Nick Barnes Simulation of Brain Mass Effect with an Arbitrary Lagrangian and Eulerian FEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yasheng Chen, Songbai Ji, Xunlei Wu, Hongyu An, Hongtu Zhu, Dinggang Shen, and Weili Lin Relating Structural and Functional Connectivity to Performance in a Communication Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jeffrey T. Duda, Corey McMillan, Murray Grossman, and James C. Gee Bayesian Classification of Multiple Sclerosis Lesions in Longitudinal MRI Using Subtraction Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Colm Elliott, Simon J. Francis, Douglas L. Arnold, D. Louis Collins, and Tal Arbel

217

225

233

241

249

257

266

274

282

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Table of Contents – Part II

XXI

Multivariate Network-Level Approach to Detect Interactions between Large-Scale Functional Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wei Gao, Hongtu Zhu, Kelly Giovanello, and Weili Lin

298

A Generalized Learning Based Framework for Fast Brain Image Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minjeong Kim, Guorong Wu, Pew-Thian Yap, and Dinggang Shen

306

Tracking Clathrin Coated Pits with a Multiple Hypothesis Based Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liang Liang, Hongying Shen, Pietro De Camilli, and James S. Duncan Shape-Based Diffeomorphic Registration on Hippocampal Surfaces Using Beltrami Holomorphic Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lok Ming Lui, Tsz Wai Wong, Paul Thompson, Tony Chan, Xianfeng Gu, and Shing-Tung Yau Detecting Brain Activation in fMRI Using Group Random Walker . . . . . Bernard Ng, Ghassan Hamarneh, and Rafeef Abugharbieh Measures for Characterizing Directionality Specific Volume Changes in TBM of Brain Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vidya Rajagopalan, Julia Scott, Piotr A. Habas, Kio Kim, Francois Rousseau, Orit A. Glenn, A. James Barkovich, and Colin Studholme Inter-subject Connectivity-Based Parcellation of a Patch of Cerebral Cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pauline Roca, Alan Tucholka, Denis Rivi`ere, Pamela Guevara, Cyril Poupon, and Jean-Fran¸cois Mangin On Super-Resolution for Fetal Brain MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Rousseau, K. Kim, C. Studholme, M. Koob, and J.-L. Dietemann Spatial Regularization of Functional Connectivity Using High-Dimensional Markov Random Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . Wei Liu, Peihong Zhu, Jeffrey S. Anderson, Deborah Yurgelun-Todd, and P. Thomas Fletcher

315

323

331

339

347

355

363

Simulation of Anatomical Structures Shell Model for Reconstruction and Real-Time Simulation of Thin Anatomical Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Olivier Comas, Christian Duriez, and St´ephane Cotin

371

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Table of Contents – Part II

Personalization of Cubic Hermite Meshes for Efficient Biomechanical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pablo Lamata, Steven Niederer, David Barber, David Norsletten, Jack Lee, Rod Hose, and Nic Smith Real-Time Surgical Simulation Using Reduced Order Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zeike A. Taylor, Stuart Crozier, and S´ebastien Ourselin Simulation of Nodules and Diffuse Infiltrates in Chest Radiographs Using CT Templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G.J.S. Litjens, L. Hogeweg, A.M.R. Schilham, P.A. de Jong, M.A. Viergever, and B. van Ginneken High-Fidelity Meshes from Tissue Samples for Diffusion MRI Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eleftheria Panagiotaki, Matt G. Hall, Hui Zhang, Bernard Siow, Mark F. Lythgoe, and Daniel C. Alexander A Dynamic Skull Model for Simulation of Cerebral Cortex Folding . . . . . Hanbo Chen, Lei Guo, Jingxin Nie, Tuo Zhang, Xintao Hu, and Tianming Liu Coupled Personalisation of Electrophysiology Models for Simulation of Induced Ischemic Ventricular Tachycardia . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Relan, P. Chinchapatnam, M. Sermesant, K. Rhode, H. Delingette, R. Razavi, and N. Ayache Real Time Ultrasound Needle Image Simulation Using Multi-dimensional Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mengchen Zhu and Septimiu E. Salcudean

380

388

396

404

412

420

429

Endoscopic and Microscopic Imaging Endoscopic Video Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selen Atasoy, Diana Mateus, Joe Lallemand, Alexander Meining, Guang-Zhong Yang, and Nassir Navab Automated Training Data Generation for Microscopy Focus Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dashan Gao, Dirk Padfield, Jens Rittscher, and Richard McKay Augmenting Capsule Endoscopy Diagnosis: A Similarity Learning Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Seshamani, R. Kumar, T. Dassopoulos, G. Mullin, and G. Hager

437

446

454

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A Fully Automated Approach to Segmentation of Irregularly Shaped Cellular Structures in EM Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aur´elien Lucchi, Kevin Smith, Radhakrishna Achanta, Vincent Lepetit, and Pascal Fua Automatic Neuron Tracing in Volumetric Microscopy Images with Anisotropic Path Searching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jun Xie, Ting Zhao, Tzumin Lee, Eugene Myers, and Hanchuan Peng An Image Retrieval Approach to Setup Difficulty Levels in Training Systems for Endomicroscopy Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Barbara Andr´e, Tom Vercauteren, Anna M. Buchner, Muhammad Waseem Shahid, Michael B. Wallace, and Nicholas Ayache 3D Localization of Pronuclei of Human Zygotes Using Textures from Multiple Focal Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Giusti, G. Corani, L. Gambardella, C. Magli, and L. Gianaroli

XXIII

463

472

480

488

Motion Compensated SLAM for Image Guided Surgery . . . . . . . . . . . . . . . Peter Mountney and Guang-Zhong Yang

496

Region Flow: A Multi-stage Method for Colonoscopy Tracking . . . . . . . . . Jianfei Liu, Kalpathi R. Subramanian, and Terry S. Yoo

505

A System for Biopsy Site Re-targeting with Uncertainty in Gastroenterology and Oropharyngeal Examinations . . . . . . . . . . . . . . . . . . Baptiste Allain, Mingxing Hu, Laurence B. Lovat, Richard J. Cook, Tom Vercauteren, Sebastien Ourselin, and David J. Hawkes Epitomized Summarization of Wireless Capsule Endoscopic Videos for Efficient Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xinqi Chu, Chee Khun Poh, Liyuan Li, Kap Luk Chan, Shuicheng Yan, Weijia Shen, That Mon Htwe, Jiang Liu, Joo Hwee Lim, Eng Hui Ong, and Khek Yu Ho Computing Maximum Association Graph in Microscopic Nucleus Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Branislav Stojkovic, Yongding Zhu, Jinhui Xu, Andrew Fritz, Michael J. Zeitz, Jaromira Vecerova, and Ronald Berezney Estimation of 3D Geometry of Microtubules Using Multi-angle Total Internal Reflection Fluorescence Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . Qian Yang, Alexander Karpikov, Derek Toomre, and James Duncan

514

522

530

538

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Table of Contents – Part II

Image Registration Recursive Green’s Function Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bj¨ orn Beuthien, Ali Kamen, and Bernd Fischer

546

Summarizing and Visualizing Uncertainty in Non-rigid Registration . . . . Petter Risholm, Steve Pieper, Eigil Samset, and William M. Wells III

554

Coupled Registration-Segmentation: Application to Femur Analysis with Intra-subject Multiple Levels of Detail MRI Data . . . . . . . . . . . . . . . . J´erˆ ome Schmid, Jinman Kim, and Nadia Magnenat-Thalmann

562

Groupwise Registration with Sharp Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . Guorong Wu, Hongjun Jia, Qian Wang, and Dinggang Shen

570

Lung Lobar Slippage Assessed with the Aid of Image Registration . . . . . . Youbing Yin, Eric A. Hoffman, and Ching-Long Lin

578

Generalization of Deformable Registration in Riemannian Sobolev Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Darko Zikic, Maximilian Baust, Ali Kamen, and Nassir Navab

586

An Efficient EM-ICP Algorithm for Symmetric Consistent Non-linear Registration of Point Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Benoˆıt Comb`es and Sylvain Prima

594

Image Registration Driven by Combined Probabilistic and Geometric Descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linh Ha, Marcel Prastawa, Guido Gerig, John H. Gilmore, Cl´ audio T. Silva, and Sarang Joshi Simultaneous Fine and Coarse Diffeomorphic Registration: Application to Atrophy Measurement in Alzheimer’s Disease . . . . . . . . . . . . . . . . . . . . . Laurent Risser, Fran¸cois-Xavier Vialard, Robin Wolz, Darryl D. Holm, and Daniel Rueckert Registration of Longitudinal Image Sequences with Implicit Template and Spatial-Temporal Heuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guorong Wu, Qian Wang, Hongjun Jia, and Dinggang Shen 3D Ultrasound to Stereoscopic Camera Registration through an Air-Tissue Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Michael C. Yip, Troy K. Adebar, Robert N. Rohling, Septimiu E. Salcudean, and Christopher Y. Nguan Automatic Learning Sparse Correspondences for Initialising Groupwise Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pei Zhang, Steve A. Adeshina, and Timothy F. Cootes

602

610

618

626

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Table of Contents – Part II

Hierarchical Multimodal Image Registration Based on Adaptive Local Mutual Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dante De Nigris, Laurence Mercier, Rolando Del Maestro, D. Louis Collins, and Tal Arbel LogDemons Revisited: Consistent Regularisation and Incompressibility Constraint for Soft Tissue Tracking in Medical Images . . . . . . . . . . . . . . . . T. Mansi, X. Pennec, M. Sermesant, H. Delingette, and N. Ayache Correspondences Search for Surface-Based Intra-Operative Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thiago R. dos Santos, Alexander Seitel, Hans-Peter Meinzer, and Lena Maier-Hein Model-Based Multi-view Fusion of Cinematic Flow and Optical Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mickael Savinaud, Martin de La Gorce, Serge Maitrejean, and Nikos Paragios Simultaneous Geometric - Iconic Registration . . . . . . . . . . . . . . . . . . . . . . . . Aristeidis Sotiras, Yangming Ou, Ben Glocker, Christos Davatzikos, and Nikos Paragios

XXV

643

652

660

668

676

Groupwise Registration by Hierarchical Anatomical Correspondence Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guorong Wu, Qian Wang, Hongjun Jia, and Dinggang Shen

684

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

693

Temporal Diffeomorphic Free-Form Deformation for Strain Quantification in 3D-US Images Mathieu De Craene1,2 , Gemma Piella1,2 , Nicolas Duchateau1,2 , Etel Silva4 , Adelina Doltra4 , Hang Gao5 , Jan D’hooge5 , Oscar Camara1,2, Josep Brugada4 , Marta Sitges4 , and Alejandro F. Frangi1,2,3 Center for Computational Imaging & Simulation Technologies in Biomedicine (CISTIB) 1 Information and Communication Technologies Department, Universitat Pompeu Fabra, Barcelona, Spain 2 Networking Center on Biomedical Research - CIBER-BBN, Barcelona, Spain 3 Institucio Catalana de Recerca i Estudis Avancats, Barcelona, Spain 4 Hospital Cl´ınic; IDIBAPS; Universitat de Barcelona, Spain 5 Department of Cardiovascular Diseases, Cardiovascular Imaging and Dynamics, Katholieke Universiteit Leuven, Belgium Abstract. This paper presents a new diffeomorphic temporal registration algorithm and its application to motion and strain quantification from a temporal sequence of 3D images. The displacement field is computed by forward eulerian integration of a non-stationary velocity field. The originality of our approach resides in enforcing time consistency by representing the velocity field as a sum of continuous spatiotemporal BSpline kernels. The accuracy of the developed diffeomorphic technique was first compared to a simple pairwise strategy on synthetic US images with known ground truth motion and with several noise levels, being the proposed algorithm more robust to noise than the pairwise case. Our algorithm was then applied to a database of cardiac 3D+t Ultrasound (US) images of the left ventricle acquired from eight healthy volunteers and three Cardiac Resynchronization Therapy (CRT) patients. On healthy cases, the measured regional strain curves provided uniform strain patterns over all myocardial segments in accordance with clinical literature. On CRT patients, the obtained normalization of the strain pattern after CRT agreed with clinical outcome for the three cases.

1

Introduction

Quantification of cardiac motion and strain provides insight about cardiac function by estimating how a given pathology affects global or local contractility of the myocardium. In clinical routine, motion and strain are usually derived from ultrasound (US) images for which 3D acquisitions are now currently available with sufficient spatiotemporal resolution for characterizing motion and strain. Nonetheless, 3D-US images have lower signal-to-noise ratio (SNR) and temporal resolution than the 2D ones, thus making their processing more challenging. Several approaches [1,2,3] have been proposed to extend 2D speckle tracking techniques to 3D and to recover myocardial motion from a sequence of 3D-US T. Jiang et al. (Eds.): MICCAI 2010, Part II, LNCS 6362, pp. 1–8, 2010. c Springer-Verlag Berlin Heidelberg 2010 

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images. One of the main drawbacks of these techniques based on pairwise registrations is that they do not make use of the temporal information embedded in the 3D-US sequences. Parametric spatiotemporal models providing continuous and smooth transformations were proposed by Ledesma-Carbayo et al. [4] to exploit temporal information in 2D-US image sequences. However, ensuring temporal smoothness of the displacement field does not render properly temporal consistency, i.e. that the displacement field at each time point is related to all the previous times. Diffeomorphic registration algorithms ([5,6] among others) ensure a continuous, differentiable and with continuous inverse, correspondence between the features to register. Thus, they are particularly well suited to handle medical image sequences as they conserve the topology and the orientation of the observed anatomical structures along time. By integrating a velocity field over time, they provide an elegant way of encoding temporal consistency. This concept was applied by Khan et al. [7] to monitor growth processes by extending the LDDMM [5] image registration algorithm. Velocities were computed using a dense grid, which did not guarantee their spatiotemporal continuity, unlike parametric registration methods. Moreover, a regularization term added to the image similarity metric involved a smoothing kernel that enforced the spatial continuity of the computed velocities. The temporal continuity of the velocities was then fully conditioned by the conservation of the topology of the observed features along the image sequence. This assumption does not hold for noisy image sequences, such as cardiac US images. Similar concepts were applied to 2D contours and 3D shapes by Durrleman et al. [8]. However, while the computational cost of dense velocity fields is acceptable for sparse topologies, its extension to dense volumetric spatiotemporal data remains critical. In this paper, we propose a diffeomorphic registration algorithm that models velocities continuously in time and space. We refer to our approach as Temporal Diffeomorphic Free-Form Deformation (TDFFD) algorithm. We extend the popular parametric FFD registration technique [6] by summing spatiotemporal B-Spline kernels to model the 3D+t velocity field. One of the main advantages of our approach is the enforcement of the continuity of the velocity field by using a continuous parametric representation. As a result, the velocity and displacement fields can be computed at any time within the temporal interval captured by the image sequence. The advantage of applying such transformation model for strain quantification purposes is demonstrated here on synthetic and real 3D-US image sequences, with the underlying objective of accurately estimating the impact of Cardiac Resynchronization Therapy (CRT) on 3D strain.

2

Registration Algorithm and Strain Computation

In this paper, we consider a sequence of N images {In , n = 1 . . . N }, each image being defined on a spatial domain Ω ⊂ IRd where d = 3 stands for the spatial dimension. Each image In is associated to a time instant tn ∈ [0, T ], with T > 0 ∈ IR. The purpose of the registration algorithm is to solve for the diffeomorphic

Temporal Diffeomorphic Free-Form Deformation

3

mapping ϕ : Ω × [0, T ] → IRd that relates any point x in the Eulerian space of coordinates of the first image in the sequence (here taken by convention as t = 0) to a continuous time t ∈ [0, T ]. The temporal dimension is introduced into the diffeomorphic registration problem by relating the mapping ϕ at any time t ∈ [0, T ] to a time-varying velocity field. In this paper, the velocity field is represented as a sum of spatiotemporal kernels. The B-Spline velocity weights given to all kernels are concatenated in a vector of parameters p, the velocity being then denoted as v(x, t, p) and computed as    t − tτ   x − xc  v(x, p, t) = β (1) B pτ,c τ c Δ Δ τ c where B(·) is the 3D tensor product of 1D cubic B-spline kernels β(·), defined on a sparse grid of 4D control points, being c the spatial index, τ the temporal index, and (Δc , Δτ ) the width of the kernels in each dimension. Hence, the ϕ mapping is obtained as  t v(ϕ(x, τ, p), τ, p)dτ . (2) ϕ(x, t, p) = x + 0

Forward eulerian integration scheme. The transport equation for computing ϕ in Eq. 2 is solved numerically using a forward Euler integration scheme in which the continuous integral is replaced by a discrete summation. The continuous time interval is now split into a collection of tk ∈ [0, T ] values where the time increment Δtk between consecutive time-steps is adapted to ensure invertibility as described in the next subsection. Using this discretization, Eq. 2 can be approximated by ϕ(x, tn , p) = x +

n−1 

v(ϕ(x, tk , p), tk , p)Δtk ,

(3)

k=0

. .  . If we define xk (p) = ϕ(x, tk , p), tk = k−1 l=0 Δtl , and vk−1 (p) = v(xk−1 , tk−1 , p) then we can recursively write xk as follows: xk (p) = xk−1 (p) + vk−1 (p)Δtk−1 .

(4)

Adaptive time-step computation. The integration of Eq. 2 using the discrete approximation of Eq. 4 requires to select a time-step sufficiently small for ensuring accurate computation and invertibility of the mapping ϕ. In our method, we start with a uniform sampling of the time interval [0, T ], arbitrarily chosen as half of the temporal spacing of the image sequence. To ensure invertibility, one needs to consider the Jacobian of the mapping xn (p), here denoted as Dxn (p) and computed from Eq. 4 using Dxn (p) =

n−1 

n−1 .  (I + Dvk (p)Δtk ) = Δϕk ,

k=0

(5)

k=0

where I stands for the identity matrix. This Jacobian must be positive definite everywhere to ensure invertibility of the transformation. A necessary condition

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for this is to have det(Dxn (p)) > 0 for all x ∈ Ω. Computing the product over k of all det(Δϕk ) gives the determinant of the Jacobian matrix in Eq. 5. When a negative value of det(Δϕk ) is detected, the value of Δtk is reduced by a factor 2 until the obtention of a positive determinant. Similarity metric and non-linear optimization. 3D-US images are characterized by a speckle spatial distribution inside the myocardial wall that is conserved along time. The Mean Squared Error (MSE) appears therefore as a good fit for capturing the optimal set of B-Spline velocity weights p from Eq. 1. Similarity is measured between the first image in the sequence and all the consecutive frames according to M SE(p) =

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(6)

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Since the number of parameters characterizing the transformation is large, and the metric is explicitly differentiable, gradient-based optimization methods are well indicated for minimizing Eq. 6. In this paper, the L-BFGS-B method was used, which searches the optimum according to the gradient and a low-rank approximation of the Hessian of the metric. For computing the total derivative of Eq. 6 with respect to the weights p of velocity kernels, we need the following derivative: dvn−1 dvn−1 ∂vn−1 dxn−1 ∂vn−1 dxn dxn−1 = Δtn−1 + where = + . dp dp dp dp ∂xn−1 dp ∂p Hence, dxn /dp can be obtained from the following recursive equation:  ∂v dxn dxn−1  n−1 = I + Dvn−1 Δtn−1 + Δtn−1 , dp dp ∂p

(7)

(8)

where D is the Jacobian on all spatial dimensions (i.e., (Dv)ij = ∂vi /∂xj ). Strain computation. The Cauchy strain tensor is estimated directly using the spatial derivatives of the displacement field from Eq. 5, obtained at any spatiotemporal location using Eq. 4. The Cauchy strain tensor is then computed as 1 (9) σ(x, tn ) = ((Dxn )t Dxn − I) . 2 Strain is obtained along a specific direction h using σh (x, t) = ht · σ(x, t) · h. The h directions considered here are the three vectors (circumferential, longitudinal, radial) of a parabolic coordinate system related to the anatomy of the left ventricle.

3

Experiments

The proposed registration algorithm was applied to three different synthetic datasets to evaluate its accuracy and was then applied to clinical routine 3D-US

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images. First, a simple pairwise strategy and the proposed temporally consistent scheme were compared taking a ground truth deformation from simulated US data as reference. Then, strain curves were estimated from 3D-US sequences for 8 volunteers and 3 CRT patients before the therapy and at 12-months follow-up. 3.1

Registration Accuracy on Simulated US Data

Elen et al. [2] simulated Left Ventricle (LV) deformation in which the LV was represented as a thick-walled ellipsoid with physiologically relevant end-diastolic dimensions. A simplified kinematic model with an ejection fraction of 60% over a cardiac cycle was used to generate the ground truth displacement field. We used this ground truth data to evaluate the accuracy of the proposed algorithm and compare it to a pairwise registration strategy at different noise levels. Various signal to noise ratios were generated by adjusting intensities inside and outside the myocardial wall using a weight w (w = 0.2, w = 0.5 and w = 0.7 in this paper). Fig. 1 shows the median magnitude and dispersion of the difference between the ground truth displacement field and the ones given by two algorithms: a pairwise FFD (see reference in [6]) and the temporal diffeomorphic FFD registration (TDFFD) algorithms. This error was computed over the entire myocardial wall. FFD pairwise registration was performed between each image and the first image in the sequence, taking the chain of previously computed transformations as bulk transformation. For the two algorithms, the B-Spline grid had an initial resolution of three control points in the longitudinal direction and five in the the two transverse directions. This resolution was then refined twice by a factor 2. For the lowest amount of noise, there was no substantial difference between FFD and TDFFD strategies. However, as the signal to noise ratio decreased, the TDFFD algorithm proved to be more robust and produced smaller errors (maximal median error of 2.6 mm for TDFFD and 3.6 mm for pairwise FFD). The dispersion was also clearly reduced when using the TDFFD algorithm for all noise levels, as observed in Fig. 1. For w = 0.7, the upper limit of the third quartile goes from 6.6 mm using pairwise FFD to 3.5 mm using TDFFD.

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3.2

Experiments on Clinical Datasets

Data acquisition. We acquired 3D echocardiographic sequences in an apical view for two populations, using a General Electric (Milwaukee, WI, USA) Vivid 7 device. The first population was made up of 8 healthy volunteers (aged 31 ± 6 years), and the second population was composed of 3 CRT patients (aged 61 ± 8 years), who were all clinical responders to CRT. The average number of images per cardiac cycle was of 17.8 for the healthy subjects and 18.3 for the CRT patients. The pixel spacing was on average of 0.9 × 0.6 × 0.9 mm3 for the healthy volunteers and 1.0 × 0.7 × 1.0 mm3 for the CRT patients. Strain in healthy volunteers. Fig. 2 shows the recovered longitudinal strain curves for the database of 8 healthy subjects at mid and basal segments of the American Heart Association (AHA). The segments either not totally included in the field of view of the 3D-US images or suffering from typical image artifacts (non visibility of lateral wall, reflections of surrounding anatomical structures, lower spatial resolution on the lateral sides of the sector) of 3D-US acquired

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clinically, were excluded from the analysis. The recovered strain curves showed a similar pattern in all volunteers, in good agreement with clinical literature [9]. The average peak systolic strain was of −16.3 ± 4.7%. This value is close the −17.5 ± 4% reported in [9] and obtained from tagged MRI images. Different phases of diastole such as the isovolumetric relaxation and the atrial contraction (acceleration of the strain at the end of the diastole) periods can be distinguished in cases with higher temporal image resolution such as Volunteers 1 and 4. Strain before and after CRT. The three CRT patients processed in this paper had dilated geometry before implantation, thus the LV did not fit entirely in the field of view. Therefore, strain was only quantified in the septal regions that usually have the best image quality. Fig. 3 shows longitudinal strain plotted using a color map for the first patient and its temporal evolution per septal segment for all the patients. Average strain curves are shown in red and the peak systolic strain value before and after CRT is indicated by an arrow. Patients 1 and 3 showed a significant improvement in peak systolic strain after CRT that correlated well with an important reverse remodeling observed in these two patients at the 12-month follow-up (reduction of end-systolic volume of 27.7% and 51.0%, respectively). For Patient 2, no substantial change in peak strain value was observed from the strain curves. This patient had lower reverse modeling as observed at the follow-up with a reduction of end-systolic volume of 16.9%. This value is very close to 15 %, which is the threshold used at our institution for defining positive CRT response.

4

Conclusion

This paper presents a new diffeomorphic registration method ensuring temporal consistency of the resulting deformation fields, which can be particularly

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useful in image sequences with substantial amount of noise and artifacts. This algorithm was applied for the quantification of strain in 3D US using synthetic datasets, and a set of healthy subjects and CRT patients. Experiments on synthetic US datasets proved an improved robustness and accuracy at high noise levels compared to classical pairwise approaches. On healthy volunteers, the method provided physiologically meaningful longitudinal strain curves with small dispersion among LV segments. On CRT patients, improved peak systolic longitudinal strain in the septum agreed with positive clinical response and reverse remodeling. Future work will include US-adapted similarity metrics and the extension of this registration framework to incorporate compounding strategies to address field of view issues in 3D-US sequences of heart failure patients with dilated LV. Acknowledgments. This research has been partially funded by the Industrial and Technological Development Center (CDTI) under the CENIT-cvREMOD program and by the European Commission’s project euHeart (FP7-ICT-224495). G. Piella and O. Camara were supported by the Ram´ on y Cajal Program from the Spanish Ministry of Science and Innovation. A. Doltra was supported by a Post-Residency Award from Fundaci´o Cl´ınic.

References 1. Grau, V., Becher, H., Noble, J.: Registration of multiview real-Time 3-D echocardiographic sequences. IEEE Trans. Med. Imag. 26(9), 1154–1165 (2007) 2. Elen, A., Choi, H., Loeckx, D., Gao, H., Claus, P., Suetens, P., Maes, F., D’hooge, J.: Three-dimensional cardiac strain estimation using spatio-temporal elastic registration of ultrasound images: a feasibility study. IEEE Trans. Med. Imag. 27(11), 1580–1591 (2008) 3. Kawagishi, T.: Speckle tracking for assessment of cardiac motion and dyssynchrony. Echocardiography 25(10), 1167–1171 (2008) 4. Ledesma-Carbayo, M., Kybic, J., Desco, M., Santos, A., Suhling, M., Hunziker, P., Unser, M.: Spatio-temporal nonrigid registration for ultrasound cardiac motion estimation. IEEE Trans. Med. Imag. 24(9), 1113–1126 (2005) 5. Beg, M., Miller, M., Trouv´e, A., Younes, L.: Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms. Int. J. Comput. Vision 61(2), 139–157 (2005) 6. Rueckert, D., Aljabar, P., Heckemann, R.A., Hajnal, J., Hammers, A.: Diffeomorphic Registration using B-Splines. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4191, pp. 702–709. Springer, Heidelberg (2006) 7. Khan, A., Beg, M.: Representation of time-varying shapes in the large deformation diffeomorphic framework. In: ISBI, pp. 1521–1524. IEEE, Los Alamitos (2008) 8. Durrleman, S., Pennec, X., Trouv´e, A., Gerig, G., Ayache, N.: Spatiotemporal atlas estimation for developmental delay detection in longitudinal datasets. In: Yang, G.Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5761, pp. 297–304. Springer, Heidelberg (2009) 9. Edvardsen, T., Gerber, B.L., Garot, J., Bluemke, D.A., Lima, J.A., Smiseth, O.A.: Quantitative Assessment of Intrinsic Regional Myocardial Deformation by Doppler Strain Rate Echocardiography in Humans: Validation Against Three-Dimensional Tagged Magnetic Resonance Imaging. Circulation 106(1), 50–56 (2002)

Tracked Ultrasound Elastography (TrUE) Pezhman Foroughi1 , Hassan Rivaz1 , Ioana N. Fleming1 , Gregory D. Hager1 , and Emad M. Boctor1,2 1 2

Dept. of Computer Science, Johns Hopkins University, Baltimore, MD, USA Dept. of Radiation Oncology, Johns Hopkins University, Baltimore, MD, USA

Abstract. This paper presents a robust framework for freehand ultrasound elastography to cope with uncertainties of freehand palpation using the information from an external tracker. In order to improve the quality of the elasticity images, the proposed method selects a few image pairs such that in each pair the lateral and out-of-plane motions are minimized. It controls the strain rate by choosing the axial motion to be close to a given optimum value. The tracking data also enables fusing multiple strain images that are taken roughly from the same location. This method can be adopted for various trackers and strain estimation algorithms. In this work, we show the results for two tracking systems of electromagnetic (EM) and optical tracker. Using phantom and ex-vivo animal experiments, we show that the proposed techniques significantly improve the elasticity images and reduce the dependency to the hand motion of user. Keywords: Ultrasound, Elastography, Elasticity, Tracking, Strain.

1

Introduction

Ultrasound elastography is an emerging medical imaging modality which involves imaging the mechanical properties of tissue and has numerous clinical applications. Among many variations of ultrasound elastography [1], our work focuses on real-time static elastography, a well-known technique that applies quasi-static compression of tissue and simultaneously images it with ultrasound. Within many techniques proposed for static elastography, we focus on freehand palpation elasticity imaging which involves deforming the tissue by simply pressing the ultrasound probe against it. Freehand ultrasound elastography has shown great potential in clinical applications especially for diagnosis and screening of breast lesions [2]. The application of elastography is not limited to breast, and other applications such as diagnosis of prostate cancer, monitoring ablation and deep vein thrombosis have also been studied. Despite the reports on success of elastography, yet it has not become a part of any routine clinical application. The main reason is that elastography is highly qualitative and user-dependent. The best result is achieved when the user compresses and decompresses the tissue uniformly in the axial direction with the proper hand motion. It is difficult to control the compression rate as it is governed by the hand motion and the frame rate of RF data. Also, small lateral T. Jiang et al. (Eds.): MICCAI 2010, Part II, LNCS 6362, pp. 9–16, 2010. c Springer-Verlag Berlin Heidelberg 2010 

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or out-of-plane motions can compromise the quality of images. However, it is difficult to induce pure axial motion with freehand compression. Sophisticated algorithms can only partially address the problem by compensating for in-plane motions and applying smoothness constraints. The images are also hard to interpret, and artifacts –caused by failure of the strain estimation algorithm or poor hand motion– may be mistaken for lesions inside the soft tissue. Developing an elastography technique that is not affected by poor hand motion and other sources of signal decorrelation will pave the way for wide-spread clinical use of elastography. To improve the reliability, quality metrics such as persistence in strain images have been developed [3,4]. This quality indicator is calculated for each image and provided to the user as feedback. Persistence is also used to merge multiple elasticity images together [3]. To measure the persistence, strain is computed for two pairs of echo frames, and the resulting images are correlated. Although these techniques offers a major advantage, there remains several limitations. First, the strain has to be estimated before the calculation of the quality metric. With typical ultrasound settings, the frame rate can reach more than 30 Hz. For subsequent frames, an efficient implementation of this image-based metric might cope with this rate. Nonetheless, the task will be extremely difficult to try all the combinations in a series of frames. Moreover, the quality metric will not be able to provide feedback to the user whether he/she should adjust the palpation in certain direction. Also, there would be minimal control over the strain rate. The ultrasound probe is often tracked in navigation/guidance systems to provide spatial information, to form freehand 3D ultrasound, or to facilitate multimodality registration. In this work, we exploit the tracking data to enhance the quality of the elasticity images. We use the tracking data to select multiple image pairs that contain the optimum deformation for the elastography algorithm. The optimum value for lateral and out-of-plane motions is zero, and the optimum axial motion is determined by the specific elastography algorithm used, which is Normalized Cross-Correlation (NCC) in this work. Next, we fuse the strain images obtained from the multiple image pairs together based on the location of each strain image to improve image quality. We assume that the ultrasound data is 2D. Nonetheless similar techniques proposed here could be extended to 3D ultrasound.

2

Methodology

Consider a sequence of RF data collected during the palpation of tissue using a tracked transducer. We have previously shown that it is possible to synchronize the RF frames with the tracking information relying only on the same data collected during palpation [5]. From synchronization, the tracking information is interpolated at the incident time of each frame. The input to our algorithm is then a series of RF frames along with their corresponding transformation. First, we need to define a distance function between two frames of RF data. For this purpose, we use a model of image decorrelation in presence of out-ofplane and lateral motion. RF signal is often modeled as the collective response

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of scatterers randomly distributed within the resolution cell of the ultrasound [6,7]. Each scatterer is assumed to have an amplitude governed by the shape of the resolution cell and a phase which is distributed from 0 to π uniformly at random. Considering a Gaussian shape for the resolution cell Prager et. al [8] δ2 calculated the correlation as a function of out-of-plane motion to be exp(− 2σ 2 ). δ and σ denote the displacement and the width of the resolution cell respectively. Although this function is only valid for fully developed speckle, it provides a convenient estimate of correlation. It should be noted that in [8], the displacement is estimated from correlation, whereas here, we intend to define an energy function based on displacement. Extending this formula to both out-of-plane and lateral displacements, we define our energy function, E(x, z), as follows: E(Dx , Dz ) = exp(−Kx · Dx2 − Kz · Dz2 ),

(1)

where Dx and Dz represent the displacement in out-of-plane and lateral directions. E does not depend on axial motion ( Dy ) since displacement in axial direction is necessary for strain estimation. Kx and Kz determine the sensitivity to a certain direction. In order to be able to use this function, we need a component-wise metric representing the distance of two frames given their homogeneous transformations. The first step is to compute the relative transformation between them. Suppose a = [ax ay az ]T is the axis-angle representation of the relative rotation, and t = [tx ty tz ]T is the relative translation. Assuming a small rotation, the relative displacement of a point, P = [x y 0]T , will be d = a × P + t. We then define the distance vector of two frames, D = [Dx Dy Dz ]T , as the RMS of the components of d for all the points in the region of interest (ROI): 1 Dx = sqrt{ (y2 − y1 )



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where sqrt{.} returns the root. Here, ROI is assumed to be rectangular and determined by x1 , x2 , y1 , and y2 . The vector D provides a measure of distance for each direction separately. We use this vector in Equation (1) which gives us an estimate of “pseudo-correlation” over the ROI. The data goes through four stages of processing to create a single high-quality strain image. In the first step, few images are selected from the data series that are approximately collected from one cross-section of tissue with minimal lateral and out-of-plane motion. To this end, the energy function of each frame is computed with respect to all other frames in the sequence. Then, the total energy is found for each frame as the sum of the energies of the M closest frames, where closeness implies higher energy, and M is the maximum number of frames to be selected. Then, the frame with the highest total energy (the center frame)

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is identified, and the M closest frames to the center frame including itself are selected. Additionally, the frames that have E of less than 0.5 with respect to the center frame are disqualified. This is applied to ensure lower number of frames are chosen when M frames from one cross-section are not available. In the next stage, the program evaluates all possible   combination of frame pairs for elastography. For M frames, there will be M = M (M − 1)/2 pair 2 combinations which will be compared using a slightly modified version of E. Since the pairs are directly compared, it suffices to minimize the exponent of Equation (1) in order to maximize E. We also add a term for axial motion that penalizes compressions that are higher than an optimum compression value, topt . Hence, a “cost function”, C1, is defined as follows: 2

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where topt implies the optimal strain, which can be theoretically defined as described in [9]. Here, topt is set depending on the robustness of the elasticity estimation algorithm. Its value might be within the range of the resolution of the tracker. Therefore, at this stage we do not assign a penalty for the compressions less than topt . If the compression is close to zero, the contrast of the reconstructed image degrades. The program filters the pairs with low compression in the next stage using image content. Similar to the first part, a maximum number of frames with lowest cost are selected provided that the cost is lower than a threshold. The threshold is not strict to ensure acceptable pairs are not filtered. The final pairs are selected by recovering the global lateral motion and compression by matching the two RF frames in each pair. The tracking information is used to initialize the search. For instance, the search range for compression is set to be from zero to the tracker reading in axial direction padded in both sides with the maximum error of the tracker. Given two frame I1 and I2 , the amount of lateral motion a, and compression, b, is found by solving cross-correlation:

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The RF data is normalized with standard variation and assumed to have zero mean. We employ two tricks which extensively increases the speed of search. First, we do not match the entire image to solve for these parameters. Instead, only pixels on a grid, G, are used as described by Equation (4). The two terms of Equation (4) ensures that the search remains reciprocal, which means switching the images only affects the sign of a and b. Second, a is recovered by matching only the top part of the two images while b is fixed to one. The reason is that the displacement due to compression is minimal in that region. Having the global motions, the cost function is modified to penalize very low compressions:

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x and D y are the global motions from Equation (4) converted to mm. c where D is a small number that limits the cost of zero compression. Finally, the pairs with the lowest cost are selected until a maximum number of frame pairs is reached or the minimum cost grows higher than the average cost. The last step involves computing the strain for all the selected frame pairs. We have implemented normalized cross-correlation (NCC) [10] to recover the displacements and least squares estimation to calculate the strain. Before calculating strain, the global lateral motion and compression from the previous step are compensated in one image using cubic interpolation. This is known to reduce the error of strain estimation [11]. The final strain image, Sf inal is the weighted average of all the strains: m  ρi wi · Si , ρi > 0.7 i=1 , wi = 1−ρi Sf inal = m (6) 0, otherwise w i=1 i where ρi is the correlation coefficient for the ith pair after applying the displacements, and m is the number of pairs. Fusing the strains in this fashion is acceptable since the algorithm only allows for compressions that are close to a predetermined amount optimal for strain estimation.

3

Experiments and Results

We acquired ultrasound data using a SONOLINE AntaresTM ultrasound system (Siemens Medical Solutions USA, Inc.) with a high-frequency ultrasound transducer (VF10-5) at center frequency of 6-8 MHz. We accessed RF through the Axius DirectTM Ultrasound Research Interface provided by Siemens. Our custom data acquisition program was connected to this interface to send the command for capturing RF data. At the same time, the program collected tracking information from either a “Polaris” optical tracker (Northern Digital Inc., Waterloo, Canada) with passive markers or the “medSAFE” EM tracker (Ascension Tech. Corp.). RF data and tracking information was captured from a breast phantom containing a harder lesion (CIRS elastography phantom, Norfolk, VA) and ex-vivo pig liver. Alginate was injected to the liver to mark a part of liver, and then, that area was ablated. The users were asked to palpate the tissue over the hard lesion in the breast phantom and the ablated lesion in the pig liver while data was being collected. Between 100 to 138 RF frames were acquired with the rate of about 30 frames per second. The first set of data was captured by an experienced user from the breast phantom. Figure 1(a) shows the translation components of hand motion with respect to the first frame. The axial motion is dominant and there is only a gradual drift in the lateral and elevational directions. Figure 1(b) depicts the high-quality strain image resulting from the TrUE algorithm.

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Applying a compression similar to the one shown in Figure 1(a) is a difficult task for novice or even intermediate users. This is especially the case where axial compression does not translate into a simple up and down motion. Ultrasound gel creates a slippery surface that makes the palpation prone to out-of-plane motion. Two case are shown in Figure 2, where one is tracked with the EM tracker and the other one with the optical tracker. In Figure 2(a) the hand motion contains a large amount of out-of-plane motion, whereas, in Figure 2(b), the user has moved the probe laterally. In both cases, the TrUE algorithm generates reliable results. Figures 2 (c) and (d) show the contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR) of the strain image. The CNR and SNR value are computed from:  2(¯ sb − s¯t )2 s¯ CNR = (7) , SNR = , σb2 + σt2 σ where s¯ and σ denote the mean and standard deviation of intensities. The t or b subscripts show that the computation is only for the target or the background region, respectively. The SNR and CNR for computing the strain from consecutive frames (the dashed curve) is compared to the SNR and CNR of the strain image from the proposed method (solid line). Using consecutive frames is the standard method of elastography in ultrasound machines. Almost in all cases the TrUE algorithm outperforms the consecutive frames by a large margin. Although the SNR and CNR provide quantitative measures to compare the strain images, they do not directly reflect the visual quality of strain. In Figure 3, we show results of elastography using our frame selection technique as well as four other strain images calculated from consecutive frames. The Figure shows the effects of improper compression in consecutive frames in the strain image. At the same time our algorithm provides a single reliable strain.

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Discussion

We presented a method of ultrasound elastography which is robust to the quality of the hand motion of the user. Using the information from an external tracker, it automatically selects multiple frame pairs with a specific compression and minimal undesired motions. Our approach does not take into account the tissue motion from other sources such as breathing or patient motion. However, these types of motions are not normally problematic since they occur with a slower pace compared to hand motion. Our experiments shows that even when the transducer has severe lateral or out-of-plane motions, the algorithm still manages to produce good results. The multi-stage frame selection and careful image fusion makes the TrUE method less sensitive to tacker accuracy and robust to strain estimation failures. We are planning to use the proposed method in a breast cancer study. For this purpose, we will be implementing our MATLAB code in C. The strain estimation which is still the bottleneck of our approach will be executed in GPU allowing for the use of sophisticated algorithms. Acknowledgments. Pezhman Foroughi, Hassan Rivaz, and Ioana Fleming are supported by the U.S. Department of Defense pre-doctoral fellowship program.

References 1. Ophir, J., Alam, S., Garra, B., Kallel, F., Konofagou, E., Krouskop, T., Varghese, T.: Elastography: ultrasonic estimation and imaging of the elastic properties of tissues. Annu. Rev. Biomed. Eng. 213, 203–233 (1999) 2. Garra, B., et al.: Elastography of breast lesions: initial clinical results. Radiology 202, 79–86 (1997) 3. Lindop, J.E., Treece, G.M., Gee, A.H., Prager, R.W.: An intelligent interface for freehand strain imaging. Ultrasound Med. Biol. 34, 1117–1128 (2008) 4. Jiang, J., Hall, T.J., Sommer, A.M.: A novel strain formation algorithm for ultrasonic strain imaging. In: IEEE Ultrasonics Symposium, pp. 1282–1285 (2006) 5. Foroughi, P., Hager, G., Boctor, E.: Robust elasticity imaging using external tracker. In: IEEE Int. Symp. Biomed. Imag., pp. 209–212 (2009) 6. Wagner, R., Smith, S., Sandrik, J., Lopez, H.: Statistics of Speckle in Ultrasound B-Scans. IEEE Trans. Sonics and Ultrasonics 17(3), 251–268 (1983) 7. Shankar, P.: A general statistical model for ultrasonic backscattering from tissues. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47(3), 727–736 (2000) 8. Prager, R., et al.: Sensorless freehand 3-d ultrasound using regression of the echo intensity. Ultrasound Med. Biol. 29, 437–446 (2003) 9. Varghese, T., Ophir, J.: A theoretical framework for performance characterization of elastography: the strain filter. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 44, 164–172 (1997) 10. C´espedes, I., Huang, Y., Ophir, J., Spratt, S.: Methods for estimation of subsample time delays of digitized echo signals. Ultrasound Imaging 17(2), 142–171 (1995) 11. Varghese, T., Ophir, J.: Performance optimization in elastography: Multicompression with temporal stretching. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 18(22), 193–214 (1996)

Evaluation of Inter-session 3D-TRUS to 3D-TRUS Image Registration for Repeat Prostate Biopsies Vaishali V. Karnik1,2, Aaron Fenster1,2,3, Jeff Bax1,2, Lori Gardi2, Igor Gyacskov2, Jacques Montreuil2, Cesare Romagnoli2, and Aaron D. Ward2 1

Biomedical Engineering Graduate Program 2 Robarts Research Institute 3 Department of Medical Biophysics, The University of Western Ontario, London, ON, Canada, N6A 5C1

Abstract. To ensure accurate targeting and repeatability, 3D TRUS-guided biopsies require registration to determine coordinate transformations to (1) incorporate pre-procedure biopsy plans and (2) compensate for inter-session prostate motion and deformation between repeat biopsy sessions. We evaluated prostate surface- and image-based 3D-to-3D TRUS registration by measuring the TRE of manually marked, corresponding, intrinsic fiducials in the whole gland and peripheral zone, and also evaluated the error anisotropy. The imagebased rigid and non-rigid methods yielded the best results with mean TREs of 2.26 mm and 1.96 mm, respectively. These results compare favorably with a clinical need for an error of less than 2.5 mm. Keywords: surface-based registration, image-based registration, accuracy, prostate, repeat biopsy, inter-session, 3D TRUS, peripheral zone.

1 Introduction Current diagnostic tests for prostate cancer (PCa) include prostate-specific antigen (PSA) tests and digital rectal exams (DRE), but two-dimensional (2D) transrectal ultrasound (TRUS) guided biopsy (Bx) is the clinical standard for definitive diagnosis. 2D TRUS guidance, however, is not without limitations. A 2D view restricts the anatomic information available to the physician for the accurate characterization of tumor location, which is vital for targeting and needle guidance. PCa is particularly difficult to target with 2D TRUS-guided Bx since this cancer tends to be small and multifocal. Furthermore, up to 80% of the cancer can be located in the prostate’s peripheral zone (PZ) [1], an area subject to deformation due to ultrasound transducer pressure during the exam (Fig. 1). These difficulties contribute to false negative rates as high as 34% [2], and the detection rate of cancer on the necessary repeat Bx ranges between 10% and 25% [3]. In order to reduce the need for repeat Bxs, and provide better planning for required repeat Bxs, improved techniques are necessary to accurately identify tumor locations and record biopsy cores so as to avoid negative areas and target precancerous lesions. Techniques for obtaining an accurate 3D record of Bx locations and providing guidance of repeated Bxs to specific locations are of T. Jiang et al. (Eds.): MICCAI 2010, Part II, LNCS 6362, pp. 17–25, 2010. © Springer-Verlag Berlin Heidelberg 2010

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profound importance to the timely diagnosis of prostate cancer, and lead to high impact on patient care and quality of life. A three-dimensional (3D) TRUS-guided prostate biopsy system has been developed in our laboratory, using a mechanically stabilized and tracked end-firing probe that provides a 3D view of the anatomy and records the 3D location of each Bx core (Fig. 1(c)) [4]. In order to accurately transform the 3D locations of Bx cores taken during a previous session into the coordinate space of the current session, 3D-TRUS to 3DTRUS image registration needs to be performed. The transformation given by this registration will compensate for differences in prostate position and deformation between sessions, which can be substantial due to the time between biopsy sessions, and may be due to differences in patient positioning, edema and swelling due to needle insertion, and bladder and/or rectum filling. In this study, we evaluate the accuracy of four algorithms for 3D-TRUS to 3DTRUS registration of prostate images taken during different biopsy sessions. We evaluate rigid and non-rigid variations of both surface-based and image-based registration algorithms. We determine a mean target registration error (TRE) for each algorithm and provide an analysis of the spatial anisotropy in the TRE. Furthermore, since the PZ of the prostate is of particular clinical interest, and we hypothesize that this region may undergo characteristically different (from the remainder of the gland) deformations due to its proximity to the ultrasound transducer, we perform a separate accuracy analysis on this region. Our primary success criterion is a clinically desired TRE of 2.5 mm or less, with a non-dominant fiducial localization error (FLE) [5]. Previous related work focuses on intra-session registration of 3D-TRUS to 3DTRUS [5, 6], and 3D-TRUS to magnetic resonance (MR) [7] prostate images, and accuracies as high as 1.50 mm have been reported. However, to the best of our knowledge, an evaluation of 3D-TRUS to 3D-TRUS inter-session registration, with its attendant challenges as described above, has not been previously conducted for image-guided prostate biopsies.

PZ

PZ

probe

probe

(a)

(b)

(c)

Fig. 1. Axial view of prostate with PZ highlighted in black (a) without deformation and (b) with deformation caused by transducer probe pressure. (c) Mechanically assisted 3D-TRUS biopsy system with real-time tracking and recording of the 3D position of the biopsy needle.

2 Materials and Methods 2.1 Materials 3D TRUS prostate images were obtained from 10 different patients who had undergone two prostate imaging sessions one week apart. The physician inserts the

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transducer probe into the patient’s rectum and rotates it (by rolling it about the probe axis) to acquire 180 2D images in 1 degree increments. The 2D US images from the US machine are digitized using a frame grabber and reconstructed into a 3D image. Acquisition of the 3D image requires approximately 10 seconds and the reconstruction occurs as the images are acquired, allowing the physician to view the 3D image as it is being acquired. The first set of scans was acquired using a HDI-3500 ultrasound machine and second was acquired using a HDI-5000. The same transducer probe (Philips C9-5) was used with both machines, but calibrated differently. From each patient, 2 images from the two different procedures were selected to be the source ( I S ) and target images ( I T ). The image dimensions were 448 × 448 × 350 (voxel size of 0.19 × 0.19 × 0.19 mm3). The selection of images for this study was based on our ability to localize in 3D a set of corresponding intrinsic fiducials (small calcifications) in the image pairs for use in computing the TRE. In all 10 image pairs, we found a total of 92 fiducial pairs, of which 18 were located in the PZ. It is important to note that the fiducials in our study are used only to evaluate the registration methods, and are not used as inputs to the registration algorithms. 2.2 Surface-Based Registration For surface-based registration, we first segmented the images semi-automatically using a dynamically deformable contour model [8]. We then rigidly registered the surfaces using the iterative closest point (ICP) algorithm [9], where both surfaces are represented by point clouds. In order to align the surfaces, a rigid transformation T is required that maps each point in the source image of patient i, ( I Si ), to its corresponding point in the target image of patient i, ( I Ti ). The algorithm proceeds by (1) establishing correspondence between closest point pairs, and (2) by estimating the transformation required to align the corresponding points. Steps (1) and (2) are iterated until a convergence criterion (RMS of the sum of squares of the closest point distances) of 0.01 mm is met [9]. Following rigid registration, we performed a non-rigid registration using a thinplate spline (TPS) [10]. Parametric correspondence between surfaces I Si and I Ti was established by radially projecting equal-angle rays from the centroid of the rigidly aligned surfaces, and corresponding the point pair lying on each ray. This approach to correspondence establishment is justified due to the approximately spherical shape of the prostate. A 3D TPS is defined in the 3D image space and aligns the corresponding points. The TPS is applied to I Si in order to register it to I Ti . 2.3 Image-Based Registration We adopt the block matching approach proposed by Ourselin et al. for rigid registration [11]. The registration consists of the following four steps: (1) dividing the source image into rectangular block regions; (2) for each block in I Si , finding the block in a local neighborhood within I Ti having the optimal value of a chosen image-to-image metric; (3) constructing a vector field mapping each I Si block to its best matching I Ti

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block; and (4) performing a least trimmed squares optimization to regularize the vector fields [12] in order to determine the transformation mapping I Si to I Ti . Steps (1) through (4) are iterated, with a progressively smaller block size, in order to provide a coarse-to-fine registration of the images. The chosen image-to-image metric is mutual information [13], due primarily to the effects of directionally-dependent shadowing artifacts present in 3D TRUS images. We used the implementation provided by MedINRIA (INRIA, Asclepios Research Team, 2009) that adopts a multiresolution approach. Results were achieved using a multi-resolution image pyramid where the finest and coarsest image resolutions used were tuned empirically to 32×32×32 and 16×16×16, respectively. The block size, N , is initialized to ⎛X Y Z⎞ N = min ⎜ , , ⎟ , where X, Y and Z are the 3D image dimensions and the initial ⎝ 8 8 8⎠ search area, Ω, is equal to 2 N [14]. The parameters are halved when refining the scale and the process stops when the block size is N = 4 . For image-based non-rigid registration, the moving image deformation is defined using a regular 3D grid of B-spline control points. We used a limited-memory Broyden Fletcher Goldfarb Shannon optimizer [15], and mutual information [13] as the image-to-image metric. We used the implementation provided by the 3D-SLICER software (Surgical Planning Lab, Harvard Medical School, Boston, USA), which permits the tuning of the following parameters: the number of optimization iterations (we set this parameter to 50), the number of elements along each side of the grid of Bspline control points (10), the number of histogram bins (20) and randomly-sampled voxels (100,000) to use in computing the mutual information metric, and the maximum allowed deformation of the B-spline grid control points (1). 2.4 TRE

We measured the TRE as the overall misalignment of manually marked, corresponding, intrinsic fiducials in I Si and I Ti . The TRE is defined, for the jth corresponding fiducial in patient i, as the Euclidean distance between the transformed fiducial ~ ij f S = T ( f Sij ) from I Si and the corresponding fiducial fTij in I Ti , written as ~ TRE ij = v ij , where v ij = ( f Tij − f Sij ) . The mean TRE for patient i is denoted as 2

TRE i =

∑ (TRE

ij 2

j

) / N i , where N i is the number of fiducials identified in

I Si . The overall mean TRE is denoted as

TRE =

∑ ∑ (TRE i

j

ij 2

) / N , where

N is the total number of fiducial pairs used in the calculation. In this study, there were 92 fiducial pairs in total, of which 18 were within the PZ of the prostates. 2.5 Error Anisotropy

We performed a 3D principal component analysis (PCA) of the 3D point ~ ~ ~ set Δ = fTxij − f Sxij , fTyij − f Syij , fTzij − f Szij ; ∀i, ∀j in order to evaluate the directional

{(

)

}

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anisotropy of the TRE. Using MATLAB (The Mathworks Inc., Natick, MA), we computed the PCA by finding the eigenvectors (ei) and eigenvalues (λi) of the covariance matrix of Δ . This was done for both the whole gland (WG) and PZ. The 95% standard error ellipsoid volumes were defined with their semi-principal axes parallel to the eigenvectors, with lengths ai = λi × χα2 ,υ , (i = 1, 2, 3 and χ α ,υ ≈ 2.80 ), where

χα2 ,υ

is the probability distribution evaluated for 95% confidence (α = 0.05)

and 3 degrees of freedom (υ = 3) [16]. 10 9 8

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Fig. 2. WG (black) and PZ (white) frequency distributions of (a) pre-registered distances between all 92 fiducial pairs, (b) rigid surface-based TREij, (c) non-rigid surface-based TREij, (d) rigid image-based TREij, (e) non-rigid image-based TREij

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3 Results 3.1 TRE

Our pre-registration mean misalignment was ~7.45 mm, ranging from 0.28-18.0 mm. The frequency distributions of the WG and PZ TREs are shown in Figure 2 and the TRE results are summarized in Table 1. The two-tailed paired t-test results shown in Table 2 indicate that surface- and image-based rigid registration TREs were statistically significantly different with p = 4.29x10-6. The surface- and image-based non-rigid TREs were also significantly different, with p = 1.60x10-9. Table 1. Whole gland (WG) and peripheral zone (PZ) mean TRE results for surface-based (SB) and image-based (IB) registration Registration

WG

PZ

SB

IB

SB

IB

Pre-registration mean TRE (mm) Rigid mean TRE (mm)

3.20 ± 1.46

2.26 ± 0.98

3.45 ± 1.21

2.30 ± 0.90

Non-rigid mean TRE(mm)

3.29 ± 1.50

1.96 ± 0.85

3.62 ± 1.12

2.11 ± 0.91

7.36 ± 4.17

5.23 ± 3.29

Table 2. t-test results for surface-based (SB), image-based (IB), rigid (R), and non-rigid (NR) registration

WG p-value PZ p-value

SB vs. IB

SB vs. IB

SB

IB

R

NR

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0.05

1.38x10-7

0.12

0.07

4.29x10-6 -4

1.88x10

1.6x10-9 -6

6.21x10

3.2 Error Anisotropy

Figure 3 shows the 95% confidence ellipsoids for the PCA performed on the directional components of the WG and PZ TREs for the non-rigid registration methods. The WG pre-registered ellipsoid volume (EV) is 4.46 cm3 while the post-registration EVs range from 0.12 cm3 to 0.41 cm3. The EVs for surface-based rigid and non-rigid TRE were greater than the image-based EVs by an average of 0.27 cm3. The PZ pre-registered EV is 1.58 cm3 while the post-registration volumes range from 0.14 cm3 to 0.37 cm3. The EVs for surface-based rigid and non-rigid TRE were greater than the EVs for image-based TRE by an average of 0.22 cm3. Table 3 shows the ratios of the eigenvalues for each registration approach as well as for the unregistered case, to illustrate any anisotropy in the error.

Evaluation of Inter-session 3D-TRUS to 3D-TRUS Image Registration

(a)

(b)

(c)

(d)

(e)

(f)

23

Fig. 3. Error ellipsoids for WG and PZ: (a) WG pre-registered data, (b) WG surface-based nonrigid registration, (c) WG image-based non-rigid registration, (d) PZ pre-registered data, (e) PZ surface-based non-rigid registration, and (f) PZ image-based non-rigid registration Table 3. Ratios of 95% TRE confidence ellipsoid eigenvalues WG Registration Method Unregistered Surface-based rigid Surface-based non-rigid Image-based rigid Image-based non-rigid

λ1 / λ2 1.16 1.51 1.76 1.16 1.51

λ2 / λ3 1.37 1.36 1.86 1.37 1.36

PZ λ1 / λ3 1.43 1.42 2.02 1.43 1.42

λ1 / λ2 1.24 2.08 2.58 1.24 2.08

λ2 / λ3 1.72 1.6 2.75 1.72 1.6

λ1 / λ3 1.95 1.6 3.13 1.95 1.6

4 Discussion Using 3D image registration to correct for prostate motion and deformation that occurs between Bx procedures is vital to accurate Bx planning and needle guidance. The desired TRE is 2.5 mm since the smallest tumor considered clinically significant has a radius of ~5 mm (for a 0.5cm3 spherical tumor) [17]. Since the TRE (RMSE) provides an estimate of the standard deviation of the normal distribution of biopsy targets given by a registration algorithm, a TRE of 2.5 mm gives a confidence interval with 95.4% of the registered targets within the clinically significant 5 mm radius. The non-rigid image-based method yielded the lowest WG and PZ TRE values of 1.96 mm and 2.11 mm, respectively. Figures 2(d) and (e) show that the image-based method outperformed the surface-based method by illustrating the right-skewed distribution of the TRE values (for both WG and PZ), with ~65% of the values below the respective means. In a previous evaluation of image registration methods in the intrasession context, the non-rigid image-based TRE for images taken 6 minutes apart was

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1.50 mm [5]. This shows that after a time gap of 1 week, the same image-based registration algorithm, tuned as in [5], is able to achieve comparable results. The t-test results in Table 2 reveal statistically significant differences in all cases except when comparing surface-based rigid and non-rigid registration values. We speculate that this could be due to the variability introduced by segmentation (±1.31 mm) [5]. The FLE [18] was 0.21 mm [5], and thus was not dominant. Figure 3 shows the anisotropy in the TRE where both WG and PZ pre-registered fiducial misalignments are predominantly in the z-direction, which is along the transducer probe axis where we might expect misalignments due to probe pressure. The surface-based errors are predominantly anisotropic in x and y, which may be the result of inconsistent segmentation due to poor image contrast at the prostate boundaries parallel to the ultrasound beam. Table 3 indicates increased error anisotropy in the PZ, in comparison to the WG. This may be due to deformation that characteristically pushes the central region of the PZ upward in response to probe pressure, while the lateral "lobes" of the PZ bulge downward and laterally. The post-registration 3D EVs are dramatically reduced (by a factor of 10–37 for WG, and 4.27–11.29 for PZ) as compared with the pre-registered EVs. Our results demonstrate that in the inter-session scenario with 1 week between sessions, the tested surface-based and image-based 3D TRUS image registration techniques yield clinically sufficient accuracy, with image-based registration giving the lowest error. Furthermore, due to the segmentation step required for surface-based registration, the two methods are comparable in execution time on a contemporary single-core workstation (90–105 s). The image-based method is preferred since it is more accurate, does not require segmentation and can potentially be automated.

References 1. Prostate Cancer Treatment Guide (2008-2010), http://www.prostate-cancer.com 2. Fink, K., et al.: Evaluation of transition zone and lateral sextant biopsies for prostate cancer detection after initial sextant biopsy. Urology 61, 748–753 (2003) 3. Kronz, D., et al.: Predicting cancer following a diagnosis of high-grade prostatic intraepithelial neoplasia on needle biopsy: Data on men with more than one follow-up biopsy. The American Journal of Surgical Pathology 25(8), 1079–1085 (2001) 4. Bax, J., et al.: Mechanically assisted 3D ultrasound guided prostate biopsy system. Medical Physics 35(12), 5397–5410 (2008) 5. Karnik, V.V., et al.: Assessment of image registration accuracy in three-dimensional transrectal ultrasound guided prostate biopsy. Medical Physics 37(2), 802–813 (2010) 6. Baumann, M., et al.: Prostate biopsy assistance system with gland deformation estimation for enhanced precision. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5761, pp. 67–74. Springer, Heidelberg (2009) 7. Hu, Y., et al.: MR to ultrasound image registration for guiding prostate biopsy and interventions. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5761, pp. 787–794. Springer, Heidelberg (2009) 8. Wang, Y., et al.: Semiautomatic three-dimensional segmentation of the prostate using twodimensional ultrasound images. Medical Physics 30(5), 887–897 (2003)

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9. Besl, P., McKay, N.: A method for registration of 3-D shapes. IEEE Trans. on Pattern Analysis and Machine Intelligence 14, 239–256 (1992) 10. Bookstein, F., et al.: Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Trans. on Pattern Analysis and Machine Intelligence 11(6), 567–585 (1989) 11. Ourselin, S., et al.: Block matching: A general framework to improve robustness of rigid registration of medical images. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 557–566. Springer, Heidelberg (2001) 12. Rousseuw, P.J., Leroy, A.M.: Robust regression and outlier detection, 1st edn. Wiley Series in Probability and Mathematical Statistics (1987) 13. Wells III, M., et al.: Multi-modal volume registration by maximization of mutual information. Medical Image Analysis 1(1), 35–51 (1996) 14. Ourselin, S., et al.: Reconstructing a 3D structure from serial histological sections. Image and Vision Computing 19, 25–31 (2000) 15. Zhu, C., et al.: L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization. ACM TMS 23(4), 550–560 (1997) 16. Irwin, M., et al.: Registered 3-D ultrasound and digital stereotactic mammography for breast biopsy guidance. IEEE TMI 27(3), 391–398 (2008) 17. Epstein, J.I., et al.: Utility of saturation biopsy to predict insignificant cancer at radical prostatectomy. Urology 66(2), 356–360 (2005) 18. Fitzpatrick, J.M., et al.: Predicting error in rigid-body point-based registration. IEEE TMI 17(5), 694–702 (1998)

Manifold Learning for Image-Based Breathing Gating with Application to 4D Ultrasound Christian Wachinger, Mehmet Yigitsoy, and Nassir Navab Computer Aided Medical Procedures (CAMP), TUM, Munich, Germany {wachinge,yigitsoy,navab}@cs.tum.edu

Abstract. Breathing motion leads to a significant displacement and deformation of organs in the abdominal region. This makes the detection of the breathing phase for numerous applications necessary. We propose a new, purely image-based respiratory gating method for ultrasound. Further, we use this technique to provide a solution for breathing affected 4D ultrasound acquisitions with a wobbler probe. We achieve the gating with Laplacian eigenmaps, a manifold learning technique, to determine the low-dimensional manifold embedded in the high-dimensional image space. Since Laplacian eigenmaps assign each ultrasound frame a coordinate in low-dimensional space by respecting the neighborhood relationship, they are well suited for analyzing the breathing cycle. For the 4D application, we perform the manifold learning for each angle, and consecutively, align all the local curves and perform a curve fitting to achieve a globally consistent breathing signal. We performed the imagebased gating on several 2D and 3D ultrasound datasets over time, and quantified its very good performance by comparing it to measurements from an external gating system.

1

Introduction

Imaging organs in thorax and abdomen is affected by respiratory motion. For consecutive processing steps, it is often necessary to assign to each image its corresponding breathing phase. This is achieved with external gating devices, which the patient gets connected to. These devices, however, have long setup times, prolong the overall acquisition, are costly, and consequently, rarely used in practice. Moreover, the synchronization of image data and breathing signal is not trivial. While certain imaging devices, such as CT and MR scanners, support the connection of respiratory gating systems, we are not aware of such a possibility for ultrasound; leaving the synchronization to the user. We propose an image-based respiratory gating system for ultrasound using manifold learning. Moreover, we use this technique to provide a solution for acquiring breathing affected 4D ultrasound with a wobbler probe. The proposed method is fully automatic, and does not need any prior information or training data. 

This work was partly funded by the European Commission. We want to thank Athanasios Karamalis and Oliver Kutter for discussions.

T. Jiang et al. (Eds.): MICCAI 2010, Part II, LNCS 6362, pp. 26–33, 2010. c Springer-Verlag Berlin Heidelberg 2010 

Manifold Learning for Image-Based Breathing Gating

Wobbler

27

Uj angle

Breathing d

phase

time Fig. 1. Wobbler angle (blue) and respiratory phase (gray) over time. Dashed lines indicate respiratory change d within one sweep. Dash dotted line indicates frames from same angle over several breathing cycles.

One of the applications for which the assignment of the respiratory phase is important is 2D and 3D ultrasound mosaicing. In order to achieve good results, images from the same respiratory phase have to be combined. An alternative to breathing gating are breath-hold acquisitions, but they further complicate the procedure and are dependent on the patients ability for breath-hold. Another application that we investigate in more details throughout the article, and for which we have not yet found a solution proposed in the literature, is the acquisition of breathing affected 4D ultrasound with a mechanically steered transducer, also referred to as wobbler. The problems for using a wobbler in such a scenario is that images in one sweep do not contain consistent information, but represent the anatomy in different breathing phases. We illustrate this in figure 1, where we schematically plot the deviation angle of the wobbler together with the respiratory signal over time. The phase difference d indicates the range of breathing phases accumulated in one sweep. We propose to select all frames acquired from the same angle (dash dotted line) and apply the image-based gating on each of those sets of images. Having the respiratory signal estimated for each angle, we align these curves and apply a robust spline curve fitting to create a globally consistent respiratory signal. This, consequently, allows us to reconstruct volumes for specific breathing stages. An alternative to the application of a wobbler would be a native 3D transducer with elements arranged on a 2D array. Those systems, however, are still expensive and the access to their data streaming and radio frequency data is very restricted. 1.1

Related Work

There are several papers on image-based gating in ultrasound for detecting the cardiac motion [1,2,3,4]. These approaches apply techniques that are either (i) specific to detecting the cardiac signal e.g. centroid algorithm [4], (ii) based on user interaction [1], or (iii) designed for intravascular ultrasound [2,3]. We are only aware of the work of Sundar et al . [5], where an automatic technique for breathing gating in ultrasound is proposed. It bases on the phase correlation technique to estimate the motion between successive frames. The breathing phase is estimated from the energy change between consecutive frames. The inherent

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limitation of the phase correlation algorithm is that it finds the global translation in the image plane. Considering the case of 2D ultrasound, the organ motion is not necessarily in-plane, and consequently, there is no uniform global translation. Several manifold learning techniques were proposed in the literature with common techniques being Isomap [6] and Laplacian eigenmaps [7]. Since its introduction, manifold learning has been applied for a multitude of applications, including segmentation [8], registration [9], tracking [10], recognition [11], and 4D CT reconstruction [12]. The approach taken in the reconstruction is similar to ours because Isomap is used to estimate the breathing phase on CT slabs. In our work, we deal with the specific challenges of the integration of 4D ultrasound wobbler data. To this end, we focus on Laplacian eigenamps, since we achieved better results in comparison to Isomap.

2

Method

The general idea of manifold learning is to project a manifold in high dimensional space RN to a low dimensional space Rn , while preserving the local neighborhood. For our application, we consider one dimension of the ambient space for each image pixel, so N is corresponding to the resolution of the ultrasound images. For the low dimensional space, we set n = 1, because we want to use the coordinate of the points directly as breathing phase estimation. Considering k ultrasound images U = {u1 , . . . , uk } that are acquired over several breathing cycles, the manifold learning m assigns each image a coordinate in the low dimensional space φi m : RN → R1 → φi , ui 

(1) (2)

with 1 ≤ i ≤ k. The suggestion that ultrasound images lie on a low dimensional manifold in the ambient space seems to be justified because variations between neighboring slices are smooth, and further, slices from the same respiratory phase but different acquisition times are similar. Moreover, since manifold learning techniques try to optimally preserve local information [7], meaning that similar images are mapped to similar positions in the low dimensional space, it is reasonable to use φi as an estimate for the respiratory phase. 2.1

Laplacian Eigenmaps

We propose the application of Laplacian eigenmaps [7] for the respiratory phase estimation because the technique is well founded on mathematical concepts (Laplace Beltrami operator) and computationally efficient. Laplacian eigenmaps build upon the construction of a graph, which represents the neighborhood information of the data set. Subsequently, the graph Laplacian is applied to calculate a low-dimensional representation of the data that preserves the local neighborhood information in an optimal way.

Manifold Learning for Image-Based Breathing Gating

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Fig. 2. Breathing signals from manifold learning. Illustrated is the case for 3 angles (3 colors). X-axis indicates ultrasound frame number. The plots show the signals before and after alignment.

We construct a graph with a node for each point ui and with edges connecting neighboring nodes. We select for each image ui the l nearest neighbors, by evaluating the norm ||ui − uι ||2 . Further, heat kernel-based weights are assigned 2 2 to the edges with wiι = e−||ui −uι || /(2·σ ) and σ 2 the variance [7]. The similarity measure is important for neighborhood selection and weighting, where the calculation of the Euclidean norm between the points is equivalent to calculating the sum of squared differences (SSD) between the images. A vast number of similarity measures is proposed in the context of medical image registration. Since we deal with monomodal data for our application, we investigate the performance of SSD and the correlation coefficient (CC). The calculation of CC is similar to the calculation of SSD on normalized input images. Once the neighborhood graph is constructed, the eigenvectors of the graph Laplacian provide the embedding map. 2.2

Global Consistency

After the breathing gating is performed for each angle, we have to establish the correspondence between different angles in order to construct the global respiratory signal. Be U the set of all acquired images. We partition the set in disjunct subsets U 1 , . . . , U α , corresponding to the number of different deflection angles α of the wobbler (dash dotted region in figure 1). We perform the manifold learning for each of the subsets separately mj (ui ) = φji , with 1 ≤ j ≤ α. So depending on the acquisition angle of the ultrasound image ui , the corresponding manifold learning mj is performed. Considering all the phases estimated from one angle, we have the local respiratory signals Φj = {φj1 , . . . , φjv }, with v the number of frames per angle. Each local signal contains a consistent estimation of the breathing signal. It is, however, not possible to directly compare local signals, because the 1D projection of the manifold learning can be in an arbitrary range. This is illustrated in figure 2(a) with exemplary three local signals corresponding to three angular positions. A simple normalization of each of the local signals Φj is not sufficient because the extreme positions of the breathing cycle may not

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be reached within them. Consequently, we affinely register local signals in order to retrieve the best scaling sj and translation tj Φj  → sj · Φj + tj .

(3)

This is, in fact, a groupwise registration scenario, where we choose to align each pair of neighboring curves with a pairwise registration, starting from the middle one. The result of the alignment is shown in figure 2(b). The values of the partial signals Φj are now comparable, however, may still contain outliers. Consequently, we apply a robust curve fitting to all the sample points to retrieve the global breathing signal. We experimented with various curve models, including Fourier, sum of sine waves, and splines. We achieved best results with fitting a spline curve because it allows for the most flexibility, which is important due to irregularity of breathing. The value of the fitted curve then represents the breathing phase of the ultrasound frames. In a final step, the breathing cycle is classified into several breathing stages. For each of the breathing stages, the ultrasound frames along the various angles are gathered, and compounded into a final volume, see figure 3.

3

Experiments

For our experiments we use the ultrasound system from Ultrasonix (Richmond, Canada) and the optical tracking system from A.R.T. (Weilheim, Germany). Both systems are connected to a workstation PC. For the synchronization, we time stamp the data on the tracking system and use a network time server to calculate the time offset. For the ultrasound data, we use the direct streaming of B-mode images over the network. We perform tests on multiple patient datasets acquired from different positions, focusing on the liver and kidney. In order to validate our results, we compare them to the measurements of an external gating system. In [13], four different gating systems are compared with

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best results for an elastic belt and an optical tracking system. We use the tracking system with markers attached to the chest of the patient. We apply a principal component analysis of the 6D tracking data to find the principal component along whose direction we measure the breathing motion. Further, we low-pass filter the signal to remove cardiac motion and extract the respiratory signal. We refer to the tracked signal as ground truth, which is not completely correct because it contains tracking errors. However, it is the best that can currently be achieved [13] and is sufficient to validate the performance of our image-based approach. We compare our approach to the phase correlation technique [5]1 . Unfortunately, we do not achieve meaningful results for our datasets. We think that this is due to the limitation of the technique of approximating the 3D motion with a global translation in 2D. In order to illustrate this limitation, we produced synthetic images which show periodic motion. The first scenario consists of a rectangle moving up and down, see figure 4. For the second, we add a fixed rectangle, and for the third we add a rectangle that grows and shrinks (see additional material for videos). We plot the corresponding energy curves of the phase correlation technique. For the first scenario (blue) the signal is correct. The addition of a fixed object (red) already leads to a slight distortion, while the addition of the shrinking/growing object (green), leads to an extraction of a false motion signal. Since already the addition of the shrinking/growing object avoids the extraction of the correct motion, it is comprehensible that this approach is not best suited for breathing estimation in a noisy ultrasound environment with 3D anatomy moving in and out of plane. The resolution of our ultrasound images is 640 × 480 pixels. We downsample the images in each direction by a factor of 2, leading to N = 14 · 640 · 480. This enables a faster processing and leads to no noticeable degradation of the manifold learning. We show excerpts of two data sets in figure 5. We perform all our experiments with a graph neighborhood of l = 14. The number of images for manifold learning varies between 100 and 300, where we did not notice a dependency of the performance on the number of input samples. In figure 6, we show the result of the respiratory gating for one of the 2D datasets together with the ground truth signal. We also calculate the correlation coefficient for multiple 2D data sets, shown in table 1. It is remarkable that the 1

We want to thank the authors of [5] for sharing source code.

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Fig. 5. 2D Ultrasound images over time from liver (abdomen, right upper quadrant, oblique section) and kidney (left lateral decubitus position, right intercostal flank section)

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ground truth signal is almost perfectly detected. All peaks in the ground truth signal also appear in the detection. Further, the calculation of the correlation, which is in the range of 95%, confirms the visual similarity of the graphs. We also experimented with normalizing the images before passing them to the manifold learning, noticed however no significant improvement. For the 4D experiments, we show the result of a fitted curve in figure 2. We also calculate the correlation coefficient between the fitted curves and ground truth for four datasets, see table 2. We experimented with three different angular ranges, 30◦ , 45◦ , and 60◦ (maximum of probe), for which the probe steers to 15, 21, and 29 different angular positions. We split the breathing signal into 9 different breathing stages, and compound a 3D volume for each of the stages. A volume rendering of one of the volumes is shown in figure 3. The additional material contains a video showing the 4D volume rendering. All image-based approaches rely on ultrasound acquisitions from the same position, because otherwise it is not possible to differentiate between probe motion and breathing motion. To investigate this assumption, we attached a tracking target to the transducer and analyzed its trajectory. This analysis showed only a negligible deviation. The still position therefore does not limit the applicability of our method, which is also confirmed by our good gating results.

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Conclusion

We presented an automatic, image-based respiratory gating method for ultrasound using manifold learning. Moreover, we proposed a solution for acquiring 4D breathing data with a wobbler probe. Our method has the advantage that it is fully automatic and does not require a training phase or prior information about the underlying anatomy. We demonstrated this in our experiments by performing our analysis on various datasets showing different organs and sections. The results of these experiments were very good, for both, 2D and 3D ultrasound data over time. Our approach therefore presents an attractive alternative to external tracking and gating systems with their various setup issues and synchronization problems.

References 1. Treece, G., Prager, R., Gee, A., Cash, C., Berman, L.: Grey-scale gating for freehand 3D ultrasound. In: ISBI, pp. 993–996 (2002) 2. Zhu, H., Oakeson, K., Friedman, M.: Retrieval of cardiac phase from IVUS sequences. In: Proceedings of SPIE, vol. 5035, p. 135 (2003) 3. de Winter, S., Hamers, R., Degertekin, M., Tanabe, K., Lemos, P., Serruys, P., Roelandt, J., Bruining, N.: A novel retrospective gating method for intracoronary ultrasound images based on image properties. In: Computers in Cardiology (2003) 4. Karadayi, K., Hayashi, T., Kim, Y.: Automatic image-based gating for 4d ultrasound. In: Engineering in Medicine and Biology Society (2006) 5. Sundar, H., Khamene, A., Yatziv, L., Xu, C.: Automatic image-based cardiac and respiratory cycle synchronization and gating of image sequences. In: Yang, G.Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5762, pp. 381–388. Springer, Heidelberg (2009) 6. Tenenbaum, J., Silva, V., Langford, J.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319 (2000) 7. Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6) (2003) 8. Zhang, Q., Souvenir, R., Pless, R.: On manifold structure of cardiac MRI data: Application to segmentation. In: CVPR, vol. 1, pp. 1092–1098 (2006) 9. Hamm, J., Davatzikos, C., Verma, R.: Efficient large deformation registration via geodesics on a learned manifold of images. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5761, pp. 680–687. Springer, Heidelberg (2009) 10. Lee, C., Elgammal, A.: Modeling view and posture manifolds for tracking. In: ICCV (2007) 11. Wachinger, C., Mateus, D., Keil, A., Navab, N.: Manifold Learning for Patient Position Detection in MRI. In: ISBI (April 2010) 12. Georg, M., Souvenir, R., Hope, A., Pless, R.: Manifold learning for 4d ct reconstruction of the lung. In: MMBIA (2008) 13. Martinez-M¨ oller, A., Bundschuh, R., Riedel, M., Navab, N., Ziegler, S., Schwaiger, M., Nekolla, S.: Comparison of respiratory sensors and its compliance for respiratory gating in emission tomography. Journal of Nuclear Medicine (2007)

Measurement of the Skin-Liver Capsule Distance on Ultrasound RF Data for 1D Transient Elastography Stéphane Audière1,2, Maurice Charbit1, Elsa D. Angelini1, Jennifer Oudry2, and Laurent Sandrin2 1 2

Institut Telecom, Telecom ParisTech, CNRS LTCI, Paris, France Echosens, Research and Development Department, Paris, France

Abstract. Vibration-controlled transient elastography (VCTE™) technique is routinely used in clinical practice to assess non-invasively the liver stiffness which is correlated to hepatic fibrosis. Adequate use of the VCTE™ probe requires the knowledge of the distance between the skin and the liver parenchyma. This paper compares two methods to estimate this distance using spatial variations of the spectral content of ultrasound radiofrequency (RF) lines, obtained from a probe consisting of a single element ultrasound transducer placed in front of the liver right lobe. Results on a database of 188 patients, including normal-weight and obese persons, show that the spectral variance can accurately discriminate the subcutaneous fat from the liver tissue. The proposed algorithm works in real-time and is suitable for VCTE™ scanning protocol setup. Keywords: ultrasound, RF lines, liver, spectral analysis, elastography.

1 Introduction Vibration-controlled transient elastography (VCTE™) technique [1] is routinely used in clinical practice to quantify liver stiffness by measuring the velocity of a lowfrequency shear wave generated and travelling through the liver. It has been demonstrated that stiffness is highly correlated with fibrosis stage assessed by liver biopsy [2]. The VCTE™ device can be operated with different 1D-ultrasound probes, operating at different frequencies, depending on the patient morphology. The highest frequency probe provides higher spatial resolution but cannot be used on patients with a thick fat layer, due to frequency-dependent ultrasound attenuation in the fat. Therefore, the choice of the probe during an examination depends on the distance between the probe (in contact with the skin surface) and the liver. This distance corresponds to the subcutaneous thickness, called skin-liver capsule distance (SCD). The SCD is currently measured manually on ultrasound B-mode imaging. Automatic measurement of the SCD is therefore of great interest for VCTE™ scanning protocol setup to alleviate manual measurements, reduce operator dependency, and standardize the measurement technique. Ultrasound segmentation methods have mainly focused on B-mode imaging given the difficulty in getting access to raw RF data on commercial systems and the complexity of the RF signal content. Unfortunately, B-mode images are formed from the detection of the RF ultrasound line envelopes, which removes T. Jiang et al. (Eds.): MICCAI 2010, Part II, LNCS 6362, pp. 34–41, 2010. © Springer-Verlag Berlin Heidelberg 2010

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rich spectral information that could be used to characterize soft tissue properties. Among the few works dedicated to RF-based ultrasound segmentation, we can cite Hammoude et al. [3] who used changes in central frequency due to tissue attenuation to segment the heart muscle but had to face erratic changes in ultrasound signal. Boukerroui et al. [4] proposed a segmentation framework based on gray scale levels and texture analysis from the ultrasound envelope signal, combined with tissue characterization from the analysis of the central frequency spectrum of the ultrasound RF lines. More recently, Dydenko et al. [5] combined RF autoregressive spectrum parameters with the estimation of ultrasound propagation speed to characterize cardiac tissues and obtained good results using the estimated speed variance on in vivo signals. Moradi et al. [6] used the fractal dimension of RF time series for tissue characterisation, but needed high pulse repetition frequency rates. Davignon et al. [7] used the “integrated backScatter coefficient” (IBS) and the average central frequency to improve a segmentation method based on the ultrasound envelope signal. These studies all confirmed that the spectral information of the ultrasound RF lines was adapted for segmentation tasks, providing discriminant information on the acoustic properties of the different tissues. To our knowledge, few studies have been performed on the automatic measurement of the thickness of the subcutaneous layer, or on the skin-liver capsule distance. Ng et al. [8] recently showed that changes in the spectral content of 2D-spatial RF images enabled to accurately measure subcutaneous layer thickness on humans, but required spatial compounding. In this paper, a real-time implementation of the spectral analysis proposed by Ng et al. [8], but applied to 1D ultrasound RF lines, was evaluated and compared to the exploitation of the IBS parameter from [7].

2 Materials and Methods The SCD includes the layers of tissues connecting the epidermis of the skin surface to the liver. Fibrous membranes of connective tissues may vary in thickness and density between individuals. Furthermore, the fibrous membranes may contain varying proportion of fat and are more echogenic than the liver parenchyma, as illustrated in Fig. 1. Overall the subcutaneous layer has a rather heterogeneous appearance while the liver is rather homogeneous. 2.1 Spectral RF Analysis In most cases, the liver capsule is not precisely detectable on 1D ultrasound RF lines. Indeed, the direction of the ultrasound beam and the surface of the capsule must be perfectly perpendicular to accurately detect the echo generated by the capsule, as illustrated in Fig. 1. Since it is not possible to visually control the orientation of the VCTE™ ultrasound beam with respect to the liver surface, the echo amplitude cannot be directly used to determine the SCD. On the other hand, distinction between the subcutaneous layer and the liver can be performed via spectral analysis of the RF lines, based on the fact that ultrasound attenuation is tissue- and frequency-dependent, as detailed below.

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Fig. 1. (a) Positioning of the ultrasound (US) transducer for a VCTE™ and B-mode scanning, at the level of the 7th right intercostal space. (b) B-mode image (the position of the capsule is identified with a dashed line.). (c) Ultrasound RF line acquired with the VCTE™ probe.

The spectrogram S ( f , z ) of the RF signal at frequency f and at a distance z from the probe is generally modelled as: 2

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where H is the transfer function of the ultrasonic source, R is the backscatter component from the echoes and A is the attenuation term. In human soft tissues, ultrasound RF lines are exponentially attenuated in depth, leading to the following model for A: A( f , z ) = e −α ( f ) z ,

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Within the limited bandwidth of the ultrasound transducer, experimental measures have shown that soft tissues create attenuation phenomena of the RF lines which are linearly proportional to its frequency. Huisman et al. [9] have proposed the following attenuation law:

α ( f ) = α0 + β ( f − fc ) ,

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where α 0 is the tissue-specific attenuation coefficient at the central frequency f c of the transducer and β is the slope of the frequency-dependent linear attenuation. This attenuation model, exponential in z and with an attenuation coefficient linear in f naturally motivates the choice of a spectral analysis of the ultrasound RF signal for tissue characterization (different tissues being encountered along the z-axis). RF Spectral parameters: Two parameters were calculated from the spectrograms of acquired RF lines: the total energy reflected by the tissues (measured with the IBS) and the spectral variance. The IBS was proposed in [7] as a suitable discriminant

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parameter for tissue characterization. In our case, the tissues constituting the subcutaneous layer are hyper-echogenic relative to the liver parenchyma, leading to potentially higher IBS values. The spectral variance σ2 characterizes the local variation of the centroid frequency content of the spectrogram. Both can be calculated with the moment method, as proposed in [10], IBS corresponding to m0 and the spectral variance being computed as: 2

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m2 ( z ) ⎛ m1 ( z ) ⎞ ⎟ , −⎜ m0 ( z ) ⎜⎝ m0 ( z ) ⎟⎠

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with BW being the useful bandwidth of the transducer. The spectral variance σ2 does not depend on the echogeneity difference between tissues (i. e. RF signal strength), but rather on the heterogeneity of the tissues. From Eq. (3), σ2 is also independent of α 0 and f c but only depends on the tissue-dependent attenuation coefficient β . 2.2 Ultrasound RF Scanning Setup and Procedure The VCTE™ device used in this study was composed of a probe containing a lowfrequency vibrator, an ultrasonic transducer operating, depending on the probe, at 2.5 MHz or 3.5 MHz, a dedicated electronic system and a control unit. The sampling frequency of the ultrasound signal was 50 MHz with a 14-bit resolution. A single ultrasound element was used both as an emitter and a receiver. For each volunteer, 400 ultrasound RF lines were acquired, along a fixed scan line, at a pulse repetition frequency of 20 Hz during 20 s. In this study, the following acquisition protocol was used: the liver was first identified with B-mode ultrasound images and the skin capsule distance was manually measured on the images (as illustrated in Fig. 1). The VCTE™ probe was then placed at the same scanning location, but with the application of a controlled pressure on the skin surface of 20 to 30 kPa, for RF recording in elastography scanning mode. Application of such pressure limits probe motion while the patient breathes. A database was acquired with the two VCTE™ probes on 188 volunteers: 85% with normal weights and 15% of obese (corresponding to a body mass index (BMI) >30 kg/m²). The ultrasound RF lines were acquired for a depth range between 5 and 65 mm, to accommodate for the variability of the skin-liver capsule distance within the volunteers population.

3 Results and Discussion 3.1 Spectral Analysis Setup For each RF line, the spectrogram was computed with short-time Fourier transform (STFT). Spatial windows of length 12λ were used for the STFT computation, where λ represents the wavelength (and 2λ the pulse length) of the emitted ultrasound signal

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Fig. 2. (a) Series of RF lines acquired with a VCTE™ probe on a moderately obese volunteer. (b) Averaged localized spectrogram profiles inside the liver and inside the subcutaneous layer.

(estimated for an average ultrasound velocity c set to 1540 m/s for human soft tissues). This spatial window size, which sets the axial precision of the spectrogram, was chosen to optimize the tradeoff between frequency and temporal resolution. Overlaps of 75% and a weighting Blackman window were applied. With these parameters, we considered that the spectrogram computation had a precision of 3λ (i.e. 3 times the axial resolution of the US transducer). In Fig. 2, an example of a series of temporal ultrasound RF lines acquired with a fixed-position VCTE™ 3.5 MHz probe is provided. The volunteer was a male patient measuring 1.67 m and weighing 82 kg (BMI = 30 kg/m², and B-mode SCD = 20 mm, corresponding to moderate obesity). Averaged profiles (over 0.5 s) of localized spectrogram data for the subcutaneous layer (z=10 mm) and inside the liver (z=40 mm) are shown on Fig. 2b. Spectral analysis of the spectrograms, to extract the IBS and spectral variance, was performed on a series of consecutive 400 RF lines acquired over 20 s, maintaining the probe in a fixed position. Spatio-temporal maps of these parameters were computed and a binarization of these maps was applied, based on Otsu’s thresholding, to separate the subcutaneous layer from the liver tissue. The series of SCD measures was then combined to provide a robust estimate and compensate for potential tissue interface motion during breathing and to attenuate the effects of noisy components. Averaging of the SCD measures over the series of RF lines was performed in two steps: (1) local averaging over temporal windows of 2 s (approximate breathing period), (2) hysteresis thresholding for outliers removal on the temporal profile of the SCD values and selection of the SCD median value. For real-time computation during VCTE™ scanning, these computations are performed in temporal streaming mode, with SCD measures refreshed every 0.5 s. Parametric maps of the normalized IBS and the normalized spectral variance parameters are illustrated in Fig. 3, along with the corresponding Otsu’s thresholding results, for two volunteers. We can clearly observe on the normal-weight volunteer the effect of the breathing on the localisation of the capsule interface, while we don’t observe such effect on the obese volunteer. On the normal-weight volunteer, with higher temporal variability on SCD values, the average measures were the following: SCDIBS = 12.08 ± 0.62 mm, SCDσ²=13.76 ± 0.52 mm, while the B-mode measure was SCDB-mode = 13 mm. Maximum and minimum SCD values over the temporal series

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Fig. 3. Spectral analysis on an obese volunteer (top row) and a normal weight volunteer (bottom row). Normalized parametric maps of the IBS (a) the spectral variance (c) are plotted along with the corresponding thresholding results (b-d).

were: SCDIBS=[11.07 mm 13.09 mm] and SCDσ² =[12.41 mm, 14.43 mm]. This corresponds to lateral liver displacement, relative to the skin surface, of 2mm which correlates well with MRI-based findings reported in [11]. 3.2 Quantitative Evaluation of the SCD Measures SCD measures based on both spectral parameters were first evaluated on an in vitro experiment to measure the layer thickness on subcutaneous pig tissues, as illustrated in Fig. 4. A pig meat sample made of fat and muscle was placed on top of a gelatin cylinder phantom mimicking the liver acoustic properties.

a)

b)

Fig. 4. In vitro experiment on pig tissues. (a) Experimental scanning setup. (b) Temporal series of RF lines. The black line on the image represents the SCD values calculated with the s² parameter (solid) and the IBS parameter (dashed).

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The subcutaneous fat layer thickness directly measured on the sample was 13.4 mm. The algorithm provided a temporal average measure of 15 mm for the σ² parameter and 25mm for the IBS parameter, both estimations having a spatial precision of 1.25 mm (for the algorithm). This experiment, performed on high-quality RF lines, showed that the IBS parameter completely failed to provide an accurate fat layer thickness measure, while the σ² parameter provided an accurate estimate, within the precision of the method. This experiment highlights the superiority of the spectral variance parameter to distinguish fat from muscle and to be less sensitive to depth-attenuation which is the predominant advantage on in vivo RF data. 3.3 Qualitative Comparison of SCD Measures on Volunteers SCD values measured with the three probes (1 B-mode and 2 VCTE™), and averaged over the whole population or separately over the normal-weight (SCDB-mode<20 mm) and the over-weight population (SCDB-mode>20 mm), are reported in Table 1. For the spectral estimations, the algorithm precision of 3λ corresponded to 1.8mm for the 2.5 MHz probe and 1.3mm for the 3.5 MHz probe. As expected, the SCD measures were smaller with VCTE™ probes which apply more pressure on the skin. The range of differences confirmed that SCDB-mode cannot be directly mapped to setup the scanning protocol with the VCTE™ probes. The two VCTE™ probes should provide similar SCD values, which was only the case with the σ² parameter. The IBS parameter estimated systematically lower SCD values with up to 3.7 mm (30%) of measure discrepancies between probes, for the over-weight population. Focusing on the normal-weight population (SCD<20 mm), the differences between the B-mode and the VCTE™-based measures should be small, given the little deformability of the subcutaneous tissues. Regarding this point, we observed that the similarity of measures was better for the σ² parameter than for the IBS. We also observed that the IBS parameter systematically underestimated the subcutaneous layer thickness, especially for the 3.5 MHz probe. Finally, we observed that higher correlations (c.f. p-values) were obtained for the σ² parameter, especially for over-weight volunteers. These results overall suggested that this parameter, even though more costly to compute, should be preferred to the IBS parameter. To evaluate the consistency between SCD measures from the B-mode and the VCTE™ probes, we performed Kendall's correlation tests on the whole database. Results are reported in Table 2, for the following parameters of the test: τ is the Kendall’s rank correlation coefficient, and p-val is the p-value for the correlation test. The p-values confirmed that the SCD measures provided by the spectral methods were well correlated with B-mode ultrasound measures, while direct comparison was biased, especially on over-weight patients. Table 1. Average SCD values measured with three probes SCD (mm) All <20 >20

B-mode 17.2±5.9 14.4±3.7 25.1±6.1

VCTE™ 2.5 MHz σ² 16.0±4.3 14.7±3.2 20.4±4.6

IBS 12.2±3.9 11.1±2.8 15.9±4.8

VCTE™ 3.5 MHz σ² 15.6±4.3 14.5±3.7 19.4±4.1

IBS 10.7±2.6 10.2±2.3 12.2±3.0

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Table 2. Kendall’s correlation test between B-mode and VCTE™ SCD measures Probe 2.5 MHz 3.5 MHz

All SCD τ = 0.6 p-val = 2.10-24 -16 IBS τ = 0.4 p-val = 6.10 -18 σ² τ = 0.5 p-val = 3.10 -9 IBS τ = 0.3 p-val = 2.10 σ²

SCDB-mode ≤ 20mm τ = 0.5 p-val = 6.10-15 τ = 0.3 p-val = 1.10-7

SCDB-mode>20mm τ = 0.4 p-val = 2.10-3 τ = 0.3 p-val = 9.10-3

τ = 0.4 p-val = 6.10-12 τ = 0.3 p-val = 1.10-6

τ = 0.2 p-val = 5.10-3 τ = 0.1 p-val = 0.19

4 Conclusion This paper presented the evaluation of a spectral analysis approach to segment ultrasound RF lines and measure subcutaneous layer thickness, for liver scanning, on a large database of subjects. A correlation study was performed to compare thickness measures with an imaging B-mode ultrasound probe. The spectral analysis was tailored to the specific scanning and acquisition setup of a VCTE™ probe, involving the tuning of the spatial window length, the weighting window and the spectral bandwidth. In vitro experiment on pig tissues reported a precision of measure of 1 to 2 mm.

References 1. Sandrin, L., Fourquet, B., Hasquenoph, J.-M., Yon, S., Fournier, C., Mal, F., Christidis, C., Ziol, M., Poulet, B., Kazemi, F.: Transient elastography: A new noninvasive method for assessment of hepatic fibrosis. Ultrasound in Medicine and Biology 29(12), 1705–1713 (2003) 2. Castera, L., Vergniol, J., Foucher, J., Bail, B.L., Chanteloup, E., Haaser, M., Darriet, M., Couzigou, P., Ledinghen, V.d.: Prospective comparison of transient elastography, Fibrotest, APRI, and liver biopsy for the assessment of fibrosis in chronic hepatitis C. Gastroenterology 128(2), 343–350 (2005) 3. Hammoude, A.: Edge detection in ultrasound images based on differential tissue attenuation rates. Ultrasonic Imaging 21(1), 31–42 (1999) 4. Boukerroui, D., Basset, O., Baskurt, A., Gimenez, G.: A multiparametric and multiresolution segmentation algorithm of 3-d ultrasonic data. IEEE Transactions on Ultrasononics, Ferroelectrics and Frequency Control 1(48), 64–77 (2001) 5. Dydenko, I., Friboulet, D., Gorce, J.-M., D’hooge, J., Bijnens, B., Magnin, I.E.: Towards ultrasound cardiac image segmentation based on the radiofrequency signal. Medical Image Analysis 7(3), 353–367 (2003) 6. Moradi, M., Mousavi, P., Abolmaesumi, P.: Tissue characterization using fractal dimension of high frequency ultrasound RF time series. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part II. LNCS, vol. 4792, pp. 900–908. Springer, Heidelberg (2007) 7. Davignon, F., Deprez, J.F., Basset, O.: A parametric imaging approach for the segmentation of ultrasound data. Ultrasonics 43(10), 789–801 (2005) 8. Ng, J., Rohling, R., Lawrence, P.D.: Automatic measurement of human subcutaneous fat with ultrasound. IEEE Transactions on Ultrasononics, Ferroelectrics and Frequency Control 56(8), 1642–1653 (2009) 9. Huisman, H.J., Thijssen, J.M.: Precision and accuracy of acoustospectrographic parameters. Ultrasound in Medicine & Biology 22(7), 855–871 (1996) 10. Fink, M., Hotteir, F., Cardoso, J.F.: Ultrasonic signal processing for in vivo attenuation measurement: Short time Fourier analysis. Ultrasonic Imaging 5(2), 117–135 (1983) 11. Rohlfing, T., Maurer Jr., C.R., O’Dell, W.G., Zhong, J.: Modeling liver motion and deformation during the respiratory cycle using intensity-based free-form registration of gated MR images. In: SPIE Medical Imaging, San Diego, CA, USA (2004)

Incremental Shape Statistics Learning for Prostate Tracking in TRUS Pingkun Yan and Jochen Kruecker Philips Research North America 345 Scarborough Road, Briarcliff Manor, NY 10510

Abstract. Automatic delineation of the prostate boundary in transrectal ultrasound (TRUS) can play a key role in image-guided prostate intervention. However, it is a very challenging task for several reasons, especially due to the large variation of the prostate shape from the base to the apex. To deal with the problem, a new method for incrementally learning the patient-specific local shape statistics is proposed in this paper to help achieve robust and accurate boundary delineation over the entire prostate gland. The proposed method is fast and memory efficient in that new shapes can be merged into the shape statistics without recomputing using all the training shapes, which makes it suitable for use in real-time interventional applications. In our work, the learned shape statistics is incorporated into a modified sequential inference model for tracking the prostate boundary. Experimental results show that the proposed method is more robust and accurate than the active shape model using global population-based shape statistics in delineating the prostate boundary in TRUS.

1

Introduction

Transrectal ultrasound (TRUS) is currently the most commonly used imaging modality for image-guided biopsy and therapy of prostate cancer due to its real-time nature, cost effectiveness, and simplicity. Accurate delineation of the prostate boundary in TRUS can play a key role in image-guided prostate interventions. However, extracting the prostate boundary in TRUS is a challenging task due to the low signal-to-noise ratio of ultrasound imaging, the large intensity variation both inside and outside of the prostate, and especially the large shape variations through the whole gland from the base to the apex. Methods for segmenting the prostate in static TRUS images have been reported in the past. Abolmaesumi and Sirouspour [1] traced the prostate boundary by moving from one estimated boundary point to the next following a trajectory described by a constant velocity dynamic model. Ladak et al. [2] employed a discrete dynamic contour guided by shape statistics to segment the prostate in TRUS. Shen et al. [3] proposed a segmentation method by first classifying a TRUS image using support vector machine with Gabor filter bank and then fitting a statistical prostate shape model to the output image. These static image segmentation methods have been successful in the mid-gland, because the T. Jiang et al. (Eds.): MICCAI 2010, Part II, LNCS 6362, pp. 42–49, 2010. c Springer-Verlag Berlin Heidelberg 2010 

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boundary shapes in that area are quite regular with small variation. However, due to the large prostate shape variation in the base and the apex areas, poor segmentation performance in those areas was indicated [3, 4]. Recently, Yan et al. [5] addressed the problem using a dynamic shape modeling approach. The prostate shape statistics is continuously recomputed from several of the most recently segmented prostate shapes. The method obtained considerable success by incorporating the adaptive local shape statistics into the segmentation process. However, due to the continuous model recalculation using the obtained shapes, this method is not computationally efficient and also requires storing all the training shapes. In this paper, we propose a new method for incrementally learning the patientspecific local shape statistics to help achieve accurate boundary delineation over the whole prostate gland in TRUS. New shapes that become available during the delineation process can be merged into the shape statistics using an incremental subspace learning method [6, 7] without explicitly recomputing using all the training shapes. Therefore, the proposed learning method is computationally efficient and removes the need of storing all the training shapes, which makes it suitable for use in interventional applications. In addition, the incremental learning method updates the shape statistics in a smoother way compared to the work in [5]. Instead of segmenting each frame separately, the shape statistics is incorporated into a modified sequential inference model for contour based tracking to exploit the shape change dynamics from frame to frame. The prostate boundary tracker starts with the global population-based shape statistics. As more and more prostate boundary shapes from a particular patient are available along with the tracking, the learned shape statistics will become patient-specific and can quickly adapt to the prostate boundaries in a local neighborhood by weighing more on the most recent shapes. Finally, since the proposed method does not employ any numerical optimization, it is much faster compared to the previous methods on prostate boundary delineation [2, 3, 5], which is a highly desired feature for use in real-time interventional applications. The performance of the method is demonstrated by tracking the prostate boundaries in a series of TRUS sequences.

2

Incremental Shape Statistics Learning

Let a prostate contour St in the frame acquired at time t represented by a series of k contour points, i.e. St = {vti |i = 1, . . . , k}. Each contour point vti is a 2D vector {xit , yti }. The contour points are equally spaced (Euclidean distance based spacing) and sampled from the shapes [5, 9]. The active shape model (ASM) introduced by Cootes et al. [8] is used in our work for shape modeling, which provides a compact statistical shape representation by modeling contour point distribution. Suppose that the shape statistics has been computed from previous n prostate boundary observations at time t0 .The shapes can be denoted by n A = {Si − S¯A |i = 1, . . . , n}, where S¯A = n1 i=1 Si is the mean shape. The observed shapes can be decomposed by using the singular value decomposition

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(SVD) as A = UΣVT , where each column of U is an eigenvector of A and Σ is a diagonal matrix containing the corresponding eigenvalues. With the computed shape statistics, a new shape S can be represented by using the mean shape and the eigenvectors linearly combined by a coefficient vector b = UT (S − S¯A ). The approximation of the shape S constrained by the shape statistics can be obtained by Sˆ = S¯A + Ub. As the TRUS probe moves to image different areas of the prostate gland, it is desirable to use the newly available shapes to update the previous shape statistics to have the patient-specific local prostate shape knowledge. Let B = {Si − S¯B |i = 1, . . . , m} represent the differences mbetween the recent m shapes acquired after t0 1 and their mean shape S¯B = m i=1 Si . The objective is to merge the new shape set B into the shape statistics computed from the set A at time t0 . To achieve this goal, the incremental subspace learning algorithm [6,7], which was originally used for learning the appearance of a rectangular area in video frames, is modified to incrementally learn the shape statistics of deformable contours. Thus, the shape statistics can be updated by merging the new observations without recomputing using all the training shapes. Let C denote the concatenation of shape sets A and B. The mean shape in the new shape statistics is computed as S¯C =

nf ¯ m ¯ SA + SB , nf + m nf + m

(1)

where f is a forgetting factor f ∈ R and 0 ≤ f ≤ 1. The smaller the value of f , the faster the information from the old shape statistics is discarded, and vice ˜ be the component of B versa. To assist the effective let B  SVD computation,   nm ˆ = B1 · · · Bm ¯B − S¯A ) . The concatenated ( S orthogonal to U and B n+m  T  V 0 ˜ matrix C can be expressed as C = [A B] = [U B]R , where R = 0 I   ˆ fΣ UT B ˜ ˆ ˆ . Finally, the incrementally updated shape statistics of C 0 B(B − UUT B) ˜U ˜ and Σ = Σ, ˜ where U ˜Σ ˜V ˜ T is the SVD of R. can be obtained as U = [U B] The proposed incremental learning algorithm involves computation of QR decomposition of a k × (m + 1) matrix and SVD of a (e + m + 1) × (e + m + 1) matrix for each update, where e is the number of eigenshapes at t0 . Compared to the simplistic approach of applying SVD to a k ×(n+m) matrix for recomputing shape statistics at each step, our proposed method learns the shape statistics in a more efficient way, especially when the number of training shapes n gets large. There is also no need to store the k × n contour points of the old training shapes. The resulted reduction in computational time and memory usage makes the algorithm well-suited for real-time image-guidance tasks.

3

Sequential Inference Model for Tracking

Instead of separately segmenting each TRUS frame, the incremental shape statistics learning algorithm is incorporated into a visual tracking framework for

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prostate boundary delineation to exploit the gradual shape transition along with the movement of the TRUS probe. Given a set of observed TRUS frames It = {Ii |i = 1, . . . , t}, the aim is to delineate the prostate shape St in the current frame t, which can be formulated as to find St that maximizes the probability p(St |It ). By using Bayes’ theorem, we have  p(St |It ) ∝ p(It |St ) p(St |St−1 )p(St−1 |It−1 )dSt−1 . (2) The probability p(St−1 |It−1 ) denotes the tracking result obtained in the previous frame. The probability p(St |St−1 ) describes the dynamic process of propagating the prostate shapes from frame t−1 to frame t. The probability p(It |St ) measures how well the propagated contour St can be fit into the frame t. The details of the probability terms on the right side of (2) are presented as follows. For computational efficiency and robustness, prostate shapes are projected into the subspace of the incrementally learned shape statistics by using an affine transformation Tt and the coefficient vector bt as in Section 2

(3) St = Tt S¯t + Ut bt . Let xt = [xt , yt , θt , st , αt , φt ]T be the translations along x and y axes, rotation angle, scale, aspect ratio, and skew direction in the affine transformation. The state vector Xt can be composed by concatenating the transformation parameters and shape representation coefficients as Xt = [xt ; bt ]. The prostate shape transition between the TRUS frames can be described as Xt = Xt−1 + ΔX = [(xt + Δx); (bt + Δb)] ,

(4)

where the difference ΔX follows normal distribution N (ΔX; 0, Ψ) and Ψ is a diagonal covariance matrix whose elements are the corresponding variances of the elements in Xt . Therefore, we have p(St |St−1 ) = p(Xt |Xt−1 ) = N (Xt ; Xt−1 , Ψ).

(5)

The probability p(It |St ) of observing TRUS frame It given a shape St can be measured by the distance between St and the detected prostate boundary. The dark-to-bright transition has been shown to be an effective prostate boundary indication feature [9], which can be computed by the pixel intensity contrast i along the normal vector of the contours. Let {Fmax |i = 1, . . . , k} denote the points with the maximal feature values corresponding to each contour point, the probability p(It |St ) can be measured 

k 1 i i 2 F − xt  , p(It |St ) ∝ exp − 2 (6) 2r k i=1 max where r is the spacing between the points on the normal vector profile. The particle filter based Condensation algorithm introduced by Isard and Blake [10] is modified for solving this deformable contour tracking problem formulated in (2). The workflow of the tracking method is shown in Fig. 1. Since the

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P. Yan and J. Kruecker Move to the next frame

Generate samples by sampling from p( S t 1 | ǿ t 1 )

Predict shapes in the current frame using p ( S t | S t 1 )

Measure the probability of observation p(I t | S t )

Obtain the final probability p(S t | I t )

Fig. 1. Workflow of the particle filter based tracking method using the sequential inference model

proposed method does not employ any numerical optimization, it runs in linear time O(N ), where N is the number of samples. The final shape can be estimated N by computing the expectation of all the samples Sˆt = i=1 p(Sti |It )Sti .

4

Experimental Results

In our experiments, the proposed method was retrospectively tested on sequences collected during TRUS guided prostate cancer biopsy procedures using an iU22 ultrasound system (Philips Healthcare, Andover, MA). The TRUS frames were digitized by a video card at 30 frames per second (fps). Each grabbed TRUS frame has 640×480 pixels and the pixel sizes were 0.1493mm and 0.1798mm in 4cm and 5cm depth settings, respectively. In total, 3215 video frames were grabbed from 20 different patients. An experienced radiologist manually delineated the prostate boundary in one out of every ten frames of the TRUS sequences, in total 316 frames, to provide the ground truth for validation. In our experiments, the tracked prostate boundary was represented by a contour with k = 64 points. The initial prostate shape statistics was computed using 62 prostate shapes previously obtained from a different data set. To quickly incorporate the newly tracked shapes into the shape statistics, the incremental learning was performed in every frame. The forgetting factor f in (1) was empirically set to 0.95 to weigh the learning more on the recently tracked contours, while maintaining the smoothness of the incrementally learned shape statistics. The number of samples N used in the particle filter is a trade-off between the efficiency and accuracy. A larger number of samples may give a bit more accurate tracking results, however, will also make the algorithm slower. The results demonstrated in this paper were obtained by using N =1000 samples. The proposed method starts tracking from a given initial contour, which can be obtained by either manual delineation or using an automatic 2D TRUS image segmentation algorithm [3, 5]. The initial values of the affine transformation parameters and the shape representation coefficients can be computed by using the initial contour. The variance of the normal distribution in the dynamical model (5) was empirically √ set to be [2.0, 2.0, 0.001, 0.05, 0.05, 0.001] for the transformation part and Σ/10 for the shape representation part. Only the first 3 most significant eigenvectors in the shape statistics were used in our work. The proposed method was developed in Matlab. Once initialized, it tracks the prostate boundary in TRUS fully automatically. On a Core2 1.86 GHz PC, we achieved

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Table 1. MAD errors (mm) of the ASM and the proposed tracking method on delineating the prostate boundary in the TRUS sequences Method seq-1 seq-2 seq-3 seq-4 seq-5 seq-6 seq-7 seq-8 seq-9 seq-10 ASM 3.28 2.54 2.24 1.66 3.09 2.54 1.73 2.67 2.34 2.80 Tracking 0.95 1.92 1.45 1.62 2.16 0.83 0.63 0.76 1.54 1.36 seq-11 seq-12 seq-13 seq-14 seq-15 seq-16 seq-17 seq-18 seq-19 seq-20 Average ASM 1.66 1.20 3.01 1.63 3.02 4.73 1.92 2.97 2.53 2.61 2.51±0.78 Tracking 1.52 0.96 1.89 1.46 2.26 1.22 1.49 1.98 1.42 1.39 1.44±0.46

S¯0

S¯0 ∓



σ10 U10

S¯1

S¯1 ∓

 σ11 U11

S¯2

S¯2 ∓

 σ12 U12

S¯3

S¯3 ∓



σ13 U13

S¯4

S¯4 ∓

 σ14 U14

Fig. 2. The 1st row shows the delineation of prostate boundary in TRUS with the manually delineated contour in red and the automatic tracking result in yellow; the 2nd row shows the mean shapes in the incrementally learned shape statistics at each stage corresponding to the video frames; the 3rd row shows the shapes generated by varying the mean shapes with the largest mode of variation

12 fps with the above parameter setting. On the same computer, the ASM segmented the sequences with 3 fps. Fig. 2 shows the tracking results of a TRUS sequence and the learned shape statistics corresponding to the displayed frames. It can be observed that the mean shapes and the major shape components gradually change towards the tracked shapes through incremental learning. Fig. 3 demonstrates the tracking results of the proposed method in different regions of the prostate gland. The initialization contours are included to show that the proposed method can successfully track the prostate boundary when the prostate boundary shape becomes significantly different from the initial shape. In general, the tracking results are close to the manually delineated contours. Besides the visual inspection, we also quantitatively evaluated the performance of the proposed method. The ASM [8], which has been widely used for segmenting the prostate in TRUS [2, 3, 5, 9], was applied to the same data set by detecting the prostate boundary using the same boundary feature and initial contours for comparison. For TRUS sequence segmentation, the result of ASM

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Fig. 3. The first column shows the initialized contours to start the tracking of each sequence. The rest two columns show the tracking results in different part of the prostate gland, where the manually delineated contours are shown in red and the tracked contours are shown in yellow. Table 2. MAD errors (mm) of the ASM and the proposed tracking method in the base, mid-gland, and apex areas over the 20 TRUS sequences, respectively Method base ASM 2.53±1.17 Tracking 1.39±0.67

mid-gland 1.48±0.59 1.20±0.42

apex 3.52±1.63 1.73±0.76

from one frame was propagated to the next as the initialization. The mean absolute distance (MAD) error was employed for quantitative measurement. As shown in Table 1, the accuracy of the proposed method was significantly better than the ASM, which uses only the global population-based shape statistics. In our work, the statistical significance was evaluated using paired t test (p <0.05). It is also interesting to see the performance of the methods in each of the base, mid-gland, and apex regions. For quantitative evaluation, the ground truth segmentations of each patient were sequentially divided into three groups with equal number of frames in each group. Since the sequence was obtained by scanning through the prostate from the base to apex, the three groups were labeled as base, mid-gland, and apex in the specified order. The evaluation results are shown in Table 2. Compared to the ASM, prostate boundary delineation

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accuracy was significantly improved in all the regions by using the proposed tracking approach with incrementally learning the shape statistics.

5

Conclusions

In this paper, we presented a new algorithm for incremental shape statistics learning, which is well-suited for use in image-guidance applications due to its computation and memory efficiency. The learning algorithm was successfully incorporated into a modified sequential inference model to help achieve more robust and accurate delineation of the prostate boundary in TRUS over the entire prostate gland. Experimental results show that the contour delineation error of the proposed method was 42.6% less than that of the ASM. Significant improvement was made in the base and apex areas with 45.1% and 50.1% less delineation errors, respectively. To the best of our knowledge, the proposed tracking algorithm is the first method that aims to extract the prostate boundary from TRUS in real-time during image-guided prostate interventions. In our future work, we will investigate more efficient software implementation of the algorithm and also explore hardware acceleration to get the program run in real-time.

References 1. Abolmaesumi, P., Sirouspour, M.R.: An interacting multiple model probabilistic data association filter for cavity boundary extraction from ultrasound images. IEEE Trans. Med. Imaging 23(6), 772–784 (2004) 2. Ladak, et al.: Prostate boundary segmentation from 2D ultrasound images. Med. Phys. 27(8), 1777–1788 (2000) 3. Shen, et al.: Segmentation of prostate boundaries from ultrasound images using statistical shape model. IEEE Trans. Med. Imaging 22, 539–551 (2003) 4. Yan, et al.: Optimal search guided by partial active shape model for prostate segmentation in TRUS images. In: Medical Imaging 2009, vol. 7261. SPIE (2009) 5. Yan, et al.: Segmenting TRUS video sequences using local shape statistics. In: Medical Imaging 2010, vol. 7625. SPIE (2010) 6. Levy, A., Lindenbaum, M.: Sequential karhunen-loeve basis extraction and its application to images. IEEE Transactions on Image Processing 9(8), 1371–1374 (2000) 7. Ross, D.A., Lim, J., Lin, R.S., Yang, M.H.: Incremental learning for robust visual tracking. International Journal of Computer Vision 77, 125–141 (2008) 8. Cootes, et al.: Active shape models – their training and application. Comput. Vision Image Understand. 61(1), 38–59 (1995) 9. Hodge, et al.: Prostate boundary segmentation from ultrasound images using 2D active shape models. Comp. Methods Prog. Biomed. 84, 99–113 (2006) 10. Isard, M., Blake, A.: CONDENSATION – conditional density propagation for visual tracking. International Journal of Computer Vision 29(1), 5–28 (1998)

Fast and Accurate Ultrasonography for Visceral Fat Measurement You Zhou1, Norihiro Koizumi1,2, Naoto Kubota2,3, Takaharu Asano3, Kazuhito Yuhashi3, Takashi Mochizuki4, Takashi Kadowaki2,3, Ichiro Sakuma1,2, and Hongen Liao1,2 1

2

Graduate School of Engineering, The University of Tokyo Translational Systems Biology and Medicine Initiative, The University of Tokyo 3 Graduate School of Medicine, The University of Tokyo 4 Aloka Co. Ltd., Japan {zhouyou,sakuma,liao}@bmpe.t.u-tokyo.ac.jp

Abstract. Visceral fat area (VFA) has close relationship with hypertension, diabetes and cardiovascular disease, and therefore serve as a reliable indicator of these diseases. Abdominal computed tomography (CT) enables precise quantification of the VFA and has been considered as the gold standard for VFA assessment. In this paper, we develope a novel method to quickly and accurately measure the VFA with ultrasonography (US). We evaluated the novel method on five volunteers and the diagnosis procedures lasted less than 30 seconds averagely. The simulation results by our method were compared with VFA estimated by abdominal CT. The correlation coefficient between them was 0.913 for men and 0.858 for women. And the mean deviation of between VFA by CT and by our method was ͳͻǤͺܿ݉ଶ for men and ͳ͵Ǥ͵ܿ݉ଶ for women.

1

Introduction

The term metabolic syndrome (MS), a combination of medical disorders that increase the risk of chronic diseases such as diabetes, hypertension, and cardiovascular disease, has been adopted by International Diabetes Federation (IDF) in 2006. MS is a major public health problem, the prevalence of which has increased worldwide. Visceral obesity, the excess accumulation of visceral fat deposits mainly around the waist, is thought to be a fundamental pathology for MS in particular. Therefore, accurate measurement of visceral fat represents an important tool in assessing MS. Visceral fat, also known as organ fat, packes in between internal organs and the torso, as opposed to subcutaneous fat which is found underneath the skin. Since visceral fat is located deep inside the body and mixed with other organs, its accurate assessment has prooven to be challenging work. Abdominal computed tomography (CT) has been considered the most accurate and reproducible technique of body fat measurement, particularly abdominal adipose tissue. Abdominal CT enables accurate quantification of the visceral fat area (VFA) and therefore serves as the gold standard for visceral fat assessment [1]. However, abdominal CT has many drawbacks, including exposure to radiation, lack of simplicity, high cost, and time-consuming. T. Jiang et al. (Eds.): MICCAI 2010, Part II, LNCS 6362, pp. 50–58, 2010. © Springer-Verlag Berlin Heidelberg 2010

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Due to these limitations, a variety of alternative methods are being used to assess visceral fat amount and distribution. Previous studies have shown that waist circumference (WC), and WC-based indices can perform as some indicators of the level of visceral obesity [2]. These measurements are recommended as a simpler and easier screening method. However, due to the lack of the individual visualization of visceral fat, these methods have fatal drawbacks such as inability to distinguish subcutaneous fat from visceral fat, inability to take into account an individual’s specific information, low level of reproducibility in the case of marked obesity, and most important, poor accuracy. In recent years, simple methods for assessing visceral fat accumulation using ultrasonography (US) have been studied and were further confirmed by strong correlations with CT-detected VFA [3][4]. Ultrasound has many advantages such as non invasive to human bodies, low-cost, easy to be operated, real time and enables the visualization of visceral fat. Therefore, US-based methods show a balance on simplicity and accuracy between abdominal CT and WC-based indices. However, due to the poor image quality and limited visual field of US, the results of the existing US-based methods are still unsatisfactory and need further improvements. In the study, a fast and accurate method is developed for visceral obesity studies to provided an estimation of the abdominal visceral fat area and distribution using ultrasonography.

2 2.1

Method Ultrasound Probe Compatible Device

To provide a quick, easy-operated and accurate way to guide the ultrasonographic procedures, three factors are important: 1) Same positions and angles for ultrasound probe on different patients during diagnosis; 2) Distinct markers easy to be observable in US image; 3) Quantitive measurement on patients’ curvature of abdomen. We designed a belt-shaped ultrasound probe compatible device to fulfill these requirements (Fig.1). Two kinds of US measurements of visceral fat are taken. Firstly, US-determined visceral fat distance is defined as the distance between the internal face of the rectus abdominis muscle and the centre of the aorta from each diagnostic position. Secondly, the images acquire from the central position were saved for further processing. Unlike CT, the ultrasound can only provide a limited scope inside one patient's body. The diagnosing angle and position of probe may differ from doctor to doctor due to their own experiences. This belt-shaped device provides doctors a standard which is easy to follow. In the visual field of an abdominal US, due to the flow of blood, the aorta is nearly the most distinct marker for US. Thus, the belt-shaped device is designed to be fixed in the exact position from where the aorta can be observed most clearly. As a result, the diagnosis process will be finished in seconds, which is convenient for patients as well. With an elastic material, this belt-shaped device would bend smoothly and mold to patient's abdomen. It is easy to understand that: a

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patient with mild visceral obesity in normal range of waist circumference would have a 'flatter' shape in abdomen, which means that the belt-shaped device will less bend when diagnosing, while a patient with more serious visceral obesity would get a 'plumper' waist, and resultingly more bent the belt-shaped device becomes when diagnosing. Hence, the curvature of the belt is proportional to the curvature of abdomen, which can serve as valuable characteristic of individual seriousness level of visceral obesity and give a reasonable classification of patients.With three probediagnosing positions rather than one, the curvature of abdomen can be described quantitively.

(a)

(b)

Fig. 1. Ultrasound probe compatible device. Distance and angle between two adjacent probes are 50mm and ͶͲι in unbent situation. (a) Belt-shaped device design (b) Measurement method.

2.2

Segmentation of Visceral Fat Area

Analyzed results based on hundreds of abdominal CT images show that most visceral area of patient in his/her abdominal cross-section could be simulated as an ellipse, with aorta in the center. Although this approach may not be very exact for individual patient, the eccentricity of ellipse reflects the curvature of abdomen and therefore serves as a quantitive description of visceral obesity. The ultrasound probe were detecting from three positions by the belt-shaped device. The information we can acquire contains: ܾ, denotes the distance between the internal face of the rectus abdominis muscle and the centre of the aorta detected from front, and is defined as semi-minor axis of ellipse; ܾ ᇱ , denotes the distance between front-end of ultrasound probe in the central diagnosing position and the centre of the aorta detected from front, ‫ݎ‬, denotes the same distance detected from one side; ݄ᇱ , denotes the distance between two probes (50mm); ݄, denotes the curve length between ܾ and ‫ ݎ‬derived from ݄ᇱ by ݄ ൌ ݄ᇱ ܾȀܾ ᇱ as showed in Fig. 2(a). Then, by ellipse circumference and ellipse parametric equation, we can calculate: ܽ, denotes the semi-major axis; ߠ, denotes the angle between two probes. For abdominal cross-section of a patient who has been diagnosed (denotes as patient‫)כ‬, we discretize the visceral area based on the ellipse approach as follow. The ellipse is divided uniformly by angle and axis length. Each section is identified by a number ݅. For patient‫כ‬, we define the area of section ݅ as ܽ௜‫ כ‬, the fat percentage of section ݅ as ‫݌‬௜‫ כ‬. Succinctly, we have ࡭‫ כ‬ൌ ሺܽଵ‫ כ‬ǡ ܽଶ‫ כ‬ǡ ǥ ǡ ܽ௡‫ כ‬ሻ் and ࡼ‫ כ‬ൌ ሺ‫݌‬ଵ‫ כ‬ǡ ‫݌‬ଶ‫ כ‬ǡ ǥ ǡ ‫݌‬௡‫ כ‬ሻ் , where ݊ refers to the total number of sections (In this paper,

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݊ ‫ Ͳ͵ ؜‬ൈ ͶͲ ൌ ͳʹͲͲ). Similar with a matrix, we can define ܰ௜‫ כ‬, the neighbourhood of ‫݌‬௜‫ כ‬as: the fat percentages of sections who share the same edges or vertices with section ݅ (Fig.2(b)). Immediately, there follows (1)

ܸ‫ ܣܨ‬ൌ ࡭‫ כࡼ ் כ‬.

The computation of ࡭‫ כ‬is trivial and main difficulty is how to give a reasonable estimation of ࡼ‫ כ‬. In order to distinguish the visceral fat from other organs, we used a Markov Random Field (MRF) based segmentation algorithm (Fig. 3). The main process of this algorithm follows [5]. We must declare here that this kind of algorithms were not developed specially for solving the fat recognition problem of ultrasonographic image, and have never been introduced into this field.

(a)

(b)

Fig. 2. Ellipse approach of abdominal cross-section. (a) Parameters of ellipse. Red part is the visceral fat. Grey part is other organs. (b) Neighbourhood in a discretized ellipse. Green part refers to ܰ௜‫ כ‬, the neighbourhood of ‫݌‬௜‫ כ‬.

(a)

(b)

(c)

Fig. 3. Distinction of visceral fat. (a) Original US image. The colorful part in central indicates aorta. (b) Segmentation of visceral fat. The white part indicates the visceral fat area. (c) Matching US visual field into the whole visceral area.

2.3

Matching with Pre- stored Data

In this part, we compare the ultrasonographic image of patient‫כ‬, with pre-stored CT scanned image of previous patients, and choose the patients whose situations are most similar with the current patient. We established a set V from 146 patients abdominal CT scanned images in a urban hospital, which cover full gamut of patients in its community. This pre-stored CT scanned images served as a pre-stored database with which the current patient‫ כ‬can compare.

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The visual field of ultrasonography is only local. So, we match the ultrasonography into the whole visceral area, and divide it into ݉ sections following the previous part (Fig. 3(c)). We denote section ݅ has area ܽ௜‫ כ‬and fat percentage ‫݌‬௜‫ כ‬, for every ݅ ൌ ͳǡʹǡ ǥ ǡ ݉. We have an estimation of ݉ components of ࡼ‫ כ‬, and the problem now is how to estimate the fat percentage of the remaining ሺ݊ െ ݉ሻ hidden sections ‫כ‬ ‫כ‬ ࡼ‫ ࢎכ‬ൌ ሺ‫݌‬௠ାଵ ǡ ‫݌‬௠ାଶ ǡ ǥ ǡ ‫݌‬௡‫ כ‬ሻ் . For CT images, the discretization of ellipse can be accomplished without difficulty. Then, section ݅ of patient ݇, has the fat percentage ܲ௜௞ . Naturally, there is ࡼ௞ ൌ ሺ‫݌‬ଵ௞ ǡ ‫݌‬ଶ௞ ǡ ǥ ǡ ‫݌‬௡௞ ሻ் ǡ ˆ‘”݇ ൌ ͳǡʹǡ ǥ ǡͳͶ͸. Now, we want to find out the patients from V whose situations are most similar with patient‫כ‬. As a result, the visceral fat distributions of those patients would serve as references for patient‫כ‬. We evaluate the correlative level between patient‫ כ‬and ‫כ‬ ௞ patient k by matching ‫݌‬ଵ‫ כ‬ǡ ‫݌‬ଶ‫ כ‬ǡ ǥ ǡ ‫݌‬௠ and ‫݌‬ଵ௞ ǡ ‫݌‬ଶ௞ ǡ ǥ ǡ ‫݌‬௠ . We use the Grey-Level Correlation Formula to accomplish it ‫ݎ‬௞ ൌ

ೖ തതതത ‫ כ‬തതത‫כ‬ത ೖ σ೘ ೔సభ൫௣೔ ି௣ ൯ቀ௣೔ ି௣ ቁ మ

തതതത ೖቁ തതത‫כ‬ത൯మ σ೘ ቀ௣ೖ ି௣ ටσ೘ ൫௣‫ି כ‬௣ ೔సభ ೔ ೔సభ ೔

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,

‫כ‬ ௞ തതത௞ refer to the average of ‫ כ ݌‬ǡ ‫ כ݌‬ǡ ǥ ǡ ‫݌‬௠ where തതത ‫ כ݌‬and ‫݌‬ and ‫݌‬ଵ௞ ǡ ‫݌‬ଶ௞ ǡ ǥ ǡ ‫݌‬௠ respecଵ ଶ tively. Before the matching process, the patients whose eccentricity ݁ and minor axis ܾ differ too large from patient‫ כ‬will be rejected in order to accelerate. The 10 patients with max value of ‫ ݎ‬௞ compose the set B. The CT image of those chosen patients would serve as the basis of fat estimation of current patient‫כ‬. We expect that ࡼ‫ ࢎכ‬can be expressed as a ‘combination’ of patients from B and this combination can reflect the visceral fat distribution of patient‫כ‬. To achieve it, we establish an optimization standard. By (3), we defines the cost at one section, and (4) is the integrally cost, which should be minimized. Consider ܰ௜‫ כࡼ ؿ כ‬, the neighbourhood of ‫݌‬௜‫ כ‬. We give a choice not only realizing optimization at single ‫݌‬௜‫ כ‬itself, but also throughout its neighbourhood ܰ௜‫ כ‬. We define the distance cost function between patient‫ כ‬and patient ݇ at section i as ଶ

(3)

൫ห‫݌‬௜‫ כ‬െ ‫݌‬௝‫ כ‬ห െ ห‫݌‬௜௞ െ ‫݌‬௝௞ ห൯ , ‫݌‬௝‫ܰ א כ‬௜‫ כ‬ǡ ‫݌‬௝௞ ‫ܰ א‬௜௞ ,

where ܰ௜‫ כ‬and ܰ௜௞ refers to the neighbourhood of ‫݌‬௝‫ כ‬and ‫݌‬௝௞ respectively. Hence, integrally, the ࡼࢎ‫ כ‬should be the vector who satisfies that ଶ

௞ ௞ ‫כ‬ ‫כ‬ ܽ‫‹ ݃ݎ‬௣೔‫ ࢎכࡼאכ‬σ௡௜ୀ௠ାଵ σଵ଴ ௞ୀଵ σ௣‫א כ‬ே ‫ כ‬ǡ௣ೖ ‫א‬ேೖ ൫ห‫݌‬௜ െ ‫݌‬௝ ห െ ห‫݌‬௜ െ ‫݌‬௝ ห൯ , ೕ

೔

ೕ

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೔

‫݌‬௜‫ א כ‬ሾͲǡͳሿ, for ݅ ൌ ͳǡʹǡ ǥ ǡ ݊. Consequently, the determination of ࡼࢎ‫ כ‬has been transformed into an optimization problem. This numerical optimization is performed automatically by a constraint nonlinear conjugate gradient method (CGM).

3

Experiment Results

In this part, all correlations between two variables were evaluated using Pearson's product-moment correlation coefficient. Comparisons between each two groups were done with an unpaired t-test.

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Evaluation Experiment of US

We tested the belt-shaped ultrasound probe compatible device on five volunteers from an urban community. All our ultrasonographic procedures were performed by the same examiner using a portable ultrasonography equipment (ȽͳͲ, ALOKA, Japan). The center of the belt-shaped device fixed exactly 2 cm left to umbilicus for each patient. Each patient assumed a supine position, and US data were measured at the end of expiration by a 6-MHz 2D abdominal probe, while the probe was making contact with patients’ skin as slight as possible (Fig.4). For each volunteer, the diagnosis procedures lasted less than 30 seconds. This is quite an acceptable time during a medical examination. In addition , More quick diagnosis speed is also expectable in the future if doctors become more proficient in this novel method.

Fig. 4. Practical diagnosis procedures for a patient. (a) Diagnosis by US. (b) Distance of visceral fat measured in US image. (c) Belt-shaped ultrasound probe compatible device.

3.2

Campare with CT Results

Simulation on 146 patients’ abdominal CT images were done and showed that there was strong correlation between the US observed VFA from front psotion and the total VFA of an individual patient. The coefficent was r = 0.883 and the level of significance was p-value < 2.2e-16 (Fig. 5). As a result, it is reasonable to use the US observed fat percentage as an indicator for total VFA. Since abdominal CT holds the most accurate quantification of the VFA, we treated it as the testing standard for visceral fat assessment. Abdominal cross-section by CT scanning was obtained in a single tomographic slice at umbilical level as ultrasound probe did. Portions with a CT number of −200 to −10 Hounsfield Units (HU) were separated as adipose tissue and their areas were automatically calculated.

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We simulated our method on 28 male and 35 female samples, and compared the results with abdominal CT. Figure 6 shows the comparisons of CT and our US-based method. The mean deviation between VFA measured by CT and our US method for each patient is ͳͻǤͺܿ݉ଶ for men and ͳ͵Ǥ͵ܿ݉ଶ for women. The correlation between these two groups is also presented. For men, the coefficent was r = 0.913 and the level of significance was p-value = 1.179e-11. For women, there are r = 0.858 and p-value = 4.674e-11. These results proofed the significant positive correlations between VFA measured by CT and by our method. And we also divided these 63 patients in both sex into three groups by the CTmeasured VFA: low ( ൑ ͳͲͲܿ݉ଶ ), medium (between ͳͲͲܿ݉ଶ and ͳͶͲܿ݉ଶ ) and high ( > ͳͶͲܿ݉ଶ ). The average and max VFA deviations between US method and CT method of these three groups were shown in Table 1. From this table, it is easy to notice that our US-based method performed better on the medium group than other two groups averagely. The reason of this is that the data per-stored data mainly laid mainly in this VFA range. Thus, the result reminds us that the pre-stored database is very essential for our method and it must cover full range of patients in enough quantities. On the other hand, the max VFA deviations are all too large in three groups. This demonstrates that there are many personal detailed characteristics of certain patients have been omitted in our method, which should be checked carefully for the further improvement of this US-based method.

Fig. 5. Scattergram of relationship between US observed VFA and the total VFA

Fig. 6. Camprison of our US-based method and CT for men and women

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Table 1. VFA deviations between US_method and CT_method in different groups

Groups Numbers of patients VFA deviations Average (ܿ݉ଶ ) Max

4

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Discussions and Conclusion

This paper proposes a novel US-based method for estimation of the VFA. A fast and convenient diagnosis method was introduced and a robust algorithm was proposed to estimate a patient’s VFA from US data automatically. As far as we know, this is the first attempt to compute VFA by ultrasound, and our results were shown to be strongly correlated with CT measurements. However, one main limitation of this present study is that all the data of patients were collected from the same ethnic group. Thus, the results cannot generalize directly to other individuals of certain ethnic groups. For instance, the female body type in particular differs largely between Westerners and Easterners. As a result, how to apply this novel method universally needs further discussions. Till now, we have developed a US-based method whose accuracy reaches the level of abdominal CT. However, it is not an entirely impossible thing that the US-based method will become a more reliable indicator for MS than abdominal CT in the future. Due to the non-invasiveness and simplity of US, diagnosis at different levels of the abdomen will be accomplished without much difficulties. Consequencely, 3D individual visualization and estimation of visceral fat can be realized by US, while usually only one slice of abdominal cross-section image can be acquired by CT in medical examination due to the harmness of rediation. Secondly, due to its real-time characteristics, US allows us to detect visceral fat over a period of time. One patient’s abdominal cross-sectional area when expiring will differ largely from inspiring. Abdominal CT cannot take this difference into consider and therefore would be less convincing than US in this respect. Further, by US, we may represent a useful method for monitoring weight loss, variations and transfer of visceral fat, which can be expected to indicate the associated risks of MS more accurately. In conclusion, although its results are still rough and there are many details need discussing, the present US-based method has proofed to be a considerably fast and accurate way for VFA estimation.

Acknowledgment This work was supported in part by Grant for Translational Systems Biology and Medicine Initiative (TSBMI) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

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References 1. Rossner, S., Bo, W.J., Hiltbrandt, E., et al.: Adipose tissue determinations in cadavers—a comparison between cross-sectional planimetry and computed tomography. Int. J. Obes. Relat. Metab. Disord. 14, 893–902 (1990) 2. Hsieh, S.D., Yoshinaga, H., Muto, T.: Waist-to-height ratio, a simple and practical index for assessing central fat distribution and metabolic risk in Japanese men and women. Int. J. Obes. Relat. Metab. Disord. 27, 610–616 (2003) 3. Chiba, Y., Saitoh, S., et al.: Relationship between Visceral Fat and Cardiovascular Disease Risk Factors: The Tanno and Sobetsu Study. Hypertension Research 30, 229–236 (2007) 4. Ribeiro-Filho, F.F., et al.: Methods of Estimation of Visceral Fat: Advantages of Ultrasonography. Obesity Research 11(12), 1488–1494 (2003) 5. Lorenz, A., Haas, C., Ermert, H.: Segmentation of ultrasonic prostate images using a probabilistic model based on Markov random processes. Ultrason Imaging 19, 44–45 (1997)

    

Real-Time Gating of IVUS Sequences Based on Motion Blur Analysis: Method and Quantitative Validation Carlo Gatta1,2 , Simone Balocco2 , Francesco Ciompi2 , Rayyan Hemetsberger3 , Oriol Rodriguez Leor3 , and Petia Radeva2 1

3

Dept. Matemtica Aplicada i Anlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain 2 Centre de Visi´ o per Computador, Bellaterra, Spain Unitat d’hemodin` amica card`ıaca hospital universitari Germans Trias i Pujol Badalona, Spain

Abstract. Intravascular Ultrasound (IVUS) is an image-guiding technique for cardiovascular diagnostic, providing cross-sectional images of vessels. During the acquisition, the catheter is pulled back (pullback) at a constant speed in order to acquire spatially subsequent images of the artery. However, during this procedure, the heart twist produces a swinging fluctuation of the probe position along the vessel axis. In this paper we propose a real-time gating algorithm based on the analysis of motion blur variations during the IVUS sequence. Quantitative tests performed on an in-vitro ground truth data base shown that our method is superior to state of the art algorithms both in computational speed and accuracy.

1

Introduction

Intravascular Ultrasound is a catheter-based invasive diagnostic procedure used intraoperatively to assess cardiovascular diseases. The ultrasound probe is placed at the tip of the catheter and, while rotating on its axis, it emits and receives ultrasound pulses, successively reconstructed in radially distributed A-lines. The envelope detection of acquired radio frequency signals allows the reconstruction of cross-sectional images of the artery. During the acquisition, the catheter is pulled back at a constant speed in order to acquire spatially subsequent images of the artery. However, during this procedure, the heart twisting produces artificial fluctuations of the probe position along the vessel axis (swinging effect). Moreover, due to the heart cyclic contraction/expansion, an apparent rotation with respect to the catheter axis and in-plane translation can be observed. The image visualization and automatic analysis, e.g. volumetric lumen segmentation and/or volumetric plaque characterization of IVUS pullbacks require a pre-processing motion compensation [1,2]. Given the intraoperative nature of IVUS imaging and the need of instantaneous diagnosis of the patient conditions, the motion compensation cannot be computed off-line and the computational cost of the gating algorithm must be very low. The combined effect of the three T. Jiang et al. (Eds.): MICCAI 2010, Part II, LNCS 6362, pp. 59–67, 2010. c Springer-Verlag Berlin Heidelberg 2010 

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movements can be reduced by image-based gating algorithms [3,4,5] i.e. by extracting the most stable frames from the pullback sequence. Such techniques are composed by two parts: 1 - the extraction of a signal (1D or 2D) correlated with the cardiac phase; 2 - the selection of stable frames based on the previously extracted signal. The method in [3] extracts two signals based on two different principles; they conclude that the more reliable is based on the computation of the Absolute Intensity Difference (AID) applied to subsequent frames of a circular ROI centered in the middle of the short-axis image. The method in [4] computes a Dissimilarity Matrix based on the Normalized Cross Correlation (NCC) between couples of frames; subsequently a dynamic programming algorithm finds optimal gating frames. In [5], the method by O’Malley et. al. [4] is modified using a textural descriptor for each frames and computes the dissimilarity matrix in a faster and robust way; moreover, the dynamic programming algorithm has been substituted by a local minima search in a 1D signal obtained from the dissimilarity matrix. It is important to stress that the quality of an image-based gating algorithm strongly depends on the ability of the method to extract a signal (1D or 2D) correlated with the actual vessel oscillation. In this paper, we present a novel and real-time image-based gating method that exploits motion blur variations during the cardiac cycle in coronary artery pullbacks. Up to now, the experiments to validate image-gating techniques are questionable. The ECG signal used in the validation of [4] has been demonstrated to be a suboptimal descriptor of the relative oscillations between the catheter tip and the coronary artery [6]. In [5] the authors propose an indirect methodology to assess the smoothness of the reconstructed sequence. In this paper a reliable validation of the technique is obtained by designing a novel ad-hoc in-vitro experiment in which ground-truth data was generated using an oscillating mechanical device. The performance of our algorithm is compared against the other state-of-the-art methods using such reference data.

2

Method

Image gating algorithms consist of two stages: the extraction of a 1D or 2D signal correlating with the cardiac cycle and the identification of the signal’s instants corresponding to the most stable cardiac frames. 2.1

Cardiac Signal Extraction

The proposed cardiac signal extraction is based on the idea that, provided a high frame rate acquisition equipment, every tissue displacement causes, in the image being captured, a motion blur proportional to the speed of the tissue movement. We propose a motion blur intensity estimator B(I) computed as minus the average of the absolute value of vertical derivative over the polar IVUS image:    δI(r, θ)    (1) B(I) = −E  δr 

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where r is the radial position and θ is the angle of the probe during the image scan. The estimation is averaged (expected value E) over all the image A-lines in order to reduce outliers effect. In order to illustrate the suitability of the proposed estimator, we simulate increasing motion blur effect in a set of in-vivo IVUS image. Such phenomenon can be modeled by a convolution between the non-degraded image with a set of linear point spread functions (PSFs) with increasing length. This causes a blurring of the image, and thus the reduction of edge sharpness [7] [8]. Figure 1 shows the plot of the estimator B over the length of the simulated motion blur PSF. Since the actual PSF in clinical images is unknown, each PSF has been rotated in steps of 10◦ . This resulted in a set of curves exhibiting similar trends. The relationship between B and the PSF length is monotonically non decreasing and thus suitable to compute comparison between different frames. In order to obtain the variation of the motion blur during the sequence, we apply equation (1) to all the images in the sequence obtaining a signal B(It ), where t is the temporal variable, as depicted in Figure 2 (a). It is important to highlight that changes in the vessel structures, e.g. plaques, bifurcations, etc., modify the image texture thus influencing the signal B(It ), as it can be seen in Figure 2 (a). Since the pullback speed is significantly lower than the speed of the oscillation [4], we can separate the oscillatory part of the signal B(It ) from the changes in the vessel structure. This has been done by applying a Butterworth high-pass filter (order = 10) with cut-off at 0.5Hz, obtaining the signal BHP (It ). An oscillation below 0.5Hz is below 30 beat per minute (BPM) and thus it cannot be related to phenomena induced by heart beating. Figure 2 (b) shows the high-pass filtered version of the signal B(It ); periodic local minima, spaced about 1 second to the other, can be easily identified (see Figure 2 (c)). This repeating pattern has a frequency of 1.02 ± 0.0¯6Hz which is in agreement with the ECG captured during the pullback (1.13Hz). The peak at about 1 Hz and the harmonics at multiple frequencies in Figure 2 (d) confirm the periodic nature of the signal. A possible explanation of the sharp periodical variations (from local minima to local maxima) in the BH P (It ) signal can be drawn from the physiology of the cardiac cycle. The systolic phase is composed by the iso-volumetric contraction followed by the blood ejection from the left chamber. During the iso-volumetric contraction the pressure increases until the

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ventricle pressure exceeds the aortic pressure, causing the abrupt opening of the aortic valve. This causes the sudden heart motion due to the rapid ejection of the blood, reflecting to a motion that can be captured by the proposed motion blur estimator. 2.2

Gating

Once the motion blur signal BHF (It ) is computed, the stable frames in an arterial IVUS sequence must be reliably identified. Unfortunately not all the local minima corresponds to stable frames, so noise artifacts must be discarded. As it can be noticed in Figure 2 (c), the local minima corresponding to a stable frame are immediately followed by a local maximum. Exploiting this fact, we propose a method that selects a set of stable frame candidates among the local minima of BHF (It ). A local minimum is retained as candidate if it is immediately followed by a local maximum which satisfy a zero-crossing criteria. The list of candidates is further refined by removing cases in which the gradient between the couple of minimum-maximum is lower than a certain threshold T . T is computed such that it separates the gradient distribution in two distinct modes.

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63

Results

In this section, the proposed image-gating algorithm is quantitatively validated, and its performance are compared against the state-of-the-art methods. Reliable ground-truth data was obtained by designing a novel ad-hoc experiment. 3.1

In vitro Experiment

A mechanical device simulating the periodical heart movements has been designed in order to generate reliable ground-truth data. Figure 3 shows the mechanical device and its power supply. The apparatus is composed by a rotating eccentric wheel connected to a transversal arm generating horizontal swinging oscillations. The amplitude of the oscillation ΔL can be tuned using a regulating knob from 1 to 5 mm, in steps of 1 mm. The oscillation speed can be controlled setting the power supply voltage V , following the equation F [BP M ] = 4.1912 [BP M/V olts] V [V olts]. The catheter guide is connected to the oscillating arm. A total of 21 pullbacks from three post-mortem arteries have been acquired at 30 f rame/s using a Galaxy II IVUS Imaging System (Boston Scientific) and a catheter Atlantis SR Pro 40 MHz (Boston Scientific). For each artery 7 pullbacks have been recorded varying the mechanical device parameters (ΔL = {1, 2, 3, 4} mm, F = 60 [BPM] and ΔL = 3 mm, F = {50, 60, 70, 80} [BPM]). Each sequence contains 1000 frames, of 33.3 s duration. It is worth to note that the maximal frequency resolution using a 30 f rame/s acquisition setup is of 0.0¯ 6 Hz (4 BPM) and that the methodological incertitude induced by the power supply, (approximately ±0.5 V), produces a methodological error in the oscillation frequency of ±2 [BPM]. Such uncertainties must be accounted in the method evaluation. The sequences are available for research purpose and can be obtained under request.

Fig. 3. Picture of the ad-hoc oscillating device and its power supply

3.2

Quantitative Evaluation

To quantitatively and fairly assess the performance of each image gating methods, we designed a measure that is robust to the methodological uncertainties.

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For every sequence the nominal oscillation frequency fN is known. Thus, we introduce the Signal to Noise Ratio (in dB) defined as follows:  SN RdB = 20 log

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Fig. 6. Longitudinal cut of an input IVUS sequence and the reconstructed longitudinal cuts obtained using different image-based gating algorithms

where S(ξ) is the Fourier transform of the signal s(t) produced by a given algorithm; H is a frequency filter designed to filter out the frequencies that are not related with the nominal one (fN ). Hence, the numerator of equation (2) represents the energy of the signal, related to the nominal frequency fN , while the denominator corresponds to the energy of the signal not related with the oscillation, i.e. the noise of the signal. In such way, the higher is the SNR, the better the image-gating technique extracts the oscillatory component from the image sequence. The filter H(ξ) is designed as follows:   (ξ − nfN )2 HfN (ξ) = exp − 2 2σM n=1 M 

(3)

An example of |S(ξ)| and the filter HfN (ξ), are shown in figure 4 in solid and dashed lines respectively. Since the catheter can bend inside the artery, the catheter tip oscillation is not perfectly sinusoidal. To account for this mechanical limitation, the filter of equation (3) includes higher harmonics. Using the defined SNR measure, we tested the methods in [3] (AID method), [4] (OM algorithm) and [5] (GA) compared with our technique (MOT). Figure 5 (a-c) shows the results on three different post-mortem arteries. As it can be notice, the proposed method outperforms other methods in all three arteries. However, for the artery in figure 5 (b), the dispersion of AID and MOT is large. The ANOVA test confirmed that the results of our method are statistically significant with respect to AID for the first two arteries, while it is not for the third one. Figure 5 (d) shows the average computational time, for a 1000 frame sequence, in

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seconds. The computational time of our method is of the same order of the fastest algorithm (AID) as it can be seen in figure 5 (d). 3.3

Qualitative In-vitro Evaluation

A qualitative comparison of the image-gating methods is illustrated in figure 6, showing a longitudinal cut of an IVUS sequence and the resulting longitudinal cuts obtained using the four gating algorithms. The input longitudinal cut has been obtained from a sequence of the proposed ground-truth data; its appearance is very similar to in-vivo acquired sequences, showing the typical saw-tooth shaped artifact. It can be noticed that the result of OM and GA are very similar since GA is an improvement of OM. In this sequence, the difference between AID and MOT is not easily noticeable, while their superior performance with respect to OM and GA is evident, especially observing the arterial tissue sharpness.

4

Conclusion

In this paper we proposed a real-time gating algorithm based on the analysis of motion blur variations during the IVUS sequence. For the first time in literature, a reliable validation of image-based gating techniques is performed. The algorithm have been tested on ground-truth data generated by an ad-hoc oscillating mechanical device. The proposed method outperforms the other state-of-the-art algorithms both in SNR and computational complexity. Future work will be addressed to an extensive validation of the method with several post-mortem arteries.

Acknowledgments This work was supported in part by the research projects TIN2009-14404-C0202, FIS PI061290 y CSD2007-00018. The work of C. Gatta and S. Balocco is supported by the Catalan Agency for Administration of University and Research (AGAUR) under a Beatriu de Pinos Fellowship.

References 1. Arbab-Zadeh, A., DeMaria, A.N., Penny, W., Russo, R., Kimura, B., Bhargava, V.: Axial movement of the intravascular ultrasound probe during the cardiac cycle: Implications for three-dimensional reconstruction and measurements of coronary dimensions. American Heart Journal 138, 865–872 (1999) 2. Bruining, N., von Birgelen, C., de Feyter, P.J., Ligthart, J., Li, W., Serruys, P.W., Roelandt, J.: Ecg-ated versus nongated three-dimensional intracoronary ultrasound analysis: Implications for volumetric measurements. Catheterization and Cardiovascular Diagnosis 43, 254–260 (1998) 3. Zhu, H., Oakeson, K.D., Friedman, M.H.: Retrieval of cardiac phase from IVUS sequences. In: Medical Imaging 2003: Ultrasonic Imaging and Signal Processing, vol. 5035, pp. 135–146 (2003)

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4. O’Malley, S.M., Granada, J.F., Carlier, S., Naghavi, M., Kakadiaris, I.A.: Imagebased gating of intravascular ultrasound pullback sequences. IEEE Transactions on Information Technology in Biomedicine 12(3), 299–306 (2008) 5. Gatta, C., Pujol, O., Leor, O.R., Ferre, J.M., Radeva, P.: Robust image-based ivus pullbacks gating. Med. Image Comput. Assist. Interv. Int. 11(Pt 2), 518–525 (2008) 6. O’Malley, S.M., Carlier, S.G., Naghavi, M., Kakadiaris, I.A.: Image-based frame gating of IVUS pullbacks: A surrogate for ecg. In: Proc. IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2007, April 15-20, vol. 1, pp. I-433–I-436 (2007) 7. Yitzhaky, Y., Kopeika, N.S.: Identification of blur parameters from motion blurred images. Graphical Models and Image Processing 59(5), 310–320 (1997) 8. Dai, S., Wu, Y.: Motion from blur. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2008, pp. 1–8 (June 2008)

Registration of a Statistical Shape Model of the Lumbar Spine to 3D Ultrasound Images Siavash Khallaghi1, Parvin Mousavi1 , Ren Hui Gong1 , Sean Gill1 , Jonathan Boisvert2, Gabor Fichtinger1 , David Pichora3, Dan Borschneck3, and Purang Abolmaesumi4 1

Queen’s University, Kingston, ON, Canada National Research Council, Ottawa, ON, Canada 3 Kingston General Hospital, ON, Canada University of British Columbia, Vancouver, BC, Canada [email protected] 2

4

Abstract. Motivation: Spinal needle injections are technically demanding procedures. The use of ultrasound image guidance without prior CT and MR imagery promises to improve the efficacy and safety of these procedures in an affordable manner. Methodology: We propose to create a statistical shape model of the lumbar spine and warp this atlas to patient-specific ultrasound images during the needle placement procedure. From CT image volumes of 35 patients, statistical shape model of the L3 vertebra is built, including mean shape and main modes of variation. This shape model is registered to the ultrasound data by simultaneously optimizing the parameters of the model and its relative pose. Ground-truth data was established by printing 3D anatomical models of 3 patients using a rapid prototyping. CT and ultrasound data of these models were registered using fiducial markers. Results: Pairwise registration of the statistical shape model and 3D ultrasound images led to a mean target registration error of 3.4 mm, while 81% of all cases yielded clinically acceptable accuracy below the 3.5 mm threshold.

1

Introduction

Spinal needle injection is widely applied in analgetic and diagnostic purposes [1]. In the management of back pain, epidural anesthesia, facet joint injections and nerve blocks are common forms of these interventions, performed in great numbers in hospitals and radiology clinics. Back pain is the second most common reason for a visit to the physician. In the United States alone, approximately 90% of adults will experience back pain at some point in their life. Nearly 50% of the current working population has reported some history of back pain; this is the leading cause for missed work time and seriously degrades on-the-job performance [2]. In back pain management, accessing the lumbar epidural space presents major difficulties. The success rate of proper needle insertion is a dismal 60% after 10 attempts [3] when no guidance is used, clearly an inadequate practice. Contemporary radiological needle guidance with CT and fluoroscopy T. Jiang et al. (Eds.): MICCAI 2010, Part II, LNCS 6362, pp. 68–75, 2010. c Springer-Verlag Berlin Heidelberg 2010 

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requires specialized facilities often unavailable to patients living in rural areas, and involve X-ray radiation. In search of a more accessible, portable, and nontoxic imaging alternative, ultrasound guidance has been considered. Watson et al. [4] and Klocke et al. [5] targeted the L3-L4 and L2-L3 interspace, a challenging procedure that, if performed inaccurately, damages the spinal cord. The results suggested that ultrasound as a solo guidance is inadequate. To address this issue, combination of ultrasound with CT has been proposed [6,7,8]. In these studies, the auxiliary information is necessary for guidance, but as stated above, either unobtainable or involves ionizing radiation. Hence, the use of statistical shape models is a logical alternative. Previously in the literature, statistical shape models (or atlases) have been considered as an alternative to pre-operative CT scans [9,10,11]. These atlases are generally divided into two main categories: those that describe the outline of objects (geometrical atlases) [9,10,11,12,13] and those that contain both the geometrical and internal density distribution of the object (volumetric atlases) [14,15,16]. As an example of geometrical atlases, [17] captures the variations in pose of each vertebra and builds a model for the curvature of the spine. The feasibility of ultrasound registration to a statistical atlas of femur has been previously investigated [18]. In [12] a geometrical atlas to ultrasound registration of the pelvis is performed. While geometrical atlases are computationally less expensive, they are prone to bone surface segmentation errors in ultrasound data. Our contribution is the first report of a volumetric vertebral atlas and its registration to 3D ultrasound without prior segmentation. We demonstrate a feasibility study on the L3 vertebrae, one of the most problematic anatomical sites in spinal pain management. In departure from the prior art using tetrahedral mesh and Bernstein polynomials [13], we employ a simple but generic approach based on the B-spline deformable transformation that allows for straightforward extension for an ensemble of vertebrae and relevant structures [14,15,16].

2 2.1

Method Construction of the Statistical Shape Model

Figure 1 demonstrates the atlas model construction process. A set of CT images, acquired from 38 patients (19 male and 19 female), was used in this study. Data was collected under the approval of the research ethics board, and the patients involved provided informed consent for this data to be used in the research. Using ITK-Snap, the L3 vertebra was semi-automatically segmented from the CT volumes (each containing 120 × 200 × 100 voxels with an isotropic spacing of 0.6 mm). The patient data was divided into two groups: 35 for constructing the atlas (hereafter referred to as training data), and 3 for validation (two male and one female). One of the CT volumes for atlas construction was chosen as the template It . Each training example, Ik , is registered to the template by a rigid registration followed by a B-spline deformable registration, such that k k (Trigid (Ik )) , where T(.) denotes a transform. B-spline registration is It ≈ Tdef performed in a 40 × 30 × 30 grid using Mattes Mutual Information metric. To

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Fig. 1. Outline of the atlas construction method from a set of CT images

reduce the deformable registration time, a three stage multi-resolution approach is implemented. Each deformable registration took between two and four hours on a Core 2 Quad CPU machine with 2.4 GHz speed and 3 GB of RAM. With the deformable transform of all the training examples known with respect to the template, principal component analysis (PCA) is performed to construct the statistical atlas for the L3 vertebrae. After the atlas is constructed it can be used to generate new instances of the population. A new instance of the atlas, defined by the deformation vector, Dnew ¯ ,can be produced by a linear combination of the mean deformation vector, φ, atlas weights, wi , and the eigenvectors of the covariance matrix generated from all the deformation fields, vi , as follows: Dnew

= φ¯ +

N 

wi vi

(1)

i=1

2.2

Statistical Atlas to Ultrasound Registration

The registration framework is shown in Figure 2. First, the mean shape of the L3 atlas is rigidly registered to the 3D ultrasound volume by simulating ultrasound images from the atlas, and performing an intra-modality registration with the 3D ultrasound images [19]. The similarity metric used is the Linear Correlation of Linear Combinations (LC2 ) [19] between the actual and the simulated ultrasound images, and is computed from the atlas volume using:  (U (x, y) − f (x, y))2 LC 2 = (2) M × V ar(U ) where f is the simulated ultrasound image, U is the actual ultrasound image and M is the number of overlapping voxels between the ultrasound and the atlas volume. We used the Covariance Matrix Adaptation Evolution Strategy (CMA-ES)

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Fig. 2. Outline of statistical atlas to ultrasound registration method

as the optimization method [20]. Following the initial rigid registration, we performed deformable registration of the atlas model to the 3D ultrasound data by simultaneously creating new instances of the atlas and updating the rigid transformation and the atlas parameters, while optimizing the LC2 similarity metric.

3 3.1

Experiments and Results Statistical Shape Model

We investigated whether the statistical shape model generated from L3 can span the space of shape variations in the patient population. For this purpose, we used a leave-one-out cross registration with the CT data. In each step, we left out one of the patient CTs for testing, created the atlas from the rest of the data, and registered the created atlas to the remaining patient CT. This process was repeated by selecting each CT data once as the testing data. Throughout the process, the template was held constant. To validate the model, we used the first 12 eigenvectors which covered 95% of the total modes of variation. The registration process used Mattes Mutual Information and deformable B-Spline registration, in conjunction with the CMA-ES optimizer to solve for the atlas model and rigid registration parameters. As in [9], the Root Mean Square (RMS) error between the closest surface points of registered atlas and the test data was used to measure the capability of the atlas to capture the deformations within the patient population. The mean error across all registrations was 0.89 mm with a standard deviation of 0.19 mm. 3.2

Registration of the Atlas to Ultrasound Images

In a second set of experiments, we aim to show how well the constructed atlas can be deformed and reoriented to match the shape and position of the patient vertebra using the acquired 3D ultrasound images. In each registration, we simultaneously optimized 12 shape and 6 rigid parameters, which correspond to the first 12 PCA eigenvectors and the pose respectively.

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Fig. 3. Transverse (left), sagittal (center), and coronal (right) slices of the original US volume overlayed with the bone contours of the misaligned (top) and registered (bottom) atlas volumes

The three excluded CT volumes from the atlas generation process (see Section 2.1) were used to construct 3D CAD models of the entire lumbar spine, including L1 to L5. These models were printed using a Cimetrix 3D shape printer (Cimetrix Solutions, Oshawa, ON, Canada). Three spine phantoms were constructed by submerging these models in an agargelatine-based tissue phantom which was designed to simulate the appearance of soft tissue in ultrasound. A high-resolution CT image (0.46 × 0.46 × 0.625 mm) and an ultrasound volume were acquired from each phantom. The ultrasound volume was reconstructed from a freehand sweep with an L14-5/38 linear-array transducer (Ultrasonix, Richmond, BC, Canada) operating at 6.6 MHz with an imaging depth of 5.5 cm. The probe was tracked using an Optotrack Certus System (Northern Digital Inc., Waterloo, ON, Canada) and calibrated using an N-wire phantom [21]. The phantom CT and ultrasound volumes were aligned using fiducial markers mounted on the exterior of the phantom box. The position of these fiducials in the ultrasound coordinate system was identified using a calibrated stylus pointer. The atlas mean shape and the ultrasound volumes were brought to an initial position by rigidly registering the mean shape to the corresponding phantom CT volume. For each phantom, thirty experiments were performed with perturbing the mean shape using a transformation generated from a uniform random distribution in the interval of [0,10] mm translation along each axis and [0-10]◦ rotation about each axis. The registration parameters were then optimized as it was discussed in Section 2.2.

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(a)

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(b)

Fig. 4. (a) Sagittal, and (b) coronal views of the registered L3 atlas to the 3D ultrasound volume. The five red circles illustrate the landmark positions.

To evaluate the accuracy of the registration, two expert orthopedic surgeons were asked to identify five corresponding landmarks, three on the spinous process and two on the target facet joints shown in Figure 4(b), on the registered atlas, the ultrasound volume and the corresponding CT. The average distance of these five landmarks was chosen as a measure of the final Target Registration Error (TRE). A registration was considered failed if the final TRE is more than 3.5 mm, as the clinically accepted error. Registration results are shown in Table 1 and an example of the initial misalignment and the registration result is depicted in Figure 3. Figure 4 shows an overlay of the registered atlas with the ultrasound volume. As seen in Table 1, the average TRE is less than 3.5 mm with success rate of 81% for all three phantoms. Our preliminary results for the registration of atlases created from L2 and L4, the neighboring vertebrae to L3, to 3D ultrasound volumes, with the same patient data set, have shown TRE below 3.2 mm based on five landmarks per vertebrae. The registration results satisfy clinical requirements for facet joint injection. They also demonstrate the feasibility of using volumetric atlases for the registration of a patient spine to 3D ultrasound data. This can enable the use of ultrasound image guidance for spinal interventions without prior CT, to improve the efficacy of these procedures in an affordable manner. On going research is aimed at addressing several goals: i) Run time; currently, a single registration of the atlas model to ultrasound data, implemented in unoptimized C++ code, takes in the order of hours on a 2.3 GHz, 16-core Pentium machine with 16 GB of RAM. Future efforts will focus on speeding up the computation, specifically by implementing the algorithm on graphics processing units (GPUs). Recently released open-source software for GPU implementation of Bspline interpolation and registration will facilitate achieving this goal; ii) Atlas generation bias; the current atlas generation process is potentially biased towards the chosen template. An alternative would be to use groupwise atlas generation methods that have become widely popular recently, especially in neuroimaging

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Table 1. Registration results for the atlas to US registration. SR (Success Rate) is defined as the ratio of the registrations where the overall TRE is less than 3.5 mm. SR is presented for each phantom with the maximum initial misalignment of 10 mm.

Phantom Mean Landmark Error mm 1 3.38 2 3.48 3 3.25

Std SR mm % 0.42 81% 0.33 79% 0.45 82%

research; iii) Spine registration; at the moment, the method only registers the atlas of a single vertebra to 3D ultrasound volumes. Registration of an atlas of the entire (or partial) spine with the ultrasound data would provide better contextual information to the physician for intervention.

References 1. An, H.S.: Percutaneous procedures in the lumbar spine. In: Principles and Techniques of Spine Surgery. Lippincott Williams & Wilkins (1998) 2. Allen, H., Hubbard, D., Sullivan, S.: The burden of pain on employee health and productivity at a major provider of business services. Journal of Occupational and Environmental Medicine 47(7), 658–670 (2005) 3. Watts, R.: A five-year prospective analysis of the efficacy, safety and morbidity of epidural anaesthesia performed by a general practitioner anaesthetist in an isolated rural hospital. Anaesth Intensive Care 20(3), 348–353 (1992) 4. Watson, M.J., Evans, S., Thorp, J.M.: Could ultrasonography be used by an anaesthetist to identify a specified lumbar interspace before spinal anaesthesia? British Journal of Anaesthesia 90(4), 509–511 (2003) 5. Klocke, R., Jenkinson, T., Glew, D.: Sonographically guided caudal epidural steroid injections. Journal of Ultrasound in Medicine 22(11), 1229–1232 (2003) 6. Moore, J., Clarke, C., Bainbridge, D., Wedlake, C., Wiles, A., Pace, D., Peters, T.: Image Guidance for Spinal Facet Injections Using Tracked Ultrasound. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5761, pp. 516–523. Springer, Heidelberg (2009) 7. Winter, S., Brendel, B., Pechlivanis, I., Schmieder, K., Igel, C.: Registration of CT and intraoperative 3-D ultrasound images of the spine using evolutionary and gradient-based methods. IEEE Transactions on Evolutionary Computation 12(3), 284–296 (2008) 8. Gill, S., Mousavi, P., Fichtinger, G., Chen, E., Boisvert, J., Pichora, D., Abolmaesumi, P.: Biomechanically Constrained Groupwise US to CT Registration of the Lumbar Spine. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5762, pp. 803–810. Springer, Heidelberg (2009) 9. Tang, T.S., Ellis, R.E.: 2D/3D Deformable Registration Using a Hybrid Atlas. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 223–230. Springer, Heidelberg (2005)

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10. Hu, Y., Ahmed, H.U., Allen, C., Pendse, D., Sahu, M., Emberton, M., Hawkes, D., Barratt, D.: MR to Ultrasound Image Registration for Guiding Prostate Biopsy and Interventions. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5761, pp. 787–794. Springer, Heidelberg (2009) 11. Michopoulo, S.K., Costaridou, L., Panagiotopulous, E., Speller, R., Panayiotakis, G., Todd-Pokropek, A.: Atlas-Based Segmentation of Degenerated Lumbar Interverbal Discs from MR Images of the Spine. IEEE Transactions on Biomedical Engineering 56(9), 2225–2231 (2009) 12. Foroughi, P., Song, D., Chintapani, G., Taylor, R.H., Fichtinger, G.: Localization of Pelvic Anatomical Coordinate System Using US/Atlas Registration for Total Hip Replacement. In: Metaxas, D., Axel, L., Fichtinger, G., Sz´ekely, G. (eds.) MICCAI 2008, Part II. LNCS, vol. 5242, pp. 871–878. Springer, Heidelberg (2008) 13. Sadowsky, O., Cohen, J.D., Taylor, R.H.: Rendering Tetrahedral Meshes with Higher-Order Attenuation Functions for Digital Radiograph Reconstruction. In: IEEE Visualization, pp. 303–310 (2005) 14. Barratt, D.C., Chan, C.S.K., Edwards, P.J., Penney, G.P., Slomczykowski, M., Carter, T.J., Hawkes, D.J.: Instantiation and Registration of Statistical Shape Models of the Femur and Pelvis Using 3D Ultrasound Imaging. Medical Image Analysis 12(3), 358–374 (2008) 15. Gong, R.H., Stewart, J., Abolmaesumi, P.: Reduction of Multi-Fragment Fractures of the Distal Radius Using Atlas-based 2D/3D Registration. In: Proceedings of the SPIE, Medical Imaging 2009: Visualization, Image-Guided Procedures, and Modeling, vol. 7261, pp. 726137-1–726137-9 (2009) 16. Jurcak, V., Fripp, J., Engstrom, C., Walker, D., Salvado, O., Ourselin, S., Crozier, S.: Atlas Based Automated Segmentation of the Quadratus Lumborum Muscle Using Non-Rigid Registration on Magnetic Resonance Images of the Thoracolumbar Region. In: 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp. 113–116 (2008) 17. Boisvert, J., Cheriet, F., Pennec, X., Labelle, H., Ayache, N.: Geometric Variability of the Scoliotic Spine Using Statistics on Articulated Shape Models. IEEE Transactions on Biomedical Engineering 27(4), 557–568 (2008) 18. Talib, H., Rajamani, K., Kowal, J., Nolte, L.P., Styner, M., Ballester, M.A.G.: A Comparison Study Assessing the Fesibility of Ultrasound-Initialized Deformable Bone Models. Computer Aided Surgery 10(5/6), 293–299 (2005) 19. Wein, W., Brunke, S., Khamene, A., Callstrom, M.R., Navab, N.: Automatic CTultrasound registration for diagnostic imaging and image-guided intervention. Medical Image Analysis 12(5), 577–585 (2008) 20. Hansen, N., M¨ uller, S.D., Koumoutsakos, P.: Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation. Evolutionary Computation 11(1), 1–18 (2003) 21. Chen, T.K., Thurstonlow, A.D., Ellis, R.E., Abolmaesumi, P.: A real-time freehand ultrasound calibration system with automatic accuracy feedback and control. Ultrasound in Medicine & Biology 1(1), 79–93 (2009)

Automatic Prostate Segmentation Using Fused Ultrasound B-Mode and Elastography Images S. Sara Mahdavi1 , Mehdi Moradi1 , William J. Morris2, and Septimiu E. Salcudean1 1

2

Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, Canada {saram,moradi,tims}@ece.ubc.ca Vancouver Cancer Center, British Columbia Cancer Agency, Vancouver, Canada [email protected]

Abstract. In this paper we propose a fully automatic 2D prostate segmentation algorithm using fused ultrasound (US) and elastography images. We show that the addition of information from mechanical tissue properties acquired from elastography to acoustic information from Bmode ultrasound, can improve segmentation results. Gray level edge similarity and edge continuity in both US and elastography images deform an Active Shape Model. Comparison of automatic and manual contours on 107 transverse images of the prostate show a mean absolute error of 2.6 ± 0.9 mm and a running time of 17.9 ± 12.2 s. These results show that the combination of the high contrast elastography images with the more detailed but low contrast US images can lead to very promising results for developing an automatic 3D segmentation algorithm.

1

Introduction

Low dose rate (LDR) prostate brachytherapy is a common method for treating patients with low risk prostate cancer. In this treatment, 40-100 small radioactive seeds are permanently inserted in the prostate and its periphery. Treatment planning and delivery relies on transrectal ultrasound (TRUS) imaging. In order to create the treatment plan, a pre-operative volume study is carried out in which a set of transverse ultrasound images are collected. These images are then manually segmented to extract the prostate boundaries. A plan is devised to deliver sufficiently high radiation dose to the cancerous tissue while maintaining a tolerable dose to healthy tissue. Reliable segmentation and visualization of the prostate is a vital step in dose planning. Manual segmentation is time consuming and, due to the low signal to noise ratio of ultrasound images, inter and intraobserver variabilities are high. Even though various 2D prostate segmentation methods and some 3D methods have been proposed in the literature [1,2,3,4,5], the effective automatic segmentation of ultrasound images of the prostate has remaining challenges such as user initialization and limited accuracy. In this paper, we propose a prostate segmentation method based on intramodality fusion of ultrasound B-mode and elastography. Elastography [6], in T. Jiang et al. (Eds.): MICCAI 2010, Part II, LNCS 6362, pp. 76–83, 2010. c Springer-Verlag Berlin Heidelberg 2010 

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which mechanical properties of tissue are characterized, has shown to be promising in improving the visibility of the prostate gland [7,8]. In a recent study, we have shown that ultrasound dynamic elastography images of the prostate have superior object-background contrast compared to B-mode ultrasound, especially at the base and apex [9]. This is due to the fact that prostate tissue is generally stiffer than the surrounding tissue. We utilize this advantage and combine elastography and US image data for 2D segmentation of the prostate. The elastography images are acquired using a system described in [9] which enables the simultaneous registered acquisition of B-mode and elastography images, thereby eliminating the concerns about image registration and cost. We use an Active Shape Model (ASM) [10] approach which starts with an initial shape extracted from a large number of elastography and B-mode prostate images. The deformation of this initial shape is restricted to conform to the statistical model and is guided by edge detection from both elastography and B-mode images based on edge gradient similarity and continuity. The use of a statistically created model ensures the compliance of the resulting contours with the overall shape of the organ. Additionally, the restricted deformation results in robustness to poor image quality. The use of a measure of edge continuity [9] in addition to gradient similarity, reduces the effects of strong speckle-induced local edges on the algorithm which improves the rate of convergence. We provide a statistical analysis of the accuracy of our 2D image segmentation method and show that the combined use of elastography and B-mode images improves the accuracy and the convergence rate. Further, we describe a preliminary framework for extending the proposed method to an automatic 3D segmentation algorithm and present an example.

2

Methods

The US and elastography images used in this paper were acquired from patients going through the standard LDR prostate brachytherapy procedure at Vancouver Cancer Center, BC Cancer Agency. Intra-operatively, prior to the procedure, RF data and US images were simultaneously collected using the system described in [9]. In this system RF data is collected at approximately 40 fps from the sagittal array of a vibrating (amplitude 0.5-2 mm, frequency range 210 Hz) and rotating (−45◦ to 50◦ ) TRUS probe (dual-plane linear/microconvex broadband 5 - 9 MHz endorectal transducer, Ultrasonix Medical Corp.). The RF data were processed [11] to obtain sagittal elastography strain images from which conventional transverse images of the prostate were achieved. Our 2D segmentation approach combines the information from elastography and US images within an Active Shape Model (ASM) which deforms based on gray level similarity and edge continuity. We follow the approach from [10]. First, we construct a training set by manually selecting 30 specific points on the prostate boundary in N = 25 mid-gland images from 7 patients. The set of images used for creating the training set does not include the images to be segmented. The manually segmented contours are aligned by using least-squaresbased iterative scaling, rotation and translation and the average of the resulting

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contours, x ¯, is used as the initial contour. Then, in order to capture the statistics N of the training set, we calculate the covariance matrix, S = i=1 dxi dxTi , where dxi in the training phase is the distance between each point on the manual contour and the corresponding point on the mean shape. The modes of variation of the shape are described by the eigenvalues, λi , and eigenvectors, pi , of S, from which the t largest eigenvalues are selected as the most  significant modes of variation. We selected t such that for i = 1, · · · , t, λi / λ > 5%. A shape instance consistent with the training set can thus be created using Eq.(1): x=x ¯ + Pb

(1) T

where P = (p1 · · · pt ) is the matrix of the first t eigenvectors and b = (b1 · · · bt ) is a vector of weights. Hence, in the shape fitting phase, given a shape deformation, dx, the shape parameter adjustments, db, can be calculated using Eq.(2). db = P T dx

(2)

To calculate the movement, dxi , for each model point i, a measure of edge gray level similarity was used in [10]. For each point i of each image j of the training set, a normalized edge derivative profile, gij normal to the boundary, centered at the model point and of length np is extracted. gij is averaged over all images from which the covariance matrix Sgi is calculated to obtain a statistical description of the gray level appearance for every point. During the shape fitting, at each iteration and for every point, sample edge derivative profiles hi (d) of distance d (d = −l, · · · , l) from the boundary point and length np are extracted in a similar manner. The square of the Mahalanobis distance of these profiles from the model profile, gi , give a measure of edge gray level similarity. For each point, the d resulting in the least Mahalanobis distance suggests the required point movement along a line normal to the boundary. The physical values of l and np are set to 8 and 5 mm, respectively. In our data set, we observed that the gray level edge similarity measure alone, gives many false positives due to ultrasound speckle or sharp edge-like structures since only 1D information (normal to the edge) is being analyzed. Therefore, in our approach, we incorporate our edge continuity measure [9] which measures the continuity of the edge in a direction orthogonal to the edge profile. At a distance d from each point, we compute the average normalized cross-correlation, ci (d), between the edge intensity profile ei (d) (obtained similar to gij ), of length np , with its two neighboring left and right edge intensity profiles. For a continuous edge (i.e. large similarity between ei (d) and its left and right neighboring profiles), ci (d) should have a shape similar to a Gaussian function with a large peak and a small standard deviation. We define the edge continuity measure, Ki (d) = Pc2i /σi (d) in which Pci characterizes the peak and σi is the standard deviation of a Gaussian function fitted to ci (d). For each point, the d resulting in the maximum continuity measure suggests the required point movement along a line normal to the boundary. We define un to be the vector normal to the boundary at the boundary point, dgE , to be the distance from the boundary point suggested by the gray level

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similarity, and dKUS , and dKE to be the distances from the boundary point computed from the edge continuity measures in US and elastography images, respectively. Based on the above equations, at each iteration, k, the following steps are performed to deform the current shape points, xcurrent into the next shape, xnext . 1. Find the required shape deformation: dx = xnext − xcurrent = df un df = α1 dgE + α2 dKU S + α3 dKE 2. Calculate the optimum pose parameters: scaling, translation and rotation, corresponding to dx, apply this transformation to obtain T (xcurrent). Adjusting the pose is required to align xcurrent to be as close as possible to xnext before adjusting the shape [10]. 3. Calculate db = P T (xnext − T (xcurrent))

α = [α1 α2 α3 ] are corresponding weights. Due to the large amount of noise in US images, gray level similarity matching in these images does not improve results but degrades convergence, and therefore, it is not included. Our criteria for convergence is when 94% of the contour points have a dx of less than np /2. Fig. 1 illustrates how dgE and dKE are obtained in an elastography image. We will provide a comparison of segmentation results using gray level similarity from elastography images, combined edge continuity and gray level similarity from elastography images and finally edge continuity and gray level similarity from both elastography and US images.

Fig. 1. An illustration of how dgE (top point) and dKE (bottom point) are obtained in an elastography image. The gray level similarity measure is compared to that of the model for each corresponding point. The edge continuity measure is maximized over the line normal to the boundary. For clarity, these measures are shown on two different points, whereas they are calculated for single points.

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Results

To evaluate our 2D segmentation results we measure the mean absolute distance (MAD) and maximum distance (MaxD) between 2D automatic and manual contours. Table 1 provides the mean and standard deviations of MAD and MaxD between 107 manual and automatic contours selected from 7 patients. The results are presented separately for elastography gray level similarity only (αa =[1 0 0]), elastography gray level similarity and edge continuity (αb =[0.5 0 0.5]), and elastography gray level similarity and edge continuity plus US edge continuity (αc =[0.5 0.25 0.25]). Fig. 2 shows an example of segmentation results for the three sets of weight parameters. The most accurate segmentation results were acquired when αc =[0.5 0.25 0.25]. By using this selection of weight parameters, deformation is mainly guided by the coarser elastography images but also refined by the finer US images. It is specifically seen in the posterior region of the prostate, where elastography image quality is low, that the addition of edge continuity in US images improves segmentation results. This can be observed in Fig. 2. The choice of αc also results in the convergence of the algorithm in an average of 22 iterations vs. 37 and 98 iterations for αb and αa . The maximum number of iterations was set to 50 for αb and αc and 100 for αa . In the case of αa , 95% of the cases did not converge within 100 iterations.

Fig. 2. 2D automatic segmentation results using elastography gray level similarity (yellow dashed line), elastography edge continuity and gray level similarity (blue line), and elastography gray level similarity and edge continuity plus US edge continuity (red line) on US (left) and elastography (right) images. The manual contour is shown as a blue/white dotted line.

4

Discussion

By visual inspection of the automatic segmentation results, we observed that most of the 2D segmentation error of the mid-gland slice was in the anterior and posterior regions. In elastography images, the blood vessels which lie on the anterior of the prostate appear as stiff tissue and are not always distinguishable

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Table 1. Comparison of 2D manual and automatic segmentation showing the Mean Absolute distance (MAD) and Maximum Distance (MaxD - positive sign meaning larger automatic contour) between manual and automatic prostate contours, the number of iterations and duration of the algorithm. K: edge continuity measure, dg : gray level similarity measure.

MAD (mm) MaxD (mm) no. of iter. duration (s)

dg in elast.

dg and K in elast.

3.4 ± 1.8 1.0 ± 9.8 98 ± 13 10.7 ± 1.4

3.4 ± 1.7 −6.5 ± 7.0 37 ± 17 17.3 ± 0.8

dg and K in elast. and K in US 2.6 ± 0.9 −4.9 ± 4.7 22 ± 15 17.9 ± 12.2

from the prostate itself. In such cases, the automatic contour extends beyond the actual boundary. In the posterior, due to the relatively low contrast in this region, the automatic contour converges to the darker tissue inside the prostate. By including edge continuity data from US images this problem has been partially resolved. We attribute this low contrast to mainly the slippage between the protective sheath on the probe and the surface of the rectum during elastography data collection. By replacing the 1D axial strain computation with 2D axial/lateral and by increasing the resolution of elastography imaging such problems can be subsided. Our current elastography data acquisition system has the benefit of collecting inherently registered elastography and US data. Currently the TRUS rotation range is within ±50◦ which may result in missing data in the mid-lateral regions of large prostates. Also, the quality of the B-mode US images acquired along with the elastography data is affected by the computational limitations of the real-time data acquisition system and the ultrasound machine. We are currently working on resolving these problems to improve segmentation results. The proposed 2D prostate segmentation method using fused elastography and US image information can be extended into 3D by modifying the method that we proposed in [12] which was based on fitting an a priori shape to a set of parallel transverse ultrasound images. The algorithm was initialized by the user manually selecting some initial boundary points on the mid-slice. These points were used to un-warp and un-taper all images resulting in a set of elliptical prostate shapes. With the aid of the Interacting Multiple Model Probabilistic Data Association (IMMPDA) [13] edge detector and ellipse fitting, a tapered ellipsoid was fitted to all contours which was then sliced at image depths. The resulting 2D contours were reversely tapered and warped to match the initial images. We showed [12] that the method is fast, and produces smooth contours that are in agreement with the brachytherapy requirements. However, the need for manual initialization limits its use for real-time applications and makes it user dependent. Also, the poor visibility of the boundary at the base and apex complicates segmentation of these regions.

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Fig. 3. An example of 3D surface of the prostate created manually (red) and by the automatic algorithm (blue)

To resolve these issues we replace the manual initialization of the 3D semiautomatic segmentation with the described 2D segmentation. Additionally, we employ elastography along with US images for propagating the mid-gland segmentation to the rest of the images. This is done by including an additional IMMPDA edge detection on the coarser elastography images to guide the edge detection on the finer US images. The described framework for automatic 3D prostate segmentation was applied to one patient data set. Fig. 3 shows 3D surfaces created from automatic (blue) and manual (red) segmentation of the prostate for this patient. 11 images were used to construct this surface model. The volume of the manually created surface is 33.9 ml, the volume of the automatically created surface is 34.4 ml, and the volume of the non-overlapping region between the two surfaces is 4.9 ml. A thorough clinical study is required to evaluate this 3D segmentation framework.

5

Conclusions

In this paper we outlined a novel 2D method of prostate segmentation that combines ultrasound elastography imaging with B-mode data. This is the first instance of using such a combination for prostate segmentation and reinforces efforts to improve US segmentation outcomes using elastography data [14]. With the fusion of information from elastic properties of tissue provided by elastography with the acoustic properties of tissue provided by B-mode we developed an automatic and accurate segmentation of the prostate which gives good results in 2D. The automatically generated 2D contours can be used to initialize the midslice for 3D segmentation and remove user variability. Additionally, the method can be utilized to register pre and intra-operative prostate images and has the potential of improving intra-operative dosimetry. Acknowledgments. This project was funded by NSERC Canada (Discovery Grant and Postdoctoral Fellowship). Data collection was funded by NIH grant R21 CA120232-01.

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References 1. Penna, M.A., Dines, K.A., Seip, R., Carlson, R.F., Sanghvi, N.T.: Modeling prostate anatomy from multiple view TRUS images for image-guided HIFU therapy. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54(1), 52–69 (2007) 2. Tutar, I.B., Pathak, S.D., Gong, L., Cho, P.S., Wallner, K., Kim, Y.: Semiautomatic 3-D prostate segmentation from TRUS images using spherical harmonics. IEEE Trans. Med. Imaging 25(12), 1645–1654 (2006) 3. Zhan, Y., Shen, D.: Deformable segmentation of 3-D ultrasound prostate images using statistical texture matching method. IEEE Trans. Med. Imaging 25(3), 256– 272 (2006) 4. Hodge, A.C., Fenster, A., Downey, D.B., Ladak, H.M.: Prostate boundary segmentation from ultrasound images using 2D active shape models: optimization and extension to 3D. Comput. Methods Programs Biomed. 84(2-3), 99–113 (2006) 5. Shen, D., Zhan, Y., Davatzikos, C.: Segmentation of prostate boundaries from ultrasound images using statistical shape model. IEEE Trans. Med. Imaging 22(4), 539–551 (2003) 6. Ophir, J., C´epedes, I., Ponnekanti, H., Yazdi, Y., Li, X.: Elastography: a quantitative method for imaging the elasticity of biological tissues. Ultrason. Imaging 13(2), 111–134 (1991) 7. Cochlin, D.L., Ganatra, R.H., Griffiths, D.F.R.: Elastography in the detection of prostatic cancer. Clin. Radiol. 57(11), 1014–1020 (2002) 8. Souchon, R., Hervieu, V., Gelet, A., Ophir, J., Chapelon, J.: Human prostate elastography: in vitro study. In: IEEE Symposium on Ultrasonics, vol. 2, pp. 1251– 1253 (2003) 9. Mahdavi, S.S., Moradi, M., Wen, X., Morris, W.J., Salcudean, S.E.: Vibroelastography for visualization of the prostate region: method evaluation. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5762, pp. 339–347. Springer, Heidelberg (2009) 10. Cootes, T., Taylor, C., Cooper, D., Graham, J.: Active shape models-their training and application. Comput. Vis. Image Underst. 61, 38–59 (1995) 11. Zahiri-Azar, R., Salcudean, S.E.: Motion estimation in ultrasound images using time domain cross correlation with prior estimates. IEEE Trans. Biomed. Eng. 53(10), 1990–2000 (2006) 12. Mahdavi, S.S., Morris, W.J., Spadinger, I., Chng, N., Goksel, O., Salcudean, S.E.: 3D prostate segmentation in ultrasound images based on tapered and deformed ellipsoids. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5762, pp. 960–967. Springer, Heidelberg (2009) 13. Abolmaesumi, P., Sirouspour, M.R.: An interacting multiple model probabilistic data association filter for cavity boundary extraction from ultrasound images. IEEE Trans. Med. Imaging 23(6), 772–784 (2004) 14. von Lavante, E., Noble, J.A.: Segmentation of breast cancer masses in ultrasound using radio-frequency signal derived parameters and strain estimates. In: IEEE ISBI, pp. 536–539 (2008)

ODF Maxima Extraction in Spherical Harmonic Representation via Analytical Search Space Reduction Iman Aganj1, Christophe Lenglet1,2, and Guillermo Sapiro1 1

Department of Electrical and Computer Engineering, University of Minnesota, USA 2 Center for Magnetic Resonance Research, University of Minnesota, USA {iman,clenglet,guille}@umn.edu

Abstract. By revealing complex fiber structure through the orientation distribution function (ODF), q-ball imaging has recently become a popular reconstruction technique in diffusion-weighted MRI. In this paper, we propose an analytical dimension reduction approach to ODF maxima extraction. We show that by expressing the ODF, or any antipodally symmetric spherical function, in the common fourth order real and symmetric spherical harmonic basis, the maxima of the two-dimensional ODF lie on an analytically derived one-dimensional space, from which we can detect the ODF maxima. This method reduces the computational complexity of the maxima detection, without compromising the accuracy. We demonstrate the performance of our technique on both artificial and human brain data.

1 Introduction Diffusion-weighted MRI significantly extends the scope of the information obtained from MRI, from being solely spatially dependent to being defined on the spatialorientational domain. Fiber microstructure and orientation are inferred using this modality from the locally measured diffusion profile of water molecules. Diffusion tensor imaging (DTI) [1] effectively models the diffusion in single-fiber voxels as a Gaussian represented by its covariance tensor. As for more complex fiber architecture, q-ball imaging (QBI) [2]–[6] has been very successful in revealing intravoxel fiber orientations by introducing the orientation distribution function (ODF) as the probability of diffusion in a given direction. Contrary to DTI, where the principal diffusion direction can be readily computed as the major eigenvector of the diffusion tensor, QBI provides a continuous spherical function which, although clearly illustrates the major diffusion orientations as its maxima, does not directly quantify them. Diffusion directions as vectors carry less information than the ODF itself does. On the other hand, their easy interpretation and their application in tractography, e.g., [7]–[9], make the ODF maxima extraction an important post-processing step still to be carefully addressed. The number of peaks can also be interpreted as a measure of white matter complexity. In addition, unlike mixture models that calculate fiber directions by describing the diffusion signal as the sum of finite discrete unidirectional components, ODF maxima are computed without any assumptions about the existence of such components. T. Jiang et al. (Eds.): MICCAI 2010, Part II, LNCS 6362, pp. 84–91, 2010. © Springer-Verlag Berlin Heidelberg 2010

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Exhaustive search via finite difference method has been exploited in the literature as a straightforward approach to ODF maxima extraction [3,10]. This generally requires a two-dimensional (2D) discretization of the unit sphere, resulting in computational complexity that grows quadratically with the desired resolution. Numerical optimization approaches such as gradient ascent [11], Newton-Raphson techniques [12], and Powell’s method [13], have also been employed. These techniques require a guarantee of convergence and careful initialization to obtain all the maxima. Lastly, polynomial based approaches, [14]–[16], have been proposed to extract the maxima as a subset of the stationary points of the ODF. These methods exploit a transformation of the real and symmetric spherical harmonic (RSSH) basis (most efficient for ODF reconstruction [3]), to the constrained symmetric tensor or constrained homogenous polynomial bases, resulting in polynomial equations which are solved numerically. In this paper, we propose a polynomial based approach to reduce the problem of ODF maxima extraction in the fourth order RSSH basis, from a 2D search on the sphere, to a one-dimensional (1D) one on an analytically-derived curve. Compared to the 2D problem, this approach significantly reduces the computational complexity of the search for the maxima of the ODF – or any antipodally symmetric spherical function – without compromising the precision. Contrary to [14]–[16], our method works directly in the RSSH basis and does not require the extra step of transforming the RSSH coefficients to other tensor-based bases. We suggest a discretization scheme for the 1D exhaustive search, and show experimental results on both artificial and human brain data. We start Sec. 2 with a brief review of the RSSH basis, and continue by describing our mathematical derivation. Experimental results are presented in Sec. 3.

2 Methods 2.1 ODF in Real and Symmetric Spherical Harmonic Basis In this work, we use the estimator derived in [6] to compute the ODF in constant solid angle (CSA). The original definition of the QBI ODF [2] does not include the Jacobian factor , thereby creating the need for normalization and artificial sharpening. In contrast, the estimator in [6] is normalized, dimensionless, and has been shown to preserve the natural sharpness of the ODF. The spherical harmonic basis is commonly used for representing spherical functions such as the ODF, allowing for sampling in any desired direction. Orthonormal spherical harmonic functions are given by

,

2

1 4

! !

cos

,

(1)

· is the associated Legendre function, and and are standard spherical where coordinates. The assumption of the ODF being real and antipodally symmetric,

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however, makes the use of the RSSH basis [3] more suitable. RSSH functions are indexed by a single parameter 1 /2 1, corresponding to and , as follows [3]: 1

,

√2Re

0

,

0 ,

√2Im

0

(2) .

The ODF can be computed in this basis first by using a minimum square scheme to approximate the signal, and then by analytically computing the Funk-Radon transform, [2], following the method introduced in [3]–[5] for the original QBI, and subsequently adapted in [6] for the CSA-QBI. 2.2 ODF Maxima Extraction RSSH functions, being smooth, allow us to find all the local maxima of the ODF , as points satisfying the following properties (subscripts indicate partial derivatives): , , det tr with the Hessian matrix

, ,

0, 0, ,

(3) (4) (5) (6)

0, 0,

,

defined as , ,

, ,

.

(7)

Equations (3) and (4) guarantee that , is either an extremum or a saddle point of the ODF. Inequalities (5) and (6) filter out, respectively, the saddle points and the local minima (including possible negative lobes), leaving us only with the local maxima of the ODF. The above expressions can all be analytically computed for an ODF expressed in the RSSH basis. However, the main challenge is to find the points that simultaneously satisfy equations (3) and (4). Once they are identified, applying inequalities (5) and (6) to filter out undesired points is trivial. Iterative approaches (e.g., Newton method) may be applied to solve equations (3) and (4). Yet, being quite sensitive to the initialization, they are not guaranteed to converge to all the maximum points. Alternatively, an exhaustive search will result in all the maxima with an accuracy determined by the discretization resolution. Nonetheless, with the ODF being a 2D manifold, the search space, and consequently the computational complexity of the algorithm, grows quadratically with the desired resolution.

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We will next show how the fourth order RSSH basis makes it possible to confine the search to a 1D space, thereby creating an efficient method to extract the maxima. 2.3 Reducing the Dimension of the Search Space Let us assume that the ODF has been approximated in the fourth order RSSH basis, as ,

,

.

(8)

Combining equations (1), (2), and (8), while substituting the values of from Table 1 leads to ,

where

3 cos

2√

1

35 cos 7 cos 7 cos sin ,

sin cos 30 cos 3 3 sin cos 1 sin

cos

,

sin

cos

sin

cos sin

(9)

, etc. (