Compensating for Quasi-periodic Motion in Robotic Radiosurgery

Compensating for Quasi-periodic Motion in Robotic Radiosurgery

Floris Ernst Compensating for Quasiperiodic Motion in Robotic Radiosurgery

Floris Ernst Institute for Robotics and Cognitive Systems University of Lübeck Lübeck, Germany ISBN 978-1-4614-1911-2 e-isbn 978-1-4614-1912-9 DOI 10.1007/978-1-4614-1912-9 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011942318 Springer Science+Business Media, LLC 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Web resources In this work, several scripts for MATLAB as well as data sets for evaluation and a motion prediction toolkit have been introduced. All these items are available for public download from http://signals.rob.uni-luebeck.de. v

Contents 1 Introduction................................................... 1 1.1 The Problem of Latency..................................... 1 1.2 Medical Background........................................ 4 1.3 Purpose of this Work........................................ 6 1.4 Organisation............................................... 7 References..................................................... 8 2 Motion Compensation in Robotic Radiosurgery................... 13 2.1 Medical Implications....................................... 13 2.2 Active Tumour Tracking in Image-Guided Radiotherapy.......... 14 2.2.1 The CyberKnife..................................... 14 2.2.2 Other Approaches.................................... 17 2.3 Gantry-Based Systems...................................... 18 2.3.1 Respiratory Gating................................... 18 2.3.2 Beam Shaping....................................... 20 2.4 Tomotherapy.............................................. 22 2.5 The CyberHeart Project..................................... 23 2.5.1 Medical Background................................. 23 2.5.2 Technical Details.................................... 24 References..................................................... 24 3 Signal Processing.............................................. 31 3.1 Determining the Latency.................................... 31 3.1.1 Experiment: Latency of Optical Tracking Devices......... 31 3.1.2 Experiment: Latency of the Robotic Setup............... 33 3.2 Evaluation Measures........................................ 35 3.2.1 Measuring the error level.............................. 35 3.2.2 Signal smoothness and stability........................ 42 3.3 Wavelet-based Noise Reduction.............................. 42 3.3.1 Final noise reduction method.......................... 43 3.3.2 Time Shift.......................................... 43 vii

viii Contents 3.3.3 Modified Measures for Smoothed Signals................ 45 3.4 Analysing the Noise Level of Tracking Devices................. 46 3.4.1 Measuring the Noise Experimental Setup............... 46 3.4.2 Noise distributions measured.......................... 48 3.4.3 Analysis of the results................................ 54 3.5 Frequency Leakage......................................... 55 3.5.1 Measurement Errors.................................. 57 3.5.2 Compensation Strategies.............................. 60 References..................................................... 62 4 On the Outside: Prediction of Human Respiratory and Pulsatory Motion........................................................ 65 4.1 Model-based prediction methods.............................. 65 4.1.1 Kalman Filtering and Extended Kalman Filtering......... 66 4.2 Model-free Prediction Methods............................... 71 4.2.1 Autoregressive approaches............................ 71 4.2.2 A Fast Lane Approach to LMS Prediction................ 80 4.2.3 Multi-step Linear Methods (MULIN)................... 84 4.2.4 Support Vector Regression............................ 87 4.3 Predicting Smoothed Signals................................. 92 4.4 Graphical Prediction Toolkit................................. 96 4.5 Evaluating the Prediction Algorithms.......................... 99 4.5.1 A Respiratory Motion Database........................ 100 4.5.2 Comparing the Algorithms............................ 100 4.5.3 Evaluation of the FLA-nLMS Algorithm................. 109 4.6 Predicting the Outcome of Prediction.......................... 111 4.7 Prediction of Human Pulsatory Motion........................ 122 4.7.1 Data Acquisition..................................... 122 4.7.2 Results............................................. 124 References..................................................... 127 5 Going Inside: Correlation between External and Internal Respiratory Motion............................................ 131 5.1 Correlation Algorithms...................................... 131 5.1.1 Polynomial Correlation............................... 132 5.1.2 Correlation with Support Vector Regression.............. 136 5.2 Experimental Validation..................................... 139 5.2.1 Animal Study....................................... 139 5.2.2 Human Data........................................ 155 References..................................................... 161 6 Conclusion.................................................... 167 6.1 Analysis of Technical Problems............................... 167 6.1.1 System Latency..................................... 167 6.1.2 Acquisition Noise.................................... 168

Contents ix 6.1.3 Inadequate Prediction and Correlation Methods........... 168 6.2 Improving Motion Tracking and Tumour Targeting.............. 169 6.2.1 System Noise....................................... 169 6.2.2 Prediction Algorithms................................ 169 6.2.3 Correlation Algorithms............................... 171 6.3 Tools..................................................... 171 6.4 Ideas..................................................... 172 6.4.1 A Standard for Signal Processing of Motion Traces........ 172 6.4.2 A Database of Signals................................ 173 6.4.3 Standards for Error Measures and Evaluation............. 174 6.5 Future Work............................................... 175 6.5.1 Using Additional Surrogates........................... 175 6.5.2 Fusion of Multiple Algorithms......................... 177 References..................................................... 178 A Mathematical Addenda......................................... 183 A.1 The à trous wavelet transform................................ 183 A.2 Support Vector Regression................................... 187 A.3 The Karush-Kuhn-Tucker condition........................... 191 A.4 Representation of Rotations.................................. 192 A.5 The QR24 and QR15 algorithms for hand-eye calibration......... 195 References..................................................... 202 B Robots and Tracking Systems................................... 205 References..................................................... 212 C Client/Server Framework for the Vivid7 Ultrasound Station.......... 213 References..................................................... 219 D Simulating Respiration......................................... 221 E Listings....................................................... 225 List of Figures..................................................... 229 List of Tables...................................................... 235 List of Companies................................................. 237 Glossary.......................................................... 239

Acknowledgements I would like to express my gratitude towards my supervisor, Prof. Dr.-Ing. Achim Schweikard, who gave me the opportunity to work on this highly fascinating topic. I am much indebted to him for allowing me to freely pursue my ideas and for always providing support. I also thank Prof. Dr. rer. nat. Bernd Fischer, my thesis second referee, for his valuable input. I would also like to thank my colleagues I really enjoyed working with you. I would especially like to mention Lars Matthäus, Ralf Bruder, and Alexander Schlaefer for their help with unfamiliar topics, for proof reading my work and for the time they spent working with me on my experiments. Parts of my work would not have been possible without the assistance of my students, especially the work of Matthias Knöpke and Norman Rzezovski should be acknowledged here. And, of course, the heart and soul of our institute, Cornelia Rieckhoff, must be mentioned: she was always willing to help with the difficulties of the English language, the pitfalls of working at the university, and the minor and major organisational and personal problems that came up during my time here. Last but not least I express my gratitude towards my family, my parents, and my friends for their support and for reading my work for clarity, spelling and grammar. Curriculum Vitae Floris Ernst was born on August 6th, 1981, in Hinsdale, Illinois/USA. He studied Mathematics at Friedrich-Alexander-University (Erlangen, Germany) and at the University of Otago (Dunedin, New Zealand). He graduated from the University of Otago in 2004 with a Postgraduate Diploma in Sciences (Mathematics). In 2006, he graduated From Friedrich-Alexander- University with a Diploma in Mathematics, minoring in Computer Sciences. From 2006 on he held a position as a research associate at the University of Lübeck s Institute for Robotics and Cognitive Systems, where he worked on motion compensation strategies in robotic radiosurgery. He graduated from this university with a Ph.D in 2011. xi