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Retrieving Information from Scattered Photons in Medical Imaging Retrieving Information from Scattered Photons in Medical Imaging Item Type text; Electronic Dissertation Authors Jha, Abhinav K. Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 27/09/2021 17:59:58 Link to Item http://hdl.handle.net/10150/301705 RETRIEVING INFORMATION FROM SCATTERED PHOTONS IN MEDICAL IMAGING by Abhinav K. Jha A Dissertation Submitted to the Faculty of the COLLEGE OF OPTICAL SCIENCES In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 2013 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the disser- tation prepared by Abhinav K. Jha entitled Retrieving Information from Scattered Photons in Medical Imaging and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy. Date: 29 March 2013 Matthew A. Kupinski Date: 29 March 2013 Harrison H. Barrett Date: 29 March 2013 Eric Clarkson Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. Date: 29 March 2013 Dissertation Director: Matthew A. Kupinski 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: Abhinav K. Jha 4 ACKNOWLEDGEMENTS This dissertation is the combined effort of a team that I consider extremely fortu- nate to be a part of. I would like to begin by thanking my parents for their constant love, support, patience, and encouragement throughout my graduate studies. This dissertation would not have been possible without the extremely supporting envi- ronment that they provided to me.Thanks also to my younger brother Abhishek for being the best younger brother in this world! I am enormously grateful to my advisor Dr. Matthew Kupinski for his sup- port and mentorship during my graduate studies, and for helping me grow as a researcher. Apart from giving me much independence to pursue my research ideas, the willingness to provide guidance whenever required, and the generosity with the professional advices, Dr. Kupinski also ensured that I worked in a stress-free, re- spectful, and cordial research environment. I am also grateful to Dr. Kupinski for the financial support during grad school and conference attendance. I would like to express my sincere gratitude to Dr. Harrison Barrett, whose positive influence motivated us to dream big and set high standards in research. I am indebted to Dr. Barrett for his mentorship and for many technical discussions in image science. I am also very thankful to Dr. Eric Clarkson for always willing to lend an ear to so many of my mathematical questions. Dr. Clarkson provided me with excellent technical guidance that helped improve my mathematical skills. I am grateful to Dr. Masud Mansuripur for his mentorship, and to Dr. Lars Furenlid, Dr. Art Gmitro, and Dr. Amit Ashok for technical discussions and profes- sional advices. Thanks also to Dr. Barrett, Dr. Gmitro, and Dr. Furenlid for their mentorship when I worked with them as a teaching assistant. My sincere gratitude also to Dr. John Hartman, Dr. Brian Hutton, Dr. Simon Arridge, Dr. Michel De- frise, Dr. Dennis Schaart, and Dr. Herman van Dam for many technical discussions. I would also like to thank my undergraduate mentor, Dr. Haranath Kar, and my Masters advisor, Dr. Jeffrey Rodriguez, for their guidance. I would like to acknowledge the funding agencies that supported this research, namely, Canon Inc. and NIH grants R37-EB000803, RC1-EB010974, and P41- EB002035. Research funding was also provided by SNMMI Student fellowship, SPIE scholarship, Wolfe Family Endowed scholarship, and the TRIF imaging fellowship. I am very fortunate to have been in the company of some great friends dur- ing my PhD. Thanks especially to Robin Palit for being a great lab mate, and to Vaibhav, Sundaresh, Srinivas, Kunal, Aakriti, Aarthi, Sushanth, Meled, Gunjan, Madhumitha, Maham, Aakash, Stefano, Luca, Esen, Jin, C´ecile, Nick, Chris, Andy, Jared, Helen, Ronan, Kashmira, Sandy, Sachi, Pavan, Veysi, Vineeth, Aiyaash gang, and many other friends for all the wonderful times during my graduate studies. 5 DEDICATION Dedicated to my parents and to Goldy Bhaiya 6 TABLE OF CONTENTS LIST OF FIGURES ................................ 10 LIST OF TABLES ................................. 15 ABSTRACT .................................... 16 CHAPTER 1 INTRODUCTION ........................ 18 1.1 Background, specific objectives and structure of the dissertation ... 18 1.2 Themes of the dissertation ........................ 23 1.3 Dissemination of the work in this dissertation ............. 25 CHAPTER 2 SCATTERING IN MEDICAL IMAGING ............ 26 2.1 Scattering mechanisms .......................... 26 2.2 Mathematical treatment of scattering .................. 29 2.2.1 Radiometric quantities ...................... 29 2.2.2 Scattering cross section ...................... 30 2.2.3 Effect of scattering on the distribution function ........ 32 2.2.4 Scattering kernel in DOT .................... 34 2.2.5 Scattering kernel in SPECT ................... 35 2.3 Radiative transport equation ....................... 38 CHAPTER 3 SIMULATING PHOTON TRANSPORT IN DOT USING THE NEUMANN-SERIES RTE ........................... 41 3.1 Introduction ................................ 41 3.2 Neumann-series RTE in the spherical harmonic and voxel basis .... 45 3.2.1 The scattering operator in spherical harmonics ......... 46 3.2.2 The attenuation operator in spherical harmonics ........ 47 3.2.3 Voxelization ............................ 48 3.3 Evaluating the RTE for a DOT setup .................. 51 3.3.1 Computing the Neumann-series terms .............. 51 3.3.2 Convergence criterion ....................... 54 3.3.3 Computing the output flux .................... 57 3.4 Implementation .............................. 58 3.5 Experiments and results ......................... 60 3.5.1 Experiment 1: Scattering medium with µsH =1 ........ 62 3.5.2 Experiment 2: Ability to handle collimated source ....... 63 7 TABLE OF CONTENTS – Continued 3.5.3 Experiment 3: Convergence with increasing number of Neumann-series terms ...................... 66 3.5.4 Experiment 4: Convergence with increasing number of spher- ical harmonics ........................... 67 3.5.5 Experiment 5: Performance of RTE with increasing value of µsH ................................ 68 3.5.6 Computational requirements ................... 70 3.6 Discussion and conclusions ........................ 74 CHAPTER 4 A GPU IMPLEMENTATION TO MODEL PHOTON TRANS- PORT IN DOT IMAGING SYSTEMS .................... 78 4.1 Introduction ................................ 78 4.2 Theory ................................... 79 4.2.1 Neumann-series in discrete basis for non-uniform media .... 79 4.2.2 Evaluating the RTE for a DOT setup with non-uniform media 82 4.3 GPU implementation of the algorithm ................. 84 4.3.1 CPU implementation ....................... 85 4.3.2 Introduction to GPU implementation .............. 87 4.3.3 Device and programming tools .................. 89 4.3.4 Parallelization scheme and software design ........... 90 4.3.5 Other optimizations for efficient memory-usage ......... 94 4.4 Experiments and results ......................... 95 4.4.1 Homogeneous medium ...................... 96 4.4.2 Heterogeneous medium ...................... 98 4.4.3 Computational requirements ...................100 4.5 Discussions and conclusions .......................102 CHAPTER 5 INVESTIGATING SIGNAL DETECTION IN DIFFUSE OP- TICAL TOMOGRAPHY ...........................108 5.1 Relation between signal detectability and Fisher information in DOT 111 5.2 Evaluating the Fisher information matrix ................112 5.3 Evaluating the gradient of the mean image data ............114 5.3.1 Implementation ..........................117 5.3.2 Methods for the specific SKE/BKE task ............118 5.4 Experiments and results .........................120 5.4.1 Signal detectability as a function of depth ...........121 5.4.2 Signal detectability as a function of the scattering coefficient of the tissue ............................121 5.4.3 Signal detectability as a function of signal size and signal depth123 8 TABLE OF CONTENTS – Continued 5.4.4 Signal detectability as a function of signal size and signal con- trast ................................123
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