Using poisson’s equation to characterize brain tumor shape




НазваниеUsing poisson’s equation to characterize brain tumor shape
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USING POISSON’S EQUATION TO CHARACTERIZE BRAIN TUMOR SHAPE


BY


BENJAMIN J. SINTAY


A Dissertation Submitted to the Graduate Faculty of


WAKE FOREST UNIVERSITY GRADUATE SCHOOL OF ARTS AND SCIENCES


in Partial Fulfillment of the Requirements


for the Degree of


DOCTOR OF PHILOSOPHY


Biomedical Engineering


in the program of


VIRGINIA TECH – WAKE FOREST UNIVERSITY
SCHOOL OF BIOMEDICAL ENGINEERING AND SCIENCES


December 2008


Winston-Salem, North Carolina


Approved By:


J. Daniel Bourland, Ph.D., Advisor ____________________________________


Examining Committee:


Robert Plemmons, Ph.D., Chair ____________________________________


Carnell Hampton, Ph.D. ____________________________________


Michael T. Munley, Ph.D. ____________________________________


Christopher Wyatt, Ph.D. ____________________________________

ACKNOWLEDGEMENTS


First and foremost, this work is dedicated to my parents, Jerry and Donna Sintay who have been there for me through every step of life. I attribute all of my successes and motivation to their selfless efforts. Mom and Dad – thank you for providing a home that celebrated creativity, integrity, and hard work. The completion of this step in my life honors both of our accomplishments.

I am especially grateful for the guidance and friendship of Dr. J. Daniel Bourland, my academic advisor. Dr. Bourland has been extremely supportive, professional, and inspiring during my time at Wake Forest University. It has truly been a pleasurable experience working for him – one that I will cherish for many years to come. To the members of my committee – Drs. Carnell Hampton, Robert Plemmons, Michael Munley, and Christopher Wyatt – thank you for your investment of time for my sake. Your insights have been extremely valuable in improving this dissertation.

I am grateful for the help of Rebecca Bishop in Clinical Trials for preparing the survival data for this dissertation and Dr. Stephen Tatter for spending many hours reviewing tumor segmentations and providing much inspiration for this work.

A special thank you is in order for the faculty and staff at Wake Forest University Baptist Medical Center, especially the members of the Radiation Oncology Physics Section. I could not have asked for a better group of people to foster my interest and understanding of the medical physics profession. Countless hours (and gray hairs) have been selflessly given for the sake of my education both in clinical practice and academic exercise. Thank you for allowing me to become a vital part of the daily operations of the clinic.

Thank you to the faculty, staff, and graduate students at Wake Forest University and within the Virginia Tech – Wake Forest University School of Biomedical Engineering and Sciences. I am extremely lucky to have been a part of this group. I cannot say enough about how wonderful the graduate school experience has been. I am especially thankful to the post-docs and graduate students in the Physics Section past and present.

To Dr. Joel Berry, Herbie Burns, and Dan Wilson – thank you for providing an escape from the pressures of graduate school. You all have been like brothers to me. To Kelli – I am lucky to have such a wonderful sister who is kind and understanding. You have always been there for me. To Monica – thank you for bringing joy into my life every day. I am proud to be your husband, and I look forward to the wonderful life that we will share together. You inspire me to do great things, and most importantly, make it all worthwhile. Finally, thank you to God for providing me with the strength and ability to accomplish my dreams.


TABLE OF CONTENTS



LIST OF TABLES ix

LIST OF FIGURES x

ABSTRACT xx

1. INTRODUCTION 1

1.1. SHAPE RECOGNITION 2

1.2. SHAPE METRICS SURVEY 4

1.3. CLINICAL SIGNIFICANCE 6

1.4. IMAGE ACQUISITION 11

2. NUMERICAL METHOD 14

2.1. POISSON’S EQUATION 14

2.2. FINITE DIFFERENCE METHOD 16

2.3. ITERATIVE TECHNIQUES FOR SOLVING POISSON’S EQUATION WITH FINITE DIFFERENCES 18

2.3.1. JACOBI’S METHOD 18

2.3.2. THE GAUSS-SEIDEL METHOD 21

2.3.3. ERROR AND PROCESSING TIME 23

2.3.4. CONVERGENCE 25

3. SHAPE CHARACTERIZATION 26

3.1. TRANSLATION, ROTATION, AND SCALE INDEPENDENCE 27

3.2. LEVEL-SET COMPLEXITY 29

3.3. DISPLACEMENT MAP 30

3.4. SHAPE CHARACTERISTIC CURVE 36

4. STATISTICAL FRAMEWORK 40

4.1. PERMUTATION TESTS 41

4.2. RANDOM PERMUTATION TESTS 42

4.3. SHAPE CHARACTERISTIC MONTE-CARLO PERMUTATION TEST 44

4.4. CLINICAL EXAMPLE: NORMAL NEUROANATOMY 45

5. SOFTWARE TOOLSET 55

5.1. IMPLEMENTATION 55

5.2. FRAMEWORK AND NOTEABLE ALGORITHMS 57

6. VALIDATION STUDIES 61

6.1. ANALYTICAL SOLUTION COMPARISON 61

6.2. TWO-DIMENSIONAL SYNTHETIC STUDIES 66

6.2.1. COMPARATIVE STUDY 66

6.2.2. VARIOUS STRUCTURE STUDY 72

6.2.3. TRANSLATION, ROTATION, AND SCALE INDEPENDENCE 76

6.2.4. TWO-CLASS 2D SILHOUETTE STUDY 81

6.3. MULTI-FIGURE SYNTHETIC SHAPE STUDIES 86

6.4. THREE-DIMENSIONAL SYNTHETIC STUDIES 91

6.5. THREE-DIMENSIONAL ANATOMIC TEST STUDIES 94

6.6. PHYSICAL PHANTOM STUDIES 100

7. CLINICAL TRIAL 113

7.1. BACKGROUND 113

7.2. METHODS 115

7.3. RESULTS 117

7.4. DISCUSSION 138

8. CONCLUSIONS AND FUTURE DIRECTIONS 141

143

REFERENCES 144

APPENDIX A: INDEX OF IMPORTANT ROUTINES AND CODE 150

EXPERIMENT SCRIPTS 150

CORE FUNCTIONS 152

APPENDIX B: TOOLSET CODE 156

VITAE 177


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