SEGMENTING THE MALE PELVIC ORGANS FROM LIMITED ANGLE IMAGES WITH ...

191 Pages·2013·3.61 MB·English

SEGMENTING THE MALE PELVIC ORGANS FROM LIMITED
ANGLE IMAGES WITH APPLICATION TO ART
Charles Brandon Frederick
A dissertation submitted to the faculty of the University of North Carolina at Chapel
Hill in partial fulfillment of the requirements for the degree of Doctor of Philosophy in
the Biomedical Engineering.
Chapel Hill
2013
Approved by:
David Lalush
Stephen Pizer
Sha Chang
Wesley Snyder
Paul Segars
(cid:13)c 2013
Charles Brandon Frederick
ALL RIGHTS RESERVED
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Abstract
CHARLES BRANDON FREDERICK: SEGMENTING THE MALE PELVIC
ORGANS FROM LIMITED ANGLE IMAGES WITH APPLICATION TO ART.
(Under the direction of David Lalush and Stephen Pizer)
Prostate cancer is the second leading cause of cancer deaths in men, and external
beam radiotherapy is a common method for treating prostate cancer. In a clinically
state-of-the-art radiotherapy protocol, CT images are taken at treatment time and are
used to properly position the patient with respect to the treatment device. In adap-
tive radiotherapy (ART), this image is used to approximate the actual radiation dose
delivered to the patient and track the progress of therapy. Doing so, however, requires
that the male pelvic organs of interest be segmented and that correspondence be estab-
lished between the images (registration), such that cumulative delivered dose can be
accumulated in a reference coordinate system. Because a typical prostate radiotherapy
treatment is delivered over 30-40 daily fractions, there is a large non-therapeutic radi-
ation dose delivered to the patient from daily imaging. In the interest of reducing this
dose, gantry mounted limited angle imaging devices have been developed which reduce
dose at the expense of image quality. However, in the male pelvis, such limited angle
images are not suitable for the ART process using traditional methods.
In this work, a patient specific deformation model is developed that is sufficient
for use with limited angle images. This model is learned from daily CT images taken
during the first several treatment fractions. Limited angle imaging can then be used for
the remaining fractions at decreased dose. When the parameters of this model are set,
it provides segmentation of the prostate, bladder, and rectum, correspondence between
the images, and a CT-like image that can be used for dose accumulation. However,
intra-patient deformation in the male pelvis is complex and quality deformation models
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cannot be developed from a reasonable number of training images using traditional
methods. This work solves this issue by partitioning the deformation to be explained
into independent sub-models that explain deformation due to articulation, deformation
near to the skin, deformation of the prostate bladder, and rectum, and any residual
deformation. It is demonstrated that a model that segments the prostate with accuracy
comparable to inter-expert variation can be developed from 16 daily images.
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TABLE OF CONTENTS
LIST OF FIGURES viii
LIST OF ABBREVIATIONS x
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Image Guided Radiotherapy . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Limited Angle Imaging . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.3 Intra-patient Deformation Models . . . . . . . . . . . . . . . . . 6
1.2 Thesis and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Document Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Background 13
2.1 Radiation Therapy in the Male Pelvis . . . . . . . . . . . . . . . . . . . 13
2.1.1 Prostate Cancer and Treatment . . . . . . . . . . . . . . . . . . 13
2.1.2 Radiation Therapy Process . . . . . . . . . . . . . . . . . . . . . 15
2.1.3 Devices and Methods for Imaging and Treatment . . . . . . . . 17
2.2 Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 Fourier Slice Theorem . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Filtered Backprojection . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.3 Iterative Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 28
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2.2.4 Limited Angle Problem . . . . . . . . . . . . . . . . . . . . . . . 35
2.3 Mathematics of Transformations . . . . . . . . . . . . . . . . . . . . . . 39
2.3.1 Introduction to Diffeomorphic Transformations . . . . . . . . . 41
2.3.2 Lie Groups and Manifolds . . . . . . . . . . . . . . . . . . . . . 44
2.4 Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.4.1 Non-rigid Registration . . . . . . . . . . . . . . . . . . . . . . . 58
2.4.2 Group-wise Registration . . . . . . . . . . . . . . . . . . . . . . 66
2.4.3 Dimensionality Reduction on Transformations . . . . . . . . . . 68
2.4.4 3D/2D Registration . . . . . . . . . . . . . . . . . . . . . . . . . 70
3 Method Overview 76
3.1 Partitioning of Variation . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.2 Poly-rigid Transformation . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.3 Mean Centering of Transformations . . . . . . . . . . . . . . . . . . . . 79
3.4 Summary of Transformations . . . . . . . . . . . . . . . . . . . . . . . 83
4 Polyrigid Deformations from Bony Anatomy 88
4.1 Poly-rigid Transformations . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.2 Determining a Weight Function . . . . . . . . . . . . . . . . . . . . . . 93
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 104
5 Multi-Deformation Models for Tissue Deformation 108
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.2 Deformation Model Learning . . . . . . . . . . . . . . . . . . . . . . . . 109
5.2.1 Group-wise Symmetric Log Demons Registration . . . . . . . . 109
5.2.2 Anatomical Constraints . . . . . . . . . . . . . . . . . . . . . . 112
5.2.3 Registration of Segmentations . . . . . . . . . . . . . . . . . . . 113
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5.2.4 Residual Registration and Correction of Gas . . . . . . . . . . . 117
5.2.5 Effects of Image Truncation During Model Learning . . . . . . . 121
5.2.6 Dimensionality Reduction . . . . . . . . . . . . . . . . . . . . . 123
5.2.7 Geodesics of Transformations . . . . . . . . . . . . . . . . . . . 126
5.3 Treatment-time Application . . . . . . . . . . . . . . . . . . . . . . . . 131
5.3.1 Inability to Calculate the Derivative . . . . . . . . . . . . . . . 131
5.3.2 Model Length Concerns During Application . . . . . . . . . . . 132
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.4.1 Method Variants . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.4.2 Context of Results . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.4.3 Multi-deformation Model . . . . . . . . . . . . . . . . . . . . . . 140
5.4.4 Single Deformation Model . . . . . . . . . . . . . . . . . . . . . 145
5.4.5 Poly-rigid and Deformation Model . . . . . . . . . . . . . . . . 147
5.4.6 Number of Training Days . . . . . . . . . . . . . . . . . . . . . 149
5.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 151
6 Discussion 153
6.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.2.1 Method Improvements . . . . . . . . . . . . . . . . . . . . . . . 159
6.2.2 Clinical Translation . . . . . . . . . . . . . . . . . . . . . . . . . 162
APPENDIX A GPU Acceleration in Medical Imaging 164
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
A.2 Parallel GPUs in Medical Image Computing . . . . . . . . . . . . . . . 164
A.3 CUDA Hardware Abstraction . . . . . . . . . . . . . . . . . . . . . . . 167
BIBLIOGRAPHY 173
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LIST OF FIGURES
2.1 Gantry Mounted Limited Angle Imaging Devices . . . . . . . . . . . . . 20
2.2 X-Ray Imaging Geometries . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Fourier Slice Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 Backprojection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Spatial Sampling of Parallel Projections . . . . . . . . . . . . . . . . . 26
2.6 Simple Backprojection and Filtered Backprojection . . . . . . . . . . . 27
2.7 Filtered Backprojection Scaling . . . . . . . . . . . . . . . . . . . . . . 28
2.8 Matrix Form for Projection . . . . . . . . . . . . . . . . . . . . . . . . 29
2.9 Iterative Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.10 Limited Angle Reconstruction Examples . . . . . . . . . . . . . . . . . 37
2.11 Simulated Nanotube Stationary Tomosynthesis Images . . . . . . . . . 38
2.12 Sphere Response of a Limited Angle Geometry . . . . . . . . . . . . . . 40
2.13 Log Mapping of the Earth . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.14 Principle Component Analysis . . . . . . . . . . . . . . . . . . . . . . . 69
3.1 Order of Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.1 Linear versus Log Domain Combination of Rotations . . . . . . . . . . 90
4.2 Interpretation of Linear versus Log Domain Combination of Rotations . 90
4.3 Poly-rigid versus Direct Fusion of Rotations . . . . . . . . . . . . . . . 92
4.4 Poly-rigid versus Direct Fusion of Rigid Transformations . . . . . . . . 93
4.5 Weight Function for Simulated Patient . . . . . . . . . . . . . . . . . . 99
4.6 Poly-rigid Transformation Space of Simulated Patient . . . . . . . . . . 100
4.7 Poly-rigid Weights and Registered Example versus Rigid Registration . 102
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4.8 Image Distance for Poly-rigid versus Rigid Transformation . . . . . . . 103
4.9 Poly-rigid Initialization Decreases Image Distance of Rigid Initialization 105
4.10 Images Supporting 4.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.1 Isosurface Rendering of a Skin Atlas . . . . . . . . . . . . . . . . . . . 116
5.2 Organ Stage Image Data . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.3 Isosurface Rendering of Organ Atlas . . . . . . . . . . . . . . . . . . . . 118
5.4 Gas Filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.5 Final Patient Atlas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.6 Possible Intermediates Along Geodesics Between Two Ellipses . . . . . 128
5.7 Organ Modes of Deformation, Log Domain . . . . . . . . . . . . . . . . 129
5.8 Organ Modes of Deformation, Linear Domain . . . . . . . . . . . . . . 130
5.9 Annotated Reprojection Image . . . . . . . . . . . . . . . . . . . . . . . 134
5.10 Rigid Segmentation Performance . . . . . . . . . . . . . . . . . . . . . 138
5.11 Experimental Patient Orientations . . . . . . . . . . . . . . . . . . . . 139
5.12 Full Method Segmentation Performance, PGA . . . . . . . . . . . . . . 142
5.13 Full Method Segmentation Performance, PCA . . . . . . . . . . . . . . 143
5.14 Method Variant Performance Summary . . . . . . . . . . . . . . . . . . 144
5.15 Sample Reconstructed Image . . . . . . . . . . . . . . . . . . . . . . . . 144
5.16 Deformed Image as an Approximation to Planning CT . . . . . . . . . 146
5.17 Simple Method Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.18 Single Deformation Model with Poly-rigid Results . . . . . . . . . . . . 150
5.19 Performance versus Number of Training Images . . . . . . . . . . . . . 151
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LIST OF ABBREVIATIONS
ART adaptive radiotherapy
AP anterior-posterior
BCH Baker-Campbell-Hausdorff formula
BFGS Broyden-Fletcher-Goldfarb-Shanno
CBCT cone beam CT
CPU central processing unit
CT X-ray computed tomography
CUDA Compute Unified Device Architecture
DSC Dice’s similarity coefficient
DVF displacement vector field
EBRT external beam radiotherapy
EM expectation-maximization
FBCT fan beam CT
FBP filtered backprojection
FIR finite impulse response
FOV field of view
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