1 Introduction 1
1.1 Motion Planning for Image-Guided Medical Procedures 2
1.2 Motion Planning Algorithms 4
1.2.1 Motion Planning for Rigid Needles 4
1.2.2 Motion Planning for Steerable Needles 5
1.2.3 Motion Planning for Radiation Sources for Cancer Treatment 6
1.3 Brachytherapy for Treating Prostate Cancer 6
1.4 Contributions 8
1.5 Overview 9
2 Physically-Based Simulation of Soft Tissue Deformations 11
2.1 Fundamentals of Continuum Mechanics 12
2.1.1 Deformable Bodies 13
2.1.2 The 1-D Case 13
2.1.3 The 3-D Case 15
2.1.4 The 2-D Case 18
2.2 Simulating Soft Tissue Deformations 18
2.2.1 Mass-Spring Method 18
2.2.2 Finite Element Method 19
2.2.3 Visualizing 2-D Simulations 23
2.3 Conclusion 24
3 Motion Planning in Deformable Soft Tissue with Applications to Needle Insertion 27
3.1 Sensorless Planning and Needle Insertion 29
3.2 Problem Formulation 30
3.3 Simulating Needle Insertion 31
3.3.1 Background on Needle Insertion Modeling and Simulation 31
3.3.2 Input Anatomy Model 32
3.3.3 Simulation Output 33
3.3.4 Simulating Needle Procedures 33
3.3.5 Simulation Visualization 36
3.4 Motion Planning for Needle Insertion 37
3.4.1 Method Overview 37
3.4.2 Planning Problem Formulation 37
3.4.3 Planning Algorithm 38
3.5 Application to Brachytherapy Cancer Treatment 39
3.5.1 Simulation Implementation 40
3.5.2 Sensorless Planner Results 41
3.6 Conclusion and Open Problems 42
4 Motion Planning in Deformable Soft Tissue with Obstacles with Applications to Needle Steering 45
4.1 Background on Needle Steering 45
4.2 Simulating Needle Steering 47
4.2.1 Soft Tissue Model 48
4.2.2 Computing Soft Tissue Deformations 48
4.2.3Needle Insertion Model 48
4.2.4 Simulating Cutting at the Needle Tip 49
4.2.5 Simulating Friction Along the Needle Shaft 50
4.2.6 Simulation Results 51
4.3 Motion Planning for Needle Steering 52
4.3.1 Problem Formulation 52
4.3.2 Optimization Method 53
4.3.3 Planner Results 54
4.4 Conclusion and Open Problems 55
5 Motion Planning for Curvature-Constrained Mobile Robots with Applications to Needle Steering 57
5.0.1 Uncertainty and Motion Planning 58
5.0.2 Background on Nonholonomic Motion Planning and MDP's 59
5.0.3 Overview of Motion Planning Method 61
5.1 Problem Definition 62
5.2 Motion Planning for Deterministic Needle Steering 64
5.2.1 State Space Discretization 64
5.2.2 Deterministic State Transitions 65
5.2.3 Discretization Error 66
5.2.4 Computing Deterministic Shortest Paths 66
5.3 Motion Planning for Needle Steering under Uncertainty 66
5.3.1 Modeling Motion Uncertainty 67
5.3.2 Maximizing the Probability of Success Using Dynamic Programming 67
5.4 Computational Results 69
5.5 Conclusion and Open Problems 73
6 The Stochastic Motion Roadmap: A Sampling-Based Framework for Planning with Motion Uncertainty 75
6.0.1 Related Work 78
6.0.2 SMR Contributions 79
6.1 Algorithm 80
6.1.1 Input 80
6.1.2 Building the Roadmap 81
6.1.3 Solving a Query 82
6.1.4 Computational Complexity 84
6.2 SMR for Medical Needle Steering 84
6.2.1 SMR Implementation 85
6.2.2 Results 86
6.3 Conclusion and Open Problems 89
7 Motion Planning for Radiation Sources during High-Dose-Rate Brachytherapy 91
7.1 Introduction to HDR Brachytherapy and Dose Optimization 92
7.2 Linear Programming for HDR Brachytherapy 93
7.2.1 Patient Data Input 95
7.2.2 Dose Calculation 95
7.2.3 Clinical Criteria 96
7.2.4 Linear Programming Formulation 97
7.3 Application to Prostate Cancer Treatment 99
7.3.1 Patient Data Sets 100
7.3.2 Evaluation Metrics 100
7.3.3 Results 101
7.4 Discussion 104
7.5 Conclusion and Open Problems 105
8 Conclusion 107
8.1 Contributions 107
8.1.1 Deformations 107
8.1.2 Uncertainty 108
8.1.3 Optimality 108
8.2 Future Directions 108
8.2.1 Realistic Simulation of Image-Guided Medical Procedures 108
8.2.2 Planning Algorithms for Image-Guided Medical Procedures 111
8.2.3 New Clinical Applications 113
8.3 Conclusion 113
References 115
A Target Localization Using Deformable Image Registration 129
A.1 Introduction to Deformable Image Registration 129
A.2 Deformable Registration with Model Parameter Estimation 132
A.2.1 Method Input 133
A.2.2 Finite Element Model of Soft Tissue Deformation 133
A.2.3 Quality Metric 134
A.2.4 Optimization of Uncertain Parameters 134
A.2.5 Visualizing Registration Output 135
A.3 Application to Prostate Cancer Treatment 135
A.3.1 Patient Image Acquisition 138
A.3.2 Application of the Deformable Registration Method 139
A.3.3 Warping the MRSI Grid 141
A.3.4 Method Evaluation and Parameter Selection 142
A.3.5 Results 142
A.3.6 Discussion 144
A.4 Conclusion and Open Problems 147
Index 149
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