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Table of Contents

Chapter 1: Introduction 27

1.1 Thoracic aorta 28

Anatomy of Healthy Thoracic Aorta 28

Development of Anatomy for Aortic Coarctation 29

1.2 Current Diagnostic Challenges for Aortic Coarctation 31

1.3 Study Design for Data Acquisition 33

Diagnostic Imaging Modalities 34

MRI Contrast Medium 36

Control of Heart Rate 38

Protocol for Collecting Clinical Data 40

Study Cohort 42

1.4 Independent Clinical Risk Factors 43

1.5 Clinical Data Acquisition Techniques 45

Magnetic Resonance Imaging 45

Phase Contrast Magnetic Resonance Volumetric Flow Rate 47

Hybrid Imaging System of X-ray and Magnetic Resonance 50

1.6 Image Processing 51

DICOM Format 52

Image Registration 53

Centreline Extraction 56

Vascular Segmentation 57

1.7 Computational Fluid Dynamics 60

Governing Model Equations 61

3D Mesh for Fluid Flow Simulation 62

Physical Properties of the Fluid 64

Flow Regimes 65

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1.8 Pressure Wave Analysis 68

1.9 Windkessel Modelling 70

1.10 Thesis Research Aims 72

Chapter 2: Aortic Segmentation 73

2.1 The Sheffield Image Registration Toolkit 74

2.2 One-Dimensional Image Processing 77

2.3 Two-Dimensional Image Processing 81

2.4 Three-Dimensional Image Processing 83

Classic Threshold Segmentation 83

Connected Threshold Segmentation 84

Otsu Segmentation 95

2.5 Region Based Region Growing Segmentation Model 97

Seed Definition 98

Input Image 99

2.6 Implementation of the RBRG Segmentation Workflow 100

Workflow Step 1: Pre-Processing and Segmentation 100

Workflow Step 2: Post-Processing of the Segmented Surface 103

Workflow Step 3: Centreline Extraction 104

Workflow Step 4: Position Choice for Surface Openings 105

2.7 Segmented Aortic Surfaces - Discussion 107

2.8 Geometrical Model for Coarctation Studies 110

2.9 Summary 112

Chapter 3: Processing of Time-Resolved 2D Phase Contrast MRI Data 113

3.1 Hemodynamics: Factors Affecting Blood Flow 114

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3.2 Processing Method 115

Visualisation of Velocity Maps 115

Requirements from the Processed Product 115

Volumetric Flow Extraction Algorithm 116

Output Data 118

3.3 Measured Volumetric Flow Profile 119

3.4 Functional Assessment of Hemodynamic Events 122

Determining the Reynolds Number 122

Estimating the Pressure Difference across the Stenosis 124

Identifying Collateral Circulation 126

3.5 Flow Waveforms for Aortic Branches 128

3.6 Summary 130

Chapter 4: Mesh Generation for the Thoracic Aorta 131

4.1 GIMIAS Tool for Mesh Generation 132

4.2 Three Dimensional Mesh Types 133

Mesh Type A: Isotropic Tetrahedral Mesh 133

Mesh Type Β: Αnisotropic Tetrahedral Mesh 134

Mesh Type C: Anisotropic Tetrahedral Mesh with Prism Boundaries 134

Methodology for Mesh Parameter Settings 136

4.3 Configurations for the Fluid Domain 137

Mildly Coarcted Aortic Study 138

Moderately Coarcted Aortic Study 140

Severely Coarcted Aortic Study 142

4.4 Mildly Coarcted Aortic Model 144

Mesh Type A: Isotropic Tetrahedral Mesh 144

Mesh Type Β: Αnisotropic Tetrahedral Mesh 146

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Mesh Type C: Anisotropic Tetrahedral Mesh with Prism Boundaries 148

4.5 Moderately Coarcted Aortic Model 150

Mesh Type A: Isotropic Tetrahedral Mesh 150

Mesh Type Β: Αnisotropic Tetrahedral Mesh 151

Mesh Type C: Anisotropic Tetrahedral Mesh with Prism Boundaries 152

4.6 Severely Coarcted Aortic Model 153

Mesh Type A: Isotropic Tetrahedral Mesh 153

Mesh Type Β: Αnisotropic Tetrahedral Mesh 154

Mesh Type C: Anisotropic Tetrahedral Mesh with Prism Boundaries 155

4.7 Summary 156

Chapter 5: Clinical Pressure Data Processing 157

5.1 The Cardiac Cycle 158

5.2 Processing Algorithm 160

Input Data 160

Product Requirements 161

Pressure Waveform Extraction Algorithm 161

Output Data 163

5.3 Idealised Aortic Blood Pressure Waveform 166

Healthy Child Aortic Geometry 167

Healthy Adult Aortic Geometry 170

5.4 Invasive Aortic Blood Pressure Waveform 172

Line Analysis 174

Pressure Trace at Different Measurement Sites 176

Augmentation Index 185

Time Domain Analysis 190

Frequency Domain Analysis 198

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5.5 Three Element Windkessel Model 198

Parameter Estimation 200

5.6 Summary 200

Chapter 6: Discussion and Final Remarks 201

6.1 Summary of Findings 201

Aortic Segmentation 201

Mesh Generation 203

Volumetric Flow Processing 204

Pressure Signal Processing 205

6.2 Discussion 207

Pre-processing Filter for Aortic Segmentation 207

Elasticity of the Aortic Wall 211

CFD Simulations – Methodology and Boundary Conditions 212

Invasive Pressure Measurements 213

6.3 Future Work 215

Aortic Segmentation 215

Mesh Generation 215

Volumetric Flow Processing 215

Pressure Signal Processing 216

Computing Pressure Wave Velocity from Clinical Images 217

Experimental Validation of Pressure Wave Propagation 218

Computing Pressure Wave Velocity from Invasive Measurements 220

Appendices 221

Appendix 1: Aortic Coarctation – World Situation 221

Appendix 2: Gadolinium-based MRI Contrast Agent 223

The Electron Configuration for the Gadolinium Atom 223

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The Gadopentetic Acid 224

Appendix 3: Hormone-Receptor Interactions 226

The Catecholamine 226

Isoprenaline and Dobutamine 229

Appendix 4: Representative Values for Human Circulation 230

Appendix 5: Segmented Aortic Geometries 231

Appendix 6: Volumetric Flow Data 238

Appendix 7: Invasive Pressure Data 242

References 245