This document provides an overview of the research aims, methodology, and key findings of a thesis related to computational modeling of aortic coarctation. It includes chapters on aortic segmentation from medical images, processing of time-resolved magnetic resonance volumetric flow data, generating meshes of the aorta, and processing invasive blood pressure signals. The goal of the research was to develop image-based models to simulate blood flow and pressure in the aorta to improve diagnosis and treatment planning for aortic coarctation.

1. 12
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

2. Contents
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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

3. Contents
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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

4. Contents
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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

5. Contents
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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

6. Contents
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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