Contents 1 Computational Haemodynamics An Introduction 2 The Human Cardiovascular System

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1 Contents 1 Computational Haemodynamics An Introduction What is Computational Haemodynamics (CHD) Advantages of CHD Applications in the Cardiovascular System CHD as a Research Tool CHD as a Training Tool Examination of Atherosclerosis Plaque Rupture Risk Assessment Preoperative Assessment of Atherosclerotic Arteries Surgical Treatment of Atherosclerotic Arteries Preoperative Assessment of Aneurysm Assessment of Medical Devices Summary Review Questions The Human Cardiovascular System Introduction Functions of the Circulatory System Organization of the Cardiovascular System Physiology of the Cardiovascular System Anatomy of the Heart Cardiac Cycle Physiology of the Aorta Physiology of the Carotid Bifurcation Physiology of the Coronary Arteries Physiology of the Vascular Network Blood Disease of the Cardiovascular System Atherosclerosis Calcification of Lesions in Plaque xi

2 xii Contents Aneurysm Thrombosis Stroke Summary Review Questions Geometric Model Reconstruction Introduction Medical Image Acquistion Image Segmentation Segmentation Approaches Threshold Segmentation Edge Based Segmentation Region Based Segmentation Using Specialised Medical Software Surface and Volume Reconstruction Examples Abdominal Bifurcation Left Atrium Left Ventricle Summary Review Questions Fundamentals of Haemodynamics Introduction Fluid Properties of Blood Viscosity of Blood Clinical Relevance of Blood Viscosity Blood Flow Properties Shear Force Pressure Force Laminar and Turbulent Flow Introduction to Internal Pipe Flow Developing and Fully Developed Regions Laminar and Turbulent Velocity Profiles in a Pipe Poiseulle s Law Bernoulli s Equation Pressure Drop Estimates Fluid Dynamics of Blood Flow Examples Carotid Artery Bifurcation Carotid Artery Bifurcation with Stenosis Curved Flow in Aortic Arch Aneursym in Abdominal Aorta Summary Review Questions... 94

3 Contents xiii 5 Computational Fluid Structure Interaction Introduction Introduction to Fluid Dynamics Mass Conservation Momentum Conservation Introduction to Turbulence Introduction to Solid Mechanics Elasticity Plane Stress Structural Dynamics Equations Elastic Properties of Arteries Computational Methods Finite Difference Method Finite Volume Method One-Dimensional Steady State Convection-Diffusion in Finite Volume Finite Element Method (FEM) Numerical Solution of Algebraic Systems Direct Solution Methods Iterative Methods Solution for a One-Dimensional Steady Diffusion Equation Fluid-Structure Interactions (FSI) FSI in Computational Haemodynamics Coupling Stability and Convergence Summary Review Questions Generation of Computational Mesh for Haemodynamics Analysis Introduction Meshing Topology Mesh Configurations Structured Mesh Body-Fitted Mesh Multi-Block Mesh Unstructured Mesh Delaunay Triangulation Quadtree/Octree Subdivision Advancing Front Connectivity Comparisons Between Structured and Unstructured Mesh Mesh Terminology Dynamic Meshing Mesh Generation Mesh Quality Mesh Design Strategy

4 xiv Contents Local Refinement and Solution Adaptation Mesh Independence Meshing Examples Flow in Blood Vessel Mesh Blocking Strategies Stenosed Artery Step-By-Step Left Coronary Artery Bifurcation Step-By-Step Summary Review Questions Case Studies of the Human Cardiovascular System Introduction Haemodynamics of a Stenosed Carotid Bifurcation Physiologically Realistic Geometrical Reconstruction from MRI Computational Mesh Generation Computational Fluid Modelling Experimental Validation Flow Visualisation Comments on Modelling Issues Downstream peripheral vascular impedance modelling Closure Comparison Analysis of Patient Specific Carotid Bifurcation Models Medical Image Reconstruction of Patient-Specific Arteries Comparison of Anatomical Geometries Comparison of Wall Shear Stress Computational Models Comparison of Haemodynamic Properties Closure Analysis of Stented Artery Based on Intra-Aneurysmal Flow Simulation Configuration of Aneurysm Stenting Modes of Aneurysmal Flow Computational Modelling and Numerical Details Aneurysmal Flow Results Parametric Study for Design of Stent in Aneurysm In-Vitro Flow Measurement of an Aneurysm, Based on PIV Closure Analysis of Blood Flow in Cardiac Chamber Introduction to Heart Chamber Flow Visualisation Application of Medical Imaging in Computational Heart Modelling

5 Contents xv Comparison of CFD and PC-MRI Vorticity Fields Computational Haemodynamics Analysis of Heart Chamber Closure Intra-Atrial Flow and Mitral Plane Velocity Profile Left Atrium Models Computational Model Setup Results Closure Summary Review Questions Applications of FSI for Cardiovascular Haemodynamics Introduction Flow in an Idealised Stenotic Artery Bifurcation Computational Considerations Simulation Details FSI Analysis of Diseased Carotid Bifurcation Comparison Between FSI and Non-FSI Models Closure Flow in a Realistic Carotid Artery Bifurcation Geometric Models and Material Properties Haemodynamics Inside the Healthy Carotid Artery Closure Flow in the Left Coronary Artery Geometric Models and Material Properties Mesh Generation and Physiological Boundary Conditions Mechanical Results Analysis Haemodynamic Results Analysis Closure Analysis of Calcified Plaque Calcified Plaque Models Boundary Conditions and Material Properties Two-Dimensional Structural Modelling Three-Dimensional Fluid-Structure Interaction Modelling Correlations Between Plaque Progression and Wall Shear Stress Mechanical Stresses in 2D Carotid Plaque Closure Flow in a Realistic Aortic Aneurysm Geometric Models and Material Properties Haemodynamics Inside the Abdominal Aortic Aneurysm Closure

6 xvi Contents 8.7 Coronary and Abdominal Arterial Bypass Grafts Geometric Configurations and Computational Details Flow Patterns and Wall Deformation in Coronary Bypass Graft Flow Patterns and Wall Deformation in Abdominal Arterial Bypass Grafts Closure Mitral Valve Dynamics Introduction Asymmetric Mitral Valve Dynamics During Diastolic Filling Closure Summary Advanced Topics and Future Trends Introduction Blood Rheology Multiphase Flow Direct Numerical Simulations of Blood Cells Blood Rheology in Large Arteries Using Lattice Boltzman Medical Imaging for Flow Validation and Analysis Imaging for Flow Validation Imaging for Flow Analysis MRI Flow Imaging Ventricular Assist Devices Simulation-Based Virtual Surgery Advanced Heart Valve Modelling Summary Appendix Bibliography Index

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