Computational Cardiovascular Mechanics (eBook)

Preface 5
Contents 6
Contributors 8
Introduction 11
1 Heart Failure 11
2 Cardiac Surgery 12
3 New Devices and Operations 13
3.1 Mechanical Circulatory Support 13
3.2 Surgical Remodeling 14
3.3 Passive Constraint 15
4 Remaining Problems 15
4.1 Emboli from Intravascular Devices 16
4.2 The Effect of Device Therapy on Ventricular Function 16
5 Cardiovascular Applications of the Finite Element Method 16
5.1 A Brief History 16
6 Computational Fluid Dynamics 18
6.1 A Brief History 18
6.2 Applications to Cardiovascular System 19
7 Our Method of Approach 19
8 Introduction to Book Chapters 20
9 Future Directions 22
References 22
Part I Computational Modeling of Cardiovascular Mechanics 26
1 In Vivo Left Ventricular Geometry and Boundary Conditions 27
1.1 Introduction 27
1.2 Anatomy of a Good Grid 28
1.3 Mesh Generation of an Axisymmetric Truncated Ellipsoid Using TrueGrid 29
1.4 Mesh Generation of an Axisymmetric Truncated Ellipsoid with Polymeric Injections Using TrueGrid 11
1.5 Mesh Generation of a Full 3-D Non-axisymmetric LV Using TrueGrid 12
1.5.1 Contouring the Epicardium and Endocardium of the Left Ventricle 34
1.5.2 Defining Aneurysm, Border Zone and Remote Regions, and Converting 2-D Contour Data to 3-D Data 13
1.5.3 Generating IGES Curves for Different Material Areas and IGES Surface for Endocardium and Epicardium 14
1.5.4 Creation of FE Mesh Using TrueGrid ® and Closer 15
1.6 Create FEA Mesh Using LaGriT-PNNL and MeshMAGIC 15
1.7 A Brief Discussion of Governing Equations and Boundary Conditions 42
References 22
2 Imaging-Based Assessment and Modeling of the Structures of the Myocardium 46
2.1 Introduction 46
2.2 Principles of MR Diffusion Tensor Imaging 47
2.2.1 Basis of Diffusion Encoding in MRI 47
2.2.2 Anisotropic Diffusion Measurements by MRI 48
2.2.3 Strategies and Practical Considerations of DTI 50
2.3 DTI Assessments of Myocardial Structures 51
2.3.1 Prior Developments 51
2.3.2 Histological Validation of DTI Measurements of Myocardial Fiber Orientation 51
2.3.3 DTI of Normal Hearts 52
2.3.4 DTI and the Myocardial Laminar Structure 53
2.3.5 Scalar DTI Measurements and Myocardial Structure 54
2.3.6 DTI of Diseased Hearts 55
2.3.7 In Vivo DTI of the Beating Heart 56
2.4 Applications of MR Diffusion Tensor Imaging 56
2.4.1 Image-to-Grid Mapping of MR-DTI Data 56
2.4.2 Anatomical and Pathological Variations in Fiber Organization 58
2.5 Future Directions 59
References 60
3 Constitutive Equations and Model Validation 63
3.1 Introduction 63
3.2 Passive Material Properties of Intact Ventricular Myocardium Determined from a Cylindrical Model 64
3.3 Mechanics of Active Contraction in Cardiac Muscle 65
3.4 Constitutive Relations for Fiber Stress That Describe Deactivation 65
3.5 Cylindrical Models of the Systolic Left Ventricle 67
3.6 The Effects of Cross-Fiber Deformation on Axial Fiber Stress in Myocardium 72
3.7 Experimental Measurements Used to Validate Regional Ventricular Mechanics Models 73
References 75
4 Determination of Myocardial Material Propertiesby Optimization 77
4.1 Introduction 77
4.2 Epicardial Suction: An Approach to Mechanical Testing of the Passive Ventricular Wall 78
4.3 Akinetic Myocardial Infarcts Must Contain Contracting Myocytes, Material Parameter Estimation 80
4.4 Informal Optimization of Regional Myocardial Contractility in a Sheep with Left Ventricular Aneurysm 85
4.5 A Computationally Efficient Formal Optimization of Regional Myocardial Contractility in a Sheep with Left Ventricular Aneurysm 87
4.6 Future Directions 92
References 93
5 Computational Models of Cardiac Electrical Activation 95
5.1 Introduction 95
5.2 Modeling History 96
5.3 Major Components of Electrical Models 97
5.3.1 The Cardiac Source Model 98
5.3.2 The Volume Conductor Model 99
5.3.3 Model Assumptions 99
5.3.4 Model Theory 99
5.4 Forward Models of Electrocardiography 101
5.5 The Inverse Problem of Electrocardiography 102
5.6 Limitations of Forward and Inverse Models 102
5.7 Clinical Application of Inverse Models 104
5.8 Future Directions for Electrical Modeling 105
5.9 Conclusion 107
References 107
6 Geometrical Features of the Vascular System 111
6.1 Introduction 111
6.2 Significance of Vessel Geometry 112
6.3 Coronary Vasculature 112
6.3.1 Reduction of Coronary Morphology 113
6.3.2 Integration of Coronary Vasculature 114
6.4 StructureFunction Relation 114
6.4.1 Volume Scaling 117
6.4.2 Resistance Scaling 117
6.5 Functional Hierarchy 118
6.5.1 Possible Mechanisms for the Functional Hierarchy 120
6.6 Potential Clinical Applications 120
6.7 The Cardiome Project: Integration of Cardiac Structure and Function 121
6.8 Summary and Conclusions 122
References 122
7 Vascular Geometry Reconstruction and Grid Generation 125
7.1 Introduction 125
7.2 Image Processing 126
7.2.1 Segmentation of the Vessel Boundary 127
7.2.2 Segmentation Under Topological Control 128
7.3 Centerline Detection 128
7.3.1 Vector Field 130
7.3.2 Determination of the Centerlines 130
7.3.3 Geometric Reconstruction 132
7.4 Grid Generation 133
7.4.1 Definition of GLFS 134
7.4.2 Layered Anisotropic Tetrahedra 136
7.4.3 Hybrid Prismatic/Tetrahedral Grids 137
7.4.4 Element Quality 138
7.5 Summary 138
References 139
8 Governing Equations of Blood Flow and Respective Numerical Methods 142
8.1 Introduction to Computational Fluid Dynamics 142
8.2 Governing Equations 143
8.3 General CFD Methods 143
8.4 Finite Difference Method 145
8.5 Finite Element Method 148
8.5.1 Two-Dimensional Flow Patterns in the Epicardial LAD Arterial Tree 152
8.5.2 Three-Dimensional Flow Patterns in the Epicardial LAD Arterial Tree 153
8.6 Conclusion 159
References 159
9 FluidStructure Interaction (FSI) Modeling in the Cardiovascular System 161
9.1 Introduction 161
9.2 The Arbitrary Lagrangian Eulerian (ALE) Method 162
9.2.1 Governing Equations 162
9.2.2 Material Models 162
9.2.3 The ALE Formulation for Fluid--Structure Interaction 163
9.2.4 A Numerical Procedure for ALE Solutions 164
9.2.5 Alternative Approach for Treatment of Fluid with Moving Boundary 164
9.2.6 Discretization and Numerical Solution of the Discrete Equations 165
9.2.7 Formulations for Fluid--Structure Coupling 166
9.2.8 Finite Element Equations of the Coupled System 166
9.2.9 Iterative Computing of Two-Way FSI Coupling 166
9.3 The Immersed Boundary (IB) Method 167
9.3.1 Introduction 167
9.3.2 Mathematical Formulation 168
9.3.3 Discretization and Numerical Methods 169
9.4 Applications 169
9.4.1 Application of the ALE FSI to Surgical Devices 169
9.4.2 Computational Studies 170
9.4.3 Possible Injury Mechanisms 170
9.4.4 Fluid Dynamics 171
9.4.5 Application of the IB Method 172
9.4.6 Valveless Pumping 172
9.4.7 Flexible Fiber in a Flow Field 173
9.5 Conclusion 174
References 175
10 Turbulence in the Cardiovascular System: Aortic Aneurysm as an Illustrative Example 178
10.1 Introduction 178
10.2 Simulation of Aortic Aneurysm Flow 179
10.3 Simulation Results 182
10.3.1 Two-Dimensional Instantaneous Flow Field 182
10.3.2 Three-Dimensional Flow Structures 184
10.3.3 Transition to Turbulence Due to Interaction Between Vortex Ring and Aortic Wall 187
10.3.4 Time History of the Instantaneous Velocity Field 188
10.3.5 Impact of Turbulence on Shear Stress Distribution in the Flow Domain 188
10.3.6 Impact of Turbulence on WSS 190
10.3.7 Model Limitations 192
10.4 Implications 192
10.5 Future Studies 193
10.6 Summary and Conclusions 193
References 194
Part II Applications in Heart Failure 196
11 Noninvasive Assessment of Left Ventricular Remodeling: Geometry, Wall Stress, and Function 197
11.1 Introduction 197
11.1.1 Left Ventricular Structural Remodeling 198
11.1.2 Left Ventricular Functional Remodeling 199
11.1.3 Changes in Left Ventricular Wall Stress After MI 200
11.2 LV Imaging and 3D Reconstruction 202
11.3 Computation of 3D Surface Shape Descriptors 202
11.3.1 Local Surface Patch Fitting 203
11.3.2 Computation of LV Surface Curvatures 206
11.4 Regional Peak Systolic Wall Stress and Wall Thickening 208
11.5 Comparison Between Ischemic Dilated Cardiomyopathy LV and Normal LV 208
11.5.1 Global LV Function Between IDCM LV and Normal LV 208
11.5.2 Variation of Curvedness, Peak Systolic Wall Stress, and Wall Thickening from Base to Apex in Normal LV 209
11.5.3 Comparison of Curvedness, Peak Systolic Wall Stress, and Wall Thickening in Ischemic Cardiomyopathy LV and Normal LV 211
11.6 Summary 212
References 212
12 Surgical Left Ventricular Remodeling Procedures 215
12.1 Introduction 215
12.2 Residual Stress Produced by Ventricular Volume Reduction Surgery Has Little Effect on Ventricular Function and Mechanics 215
12.3 Effect of Ventricular Size and Patch Stiffness in Surgical Anterior Ventricular Restoration 218
12.4 MRI-Based Finite Element Stress Analysis of Linear Repair of Left Ventricular Aneurysm 222
References 227
13 Passive Left Ventricular Constraint Devices 229
13.1 Introduction 229
13.2 Acorn CorCap Cardiac Support Device on the Failing Left Ventricle: Original Polyester Mesh Fabric Design 231
13.3 Acorn CorCap Cardiac Support Device on the Failing Left Ventricle: Modified Polyester Mesh Fabric Design 234
13.4 Adjustable Passive Constraint on the Failing Left Ventricle 236
13.5 Myosplint Decreases Wall Stress Without Depressing Function in the Failing Heart 239
13.6 Conclusion 240
References 243
14 Left Ventricular Implantation of Biomaterials 245
14.1 Introduction 245
14.2 FE Studies of Non-contractile Material Addition to the Infarct-Injured Ventricle 246
14.3 FE Studies of Non-contractile Material Addition to a Globally Failing Ventricle 249
14.4 A Method for Automatically Optimizing the Pattern of Injected Non-contractile Material for Treating Heart Failure 250
References 256
15 Computational Modeling of Heart Failure with Application to Cardiac Resynchronization Therapy 257
15.1 Introduction 257
15.1.1 Heart Failure 258
15.1.2 Dyssynchronous Heart Failure 258
15.1.3 Patient-Specific Modeling 259
15.2 Computational Modeling of Cardiac Electromechanics 259
15.2.1 Ventricular Anatomy and Fiber Architecture 259
15.2.2 Impulse Conduction 261
15.2.3 Cardiac Mechanics 262
15.2.3.1 Estimation of Properties from Global Measurements 263
15.2.3.2 Estimation of Properties from Regional Measurements 264
15.2.4 Scar Tissue 264
15.2.5 Hemodynamics 266
15.3 Model Prediction of CRT 266
References 267
16 Computational Modeling of Aortic Heart Valve Mechanics Across Multiple Scales 272
16.1 Introduction 272
16.2 Background on Modeling the Aortic Valve 273
16.3 Regional Differences in the Aortic Valve 277
16.4 Examining Aortic Root Compliance 279
16.5 The Importance of the Sinuses of Valsalva 281
16.6 Fiber-Reinforcement of Aortic Cusps 284
16.7 Multiscale Studies 285
16.8 Conclusion 289
References 290
17 Blood Flow in an Out-of-Plane Aorto-left Coronary Sequential Bypass Graft 293
17.1 Introduction 293
17.2 CFD Analysis 294
17.2.1 Geometry 294
17.2.2 Material Properties and Flow Conditions 295
17.2.3 Computational Setup 297
17.3 Simulation Results 297
17.3.1 Sequential Bypass Graft 297
17.3.2 Comparison of Sequential and Multiple Bypass Graft 302
17.3.3 Critique of Simulation 305
17.4 Implications and Limitations of Simulations 306
17.4.1 Patency of CABG Procedures 306
17.4.2 WSS, Spatial WSSG, and Atherosclerosis 307
17.5 Summary and Conclusions 309
References 310
18 Computational Fluid Dynamics Models of Ventricular Assist Devices 312
18.1 Introduction 312
18.2 Clinical Impact 312
18.3 History of VAD Use 313
18.4 Design Concerns with VADs 318
18.4.1 Blood Damage Models 320
18.5 CFD Modeling of VADs 321
18.5.1 Turbulence Models 322
18.5.2 Validation With Experimental Data 322
18.6 CFD Model Results 322
18.6.1 Pediatric VADs 325
18.6.2 Host--VAD Interaction 326
18.7 Conclusions 328
References 328
Index 332