Coronary Circulation

<p>Coronary Circulation: Anatomy, Mechanical Properties, and Biomechanics</p>

<p>Preface</p>

<p>Overview, Scope, Goal of Book, Acknowledgments</p>

<p>Chapter 1: Biomechanics<br></p>

<p>1.1 Introduction</p>

<p>1.2 Basic Terminology in Biomechanics </p>

<p>Stress, </p>

<p>Strain</p>

<p>Compliance, Stiffness, Distensibility, and Young’s Modulus, </p>

<p>Viscoelasticity</p>

<p>1.3 Approach</p>

<p>1.4 Structure and Geometry</p>

<p>1.5 Material Properties</p>

<p>1.6 Laws of Mechanics</p>

<p>1.7 Boundary Conditions</p>

<p>1.8 Boundary Value Problems</p>

<p>1.9 Solution of Boundary Value Problems</p>

<p>Computational Fluid Dynamics</p>

<p>Finite Element Method, Fluid-Structure Interaction</p>

<p>ALE Formulation for Fluid-Structure-Interaction</p>

<p>Immersed Boundary (IB) Method</p><p><br></p>

<p>Chapter 2: Morphometry of Coronary Vasculature<br></p>

<p>2.1 Introduction</p>

<p>2. 2 Coronary Vasculature</p>

<p>2.3 Reduction of Coronary Vasculature</p>

<p>Casting Material</p>

<p>Animal and Isolated Heart Preparation</p>

<p>Polymer Cast of Coronary Vasculature</p>

<p>Histological and Cast Specimens </p>

<p>Morphometric Measurements</p><p>Diameter-Defined Strahler System</p>

<p>Meshing of Histological and Cast Data</p>

<p>Segments and Elements</p>

<p>Connectivity Matrix</p>

<p>Longitudinal Position Matrix</p>

<p>Asymmetry Ratios</p>

<p>Counting Total Number of Elements</p>

<p>Arcade-Like Vessels: Epicardial Veins</p>

<p>Network-Like Vessels: Capillaries</p>

<p>Diameters and Lengths of Capillary Segments</p>

<p>Topology of Arteriolar and Venular Zones and Mean Functional Capillary Length </p>

<p>2. 4 Integration of 3D Coronary Vasculature<br></p>

<p>Node to Node Computer Reconstruction of Coronary Network</p>

<p>Anatomical Input Files</p>

<p>Statistical 3D Reconstruction of Coronary Vasculature</p>

<p>Existing database and Additional Assumptions</p>

<p>Reconstruction Approach</p>

<p>Geometric Optimization</p>

<p>Verification of Coronary Network </p>

<p>2.5 Non-Tree Structures</p>

<p>2.6 Labor Savings in Morphological Reconstruction</p>

<p>2.7 Automation: Segmentation and Centerline Detection</p>

<p>Image Processing</p>

<p>Segmentation of Vessel Boundary</p>

<p>Segmentation under Topological Control</p>

<p>Centerline Detection</p>

<p>Vector Field</p>

<p>Determination of the Centerlines</p>

<p>Geometric Reconstruction</p>

<p>2.8 Grid Generation</p><p>Element Quality</p>

<p>2.9 Visualization of Reconstructed Network</p>

<p>2.10 Patient Specific Coronary Morphometry</p><p><br></p>

<p>Chapter 3: Mechanical Properties and Microstructure of the Coronary Vasculature<br></p><p></p>

<p>3.1 Introduction</p>

<p>3.2 Compliance, Distensibility, and Stiffness</p>

<p>Epicardial Arteries</p>

<p>Capillaries </p>

<p>3.3 Effect of Surrounding Tissue: Radial Constraint and Tethering</p>

<p>Pressure-Cross Sectional Area Relation</p>

<p>Pressure-Volume Relation</p>

<p>Slackness between Vessels and Myocardium</p>

<p>3.4 Zero-Stress State</p>

<p>Circumferential Residual Strain</p>

<p>Longitudinal Distribution of Mean Stress and Strain </p>

<p>Transmural Wall Strain Distribution</p>

<p>Effect of No-Load Duration on Opening Angle</p>

<p>Effect of Osmolarity on Zero-Stress State</p>

<p>Axial Residual Strain</p>

<p>3.5 Tri-axial Testing of Coronary Arteries</p>

<p>Two-Layer Model</p>

<p>3.6 Active Mechanical Properties</p>

<p>Isovolumic Myography</p>

<p>3.7 Ultrastructure of Coronary Arteries </p>

<p>Intima</p>

<p>Media</p>

<p>Adventitia</p>

<p>Collagen and Elastin</p>

<p>Ground Substance</p>

<p>Histology</p>

<p>Multi-Photon Microscopy</p>

<p>Morphometry of coronary adventitia </p>

<p>Simultaneous mechanical loading-imaging</p>

<p>Morphometry of elastin and collagen fibers at no-distension state</p>

<p>In situ deformation of elastin and collagen fibers </p>

<p>Morphometry of coronary Media</p>

<p>Automation of Smooth Muscle Cell Measurements</p>

<p>In situ deformation of Smooth Muscle Cells&nbsp;&nbsp; </p>

<p>&nbsp;</p>

<p>Chapter 4: Constitutive Models of Coronary Vasculature</p>

<p>4.1 Introduction</p>

<p>4.2 Phenomenological Constitutive Models</p>

<p>Shear Modulus</p>

<p>Incremental Moduli</p>

<p>Strain Energy Function (SEF)</p>

<p>2D and 3D SEF Fung Model</p>

<p>Bilinear Model – Generalized Hooke’s Law</p>

<p>Shear Modulus</p>

<p>Incompressibility Condition</p>

<p>Linear Viscoelasticity and Maxwell’s Model</p>

<p>Artery</p>

<p>Opening Angle</p>

<p>Active Properties</p>

<p>4.3 Microstructure-based Constitutive models</p>

<p>Comparison of microstructural models</p>

<p>4.4 Microstructural models of Coronary Artery</p><p>Adventitia</p>

<p>Uniform field models – Behavior of Ground Substance</p>

<p>3D Microstructural model of coronary adventitia</p>

<p>Media</p>

<p>Integrated 3D Model of Coronary Artery Wall</p>

<p>Case I</p>

<p>Case II</p>

<p>Case III</p>

<p>&nbsp;<br></p>

<p>Chapter 5: Network Analysis of Coronary Circulation: I. Steady State Flow</p>

<p>5.1 Introduction</p>

<p>5.2 Steady State Coronary Blood Flow</p>

<p>Longitudinal Pressure and Flow Distributions </p>

<p>Coronary Arterial Tree Model: Statistical Connectivity</p>

<p>Coronary Arterial Tree Model: Node-to-Node Connectivity</p>

<p>Spatial Heterogeneity of Coronary Flow</p>

<p>Steady Flow Analysis in a 3D Coronary Arterial Model</p>

<p>Flow Heterogeneity with Fractal Nature</p>

<p>Role of Vascular Compliance </p>

<p>Pressure-Flow Relation in Single Coronary Artery</p>

<p>Role of Compliance and Blood Rheology on Pressure-Flow Relation in Entire Coronary Arterial Tree</p>

<p>Capillary Network Flow Analysis</p>

<p>Venous Network Flow Analysis</p>

<p>5.3 Structure-Function Relation</p>

<p>Transition from “Distributing” to “Delivering” Vessels</p>

<p>Transition from “Conduction” to “Transport”</p>

<p>Possible Mechanisms for Functional Hierarchy</p>

<p>Significance of Functional Hierarchy</p>

<p>&nbsp;</p>

<p>Chapter 6: Network Analysis of Coronary Circulation: II. Pulsatile Flow</p>

<p>6.1 Introduction</p>

<p>6.2 Pulsatile Flow in Coronary Vasculature</p>

<p>Pulsatile Flow Experiments in Passive Hearts</p>

<p>Womersley-Type Model</p>

<p>Low Frequency Flow Model Compared with Steady-State Flow</p>

<p>Experimental Validation of Womersley ModelEffect of Various Parameters (e.g., Wave Frequency, Branching Asymmetry, etc.) on Pulsatile Blood Flow</p>

<p>Hybrid One-Dimensional/Womersley Model</p>

<p>Pressure Boundary Conditions at the Inlet of LAD and LCx Arteries</p>

<p>Effect of Energy Loss at Bifurcation</p>

<p>6.3 Myocardial-Vessel Interaction Flow</p>

<p>Models of Coronary Vasculature</p>

<p>Intramyocardial Pressure (IMP)</p>

<p>Lumped Models</p>

<p>Distributive Models</p>

<p>Vessel Elasticity</p>

<p>MVI Model</p>

<p>Anatomical Model</p>

<p>Single Vessel Flow Model</p>

<p>Network Flow Model</p>

<p>Model Predictions</p>

<p>Phasic Changes</p>

<p>Test of MVI Mechanisms</p>

<p>6.4 Coronary Flow Regulation</p>

<p>Coronary Autoregulation</p>

<p>Models of Autoregulation</p>

<p>Perfusion Dispersion</p>

<p>Transmural Perfusion Heterogeneity</p>

<p>Metabolic Flow Reserve (MFR)</p>

<p>Effect of Regulation on the Coronary Flow</p>

<p>Model Predictions</p>

<p>Effect of MVI</p>

<p>Model Sensitivity</p>

<p>Myogenic sensitivity</p>

<p>Shear Sensitivity</p>

<p>Metabolic Sensitivity</p>

<p>Order Dependence of the Metabolic Diameter Regulation</p>

<p>Model Validations</p>

<p>Novel Model Predictions </p>

<p>&nbsp;</p>

<p>Chapter 7:&nbsp; Scaling Laws of Coronary Vasculature<br></p>

<p>7.1 Introduction </p>

<p>7.2 Murray’s Law</p>

<p>7.3 Zhou, Kassab, and Molloi ZKM Model</p>

<p>Validation of ZKM Model</p>

<p>Experimental Validations</p>

<p>Computational Validations</p>

<p>7.4 Validation of Scaling Laws in Other Vascular Trees</p>

<p>Optimal Power Dissipation</p>

<p>Vascular Metabolic Dissipation of Blood Vessel Wall</p>

<p>7.5 Scaling Law of Flow Resistance</p>

<p>7.6 Scaling of Myocardial Mass </p>

<p>7.7 Scaling Law of Vascular Blood Volume </p>

<p>Comparison with ZKM Model</p>

<p>7.8 Scaling laws of flow rate, vessel blood volume, vascular lengths, and transit times with number of capillaries</p>

<p>Flow Scales with Capillary Numbers</p>

<p>Crown Volume Scales with Capillary Number</p>

<p>Crown Length Scales with Capillary Number</p>

<p>Transit Time Scales with Crown Volume and Length</p>

<p>7.9 Other Design Features of Vascular Trees</p>

<p>7.10 Fractal Description of Branching Pattern </p>

<p>7.11 Intraspecific Scaling Laws of Vascular Trees </p>

<p>7.12 Constructal Law</p>

<p>&nbsp;<br></p>

<p>Chapter 8: Local Coronary Flow and Stress Distribution</p>

<p>8.1 Introduction&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </p>

<p>8.2 Local Coronary Flow Analysis</p>

<p>Flow in LAD Artery Trunk</p>

<p>Flow near Bifurcations</p>

<p>Effect of Compliance</p>

<p>8.3 Coronary Artery Wall Stress</p>

<p>Effect of Residual Stress </p>

<p>Effect of Surrounding Myocardium</p>

<p>Flow Field and Wall Shear Stress</p>

<p>Vessel Wall Stresses and Strains</p>

<p>Effect of Fluid-Solid Interaction</p>

<p>Effect of Axial Pre-Stretch </p>

<p>Microstructural 3D Model </p>

<p>Adventitia</p>

<p>Full 3D Coronary Artery Wall</p>