Coronary Circulation, 1st ed. 2019 Anatomy, Mechanical Properties, and Biomechanics

This comprehensive text examines both global and local coronary blood flow based on morphometry and mechanical properties of the coronary vasculature. Using a biomechanical approach, this book addresses coronary circulation in a quantitative manner based on models rooted in experimental data that account for the various physical determinants of coronary blood flow including myocardial-vessel interactions and various mechanisms of autoregulation. This is the first text dedicated to a distributive analysis (as opposed to lumped) and provides digital files for detailed anatomical data (e.g., diameters, lengths, node-to-node connections) of the coronary vessels. This book also provides appendices with specific mathematical formulations for the biomechanical analyses and models in the text. Written by Dr. Ghassan S. Kassab, a leader in the field of coronary biomechanics, Coronary Circulation: Anatomy, Mechanical Properties, and Biomechanics is a synthesis of seminal topics in the field and is intended for clinicians, bioengineers, and researchers as a compendium on the topic. The detailed anatomical and mechanical data provided are intended to be used as a platform to address new questions in this exciting and clinically very important research area.

Coronary Circulation: Anatomy, Mechanical Properties, and Biomechanics

Preface

Overview, Scope, Goal of Book, Acknowledgments

Chapter 1: Biomechanics

1.1 Introduction

1.2 Basic Terminology in Biomechanics

Stress,

Strain

Compliance, Stiffness, Distensibility, and Young’s Modulus,

Viscoelasticity

1.3 Approach

1.4 Structure and Geometry

1.5 Material Properties

1.6 Laws of Mechanics

1.7 Boundary Conditions

1.8 Boundary Value Problems

1.9 Solution of Boundary Value Problems

Computational Fluid Dynamics

Finite Element Method, Fluid-Structure Interaction

ALE Formulation for Fluid-Structure-Interaction

Immersed Boundary (IB) Method

Chapter 2: Morphometry of Coronary Vasculature

2.1 Introduction

2. 2Coronary Vasculature

2.3 Reduction of Coronary Vasculature

Casting Material

Animal and Isolated Heart Preparation

Polymer Cast of Coronary Vasculature

Histological and Cast Specimens

Morphometric Measurements

Diameter-Defined Strahler System

Meshing of Histological and Cast Data

Segments and Elements

Connectivity Matrix

Longitudinal Position Matrix

Asymmetry Ratios

Counting Total Number of Elements

Arcade-Like Vessels: Epicardial Veins

Network-Like Vessels: Capillaries

Diameters and Lengths of Capillary Segments

Topology of Arteriolar and Venular Zones and Mean Functional Capillary Length

2. 4 Integration of 3D Coronary Vasculature

Node to Node Computer Reconstruction of Coronary Network

Anatomical Input Files

Statistical 3DReconstruction of Coronary Vasculature

Existing database and Additional Assumptions

Reconstruction Approach

Geometric Optimization

Verification of Coronary Network

2.5 Non-Tree Structures

2.6 Labor Savings in Morphological Reconstruction

2.7 Automation: Segmentation and Centerline Detection

Image Processing

Segmentation of Vessel Boundary

Segmentation under Topological Control

Centerline Detection

Vector Field

Determination of the Centerlines

Geometric Reconstruction

2.8 Grid Generation

Element Quality

2.9 Visualization of Reconstructed Network

2.10 Patient Specific Coronary Morphometry

Chapter 3: Mechanical Properties and Microstructure of the Coronary Vasculature

3.1 Introduction

3.2 Compliance, Distensibility, and Stiffness

Epicardial Arteries

Capillaries

3.3 Effect of Surrounding Tissue: Radial Constraint and Tethering

Pressure-Cross Sectional Area Relation

Pressure-Volume Relation

Slackness between Vessels and Myocardium

3.4 Zero-Stress State

Circumferential Residual Strain

Longitudinal Distribution of Mean Stress and Strain

Transmural Wall Strain Distribution

Effect of No-Load Duration on Opening Angle

Effect of Osmolarity on Zero-Stress State

Axial Residual Strain

3.5 Tri-axial Testing of Coronary Arteries

Two-Layer Model

3.6 Active Mechanical Properties

Isovolumic Myography

3.7 Ultrastructure of Coronary Arteries

Intima

Media

Adventitia

Collagen and Elastin

Ground Substance

Histology

Multi-Photon Microscopy

Morphometry of coronary adventitia

Simultaneous mechanical loading-imaging

Morphometry of elastin and collagen fibers at no-distension state

In situ deformation of elastin and collagen fibers

Morphometry of coronary Media

Automation of Smooth Muscle Cell Measurements

In situ deformation of Smooth Muscle Cells  

Chapter 4: Constitutive Models of Coronary Vasculature

4.1 Introduction

4.2 Phenomenological Constitutive Models

Shear Modulus

Incremental Moduli

Strain Energy Function (SEF)

2D and 3D SEF Fung Model

Bilinear Model – Generalized Hooke’s Law

Shear Modulus

Incompressibility Condition

Linear Viscoelasticity and Maxwell’s Model

Artery

Opening Angle

Active Properties

4.3 Microstructure-based Constitutive models

Comparison of microstructural models

4.4 Microstructural models of Coronary Artery

Adventitia

Uniform field models – Behavior of Ground Substance

3D Microstructural model of coronary adventitia

Media

Integrated 3D Model of Coronary Artery Wall

Case I

Case II

Case III

Chapter 5:Network Analysis of Coronary Circulation: I. Steady State Flow

5.1 Introduction

5.2 Steady State Coronary Blood Flow

Longitudinal Pressure and Flow Distributions

Coronary Arterial Tree Model: Statistical Connectivity

Coronary Arterial Tree Model: Node-to-Node Connectivity

Spatial Heterogeneity of Coronary Flow

Steady Flow Analysis in a 3D Coronary Arterial Model

Flow Heterogeneity with Fractal Nature

Role of Vascular Compliance

Pressure-Flow Relation in Single Coronary Artery

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

Capillary Network Flow Analysis

Venous Network Flow Analysis

5.3 Structure-Function Relation

Transition from “Distributing” to “Delivering” Vessels

Transition from “Conduction” to “Transport”

Possible Mechanisms for Functional Hierarchy

Significance of Functional Hierarchy

Chapter 6: Network Analysis of Coronary Circulation: II. Pulsatile Flow

6.1 Introduction

6.2 Pulsatile Flow in Coronary Vasculature

Pulsatile Flow Experiments in Passive Hearts

Womersley-Type Model

Low Frequency Flow Model Compared with Steady-State Flow

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

Hybrid One-Dimensional/Womersley Model

Pressure Boundary Conditions at the Inlet of LAD and LCx Arteries

Effect of Energy Loss at Bifurcation

6.3 Myocardial-Vessel Interaction Flow

Models of Coronary Vasculature

Intramyocardial Pressure (IMP)

Lumped Models

Distributive Models

Vessel Elasticity

MVI Model

Anatomical Model

Single Vessel Flow Model

Network Flow Model

Model Predictions

Phasic Changes

Test of MVI Mechanisms

6.4 Coronary Flow Regulation

Coronary Autoregulation

Models of Autoregulation

Perfusion Dispersion

Transmural Perfusion Heterogeneity

Metabolic Flow Reserve (MFR)

Effect of Regulation on the Coronary Flow

Model Predictions

Effect of MVI

Model Sensitivity

Myogenic sensitivity

Shear Sensitivity

Metabolic Sensitivity

Order Dependence of the Metabolic Diameter Regulation

Model Validations

Novel Model Predictions

Chapter 7:  Scaling Laws of Coronary Vasculature

7.1 Introduction

7.2 Murray’s Law

7.3 Zhou, Kassab, and MolloiZKM Model

Validation of ZKM Model

Experimental Validations

Computational Validations

7.4 Validation of Scaling Laws in Other Vascular Trees

Optimal Power Dissipation

Vascular Metabolic Dissipation of Blood Vessel Wall

7.5 Scaling Law of Flow Resistance

7.6 Scaling of Myocardial Mass

7.7 Scaling Law of Vascular Blood Volume

Comparison with ZKM Model

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

Flow Scales with Capillary Numbers

Crown Volume Scales with Capillary Number

Crown Length Scales with Capillary Number

Transit Time Scales with Crown Volume and Length

7.9 Other Design Features of Vascular Trees

7.10 Fractal Description of Branching Pattern

7.11 Intraspecific Scaling Laws of Vascular Trees

7.12 Constructal Law

Chapter 8: Local Coronary Flow and Stress Distribution

8.1 Introduction         

8.2 Local Coronary Flow Analysis

Flow in LAD Artery Trunk

Flow near Bifurcations

Effect of Compliance

8.3 Coronary Artery Wall Stress

Effect of Residual Stress

Effect of Surrounding Myocardium

Flow Field and Wall Shear Stress

Vessel Wall Stresses and Strains

Effect of Fluid-Solid Interaction

Effect of Axial Pre-Stretch

Microstructural 3D Model

Adventitia

Full 3D Coronary Artery Wall

Dr. Kassab received his BS (Chemical Engineering), MS (Engineering Sciences), and PhD (Bioengineering, Summa Cum Laude) from UCSD. He previously served as the Guidant Chair and Professor at Indiana/Purdue University. He is the founder and current President of California Medical Innovations Institute in San Diego.Dr. Kassab is the recipient of the NIH Young Investigator Award, AHA Established Investigator Award, Farriborz Maseeh Best Research Award, Abraham M. Max Distinguished Professor Award, Eminent Engineer Award of Tau Beta Pi Engineering Honor Society, Indiana’s President Circle Award, and Glenn IrwinChancellor Best Research Scholar Award. Dr. Kassab has published over 300full-length publications and his scientific interests encompass the biomechanics of cardiovascular and gastroenterology systems in health and disease. He also has over 250 issued or pending patents in the areas of diagnosis and treatment of heart disease, aneurysm, and obesity. Dr. Kassab’s intellectual properties have resulted in multiple start-ups and licensesto the medical device industry.

Provides a comprehensive compendium on coronary circulation that addresses coronary circulation both globally as it relates to blood perfusion of the heart muscle, as well as locally at the site of CAD initiation and progression

Covers quantitative physiology of coronary circulation, using biomechanics to couple structure with function

Includes a detailed biomechanical synthesis of coronary circulation based on a distributive analysis of measured properties of the system (anatomy, mechanical properties, and boundary conditions)