High-Performance Computing in Biomedical Research

Theo C. Pilkington, Bruce Loftis, Thomas Palmer, Thomas F. Budinger

• Publisher: CRC Press
• Year: 2020
• Print ISBN: 9780849344749
• eBook ISBN: 9781000141504
• Topic: Biological Sciences
• Subtopic: Biology
• Index: Biological Sciences

Leading researchers have contributed state-of-the-art chapters to this overview of high-performance computing in biomedical research. The book includes over 30 pages of color illustrations. Some of the important topics featured in the book include the following:

Part I: Anatomical Heart Models and Mechanics

Chapter 1

AN ANATOMICAL HEART MODEL WITH APPLICATIONS TO MYOCARDIAL ACTIVATION AND VENTRICULAR MECHANICS

Peter J. Hunter, Poul M. F. Nielsen, Bruce H. Smaill, Ian J. LeGrice, and Ian W. Hunter

TABLE OF CONTENTS

I.	Introduction
II.	Prolate Spheroidal Coordinates
III.	Finite Element Basis Functions
IV.	Ventricular Geometry
V.	The Muscular Architecture of the Ventricles
VI.	Muscle Fiber Orientations
VII.	Myocardial Sheet Organization
VIII.	Purkinje Fibers and Coronary Vessels
IX.	Orthotropic Constitutive Laws
X.	Summary

References

ABSTRACT

A three-dimensional finite element model of the mechanical and electrical behavior of the heart is being developed in a collaboration among Auckland University, New Zealand; the University of California at San Diego, U.S.; and McGill University, Canada.

The equations of continuum mechanics from the theory of finite deformation elasticity are formulated in a prolate spheroidal coordinate system and solved using a combination of Galerkin and collocation techniques. The finite element basis functions used for the dependent and independent variables range from linear Lagrange to cubic Hermite, depending on the degree of spatial variation and continuity required for each variable. Orthotropic constitutive equations derived from biaxial testing of myocardial sheets are defined with respect to the microstructural axes of the tissue at the Gaussian quadrature points of the model. In particular, we define the muscle fiber orientation and the newly identified myocardial sheet axis orientation throughout the myocardium using finite element fields with nodal parameters fitted by least-squares to comprehensive measurements of these variables. Electrical activation of the model is achieved by solving the FitzHugh–Nagumo equations with collocation at fixed material points of the anatomical finite element model. Electrical propagation relies on an orthotropic conductivity tensor defined with respect to the local material axes. The mechanical constitutive laws for the Galerkin continuum mechanics model are (1) an orthotropic “pole–zero” law for the passive mechanical properties of myocardium and (2) a Wiener cascade model of the active mechanical properties of the muscle fibers.

This chapter concentrates on two aspects of the model: first, grid generation, including both the generation of nodal coordinates for the finite element mesh and the generation of orthotropic material axes at each computational point, and, second, the formulation of constitutive laws suitable for numerically intensive finite element computations. Extensions to this model and applications to the mechanical and electrical function of the heart are described in Chapter 2 by McCulloch and co-workers.

I. INTRODUCTION

Two recent developments, one in numerical analysis and the other in computer hardware, have provided the tools for a powerful new approach to solving an age-old problem: How does the heart beat and what should be done when it fails? First, the development of the finite element method of numerical analysis has enabled the complex anatomy of the heart to be described mathematically in a form that can be coupled with well-established physical laws governing both the mechanics and the electrical activity of deformable excitable media. Second, computer workstations capable of solving the resulting equations and displaying the time-dependent threedimensional modeling results are now available. When combined with currently available technology for clinically imaging the heart, these mathematical modeling tools offer exciting opportunities for real progress in the diagnosis and treatment of heart disease.

In this chapter, we argue that the problem of three-dimensional grid generation in cardiac modeling involves a great deal more than simply providing an accurate representation of the geometry of the heart. It is necessary to develop mathematical formulations that can incorporate appropriate descriptions of relevant cardiac anatomy at both the macroscopic and the microscopic levels. The electrical and mechanical properties of cardiac tissue are inhomogeneous and anisotropic, and the anisotropy is closely associated with the local organization of cardiac muscle cells. Although the muscular architecture of the heart is complex and spatially varying, it is nonetheless surprisingly well ordered, and we are developing a clear understanding of its hierarchical organization. As a result, it is possible to identify material axes for the formulation of constitutive laws based on local microstructure and to characterize the spatial variation of these material coordinate axes throughout the heart walls.

A solution of the governing equations on the computational heart mesh requires that the material constitutive laws be defined at the Gaussian quadrature or collocation points of...

Table of contents

• Cover
• Title Page
• Copyright Page
• Preface
• Acknowledgments
• Editors
• Contributors
• Table of Contents
• Part I: Anatomical Heart Models and Mechanics
• Part II: Grids and Bioelectric Models
• Part III: Inverse Problems and Computational Methods
• Part IV: Distributed Computing and Biomechanics
• Part V: HPC and Cardiac Electrophysiology
• Part VI: HPC and Visualization
• Part VII: The Future
• Index