Sundnes / Cai / Mardal Computing the Electrical Activity in the Heart

1. Auflage 2007
ISBN: 978-3-540-33437-8
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 318 Seiten

The heart is a fantastic machine; during a normal lifetime it beats about 2.5 billion times and pumps 200.000 tons of blood through an enormous system of vessels extending 160.000 kilometres throughout the body. For centuries, man has tried to understand how the heart works, but there remain many unsolved problems, problems that have captured the attention of thousands of researchers worldwide. There is, for example, a huge amount of research being devoted to the analysis of single heart cells. Other areas of research include trying to understand how it works as a complete muscle, and how blood ows through the heart. The entire process is extremely complex. The history of bioelectricity can be traced back to the late eighteenth century and the experiments of Luigi Galvani. A century later, in 1887, Augustus Wallers managed to measure the electrical signal generated by the heart at the surface of the body [142]. His dog Jimmy earned a place in history by being the rst to have his heart measured in this way; see Figure 1.1. In 1903 Willem Einthoven [34] - veloped the rst commercial device for recording electrocardiograms (ECGs); see Figure 1.2.

Autoren/Hrsg.

Sundnes, Joakim

Cai, Xing

Mardal, Kent-Andre

Tveito, Aslak

Inhaltsverzeichnis

1;Preface;5
2;Table of Contents;7
3;Physiological Background;12
3.1;1.1 The Electrocardiogram;13
3.2;1.2 Computer Simulations;25
4;Mathematical Models;31
4.1;2.1 Modelling the Body as a Volume Conductor;31
4.2;2.2 A Model for the Heart Tissue;34
4.3;2.3 Coupling the Heart and the Body;42
4.4;2.4 Models for the Ionic Current;43
4.5;2.5 Summary of the Mathematical Model;63
5;Computational Models;67
5.1;3.1 The Finite Element Method for the Torso;67
5.2;3.2 The Heart Equations;80
5.3;3.3 Coupling the Heart and the Torso;92
5.4;3.4 Numerical Experiments;95
6;Solving Linear Systems;108
6.1;4.1 Overview;108
6.2;4.2 Iterative Methods;109
6.3;4.3 The Conjugate Gradient Method;125
6.4;4.4 Multigrid;132
6.5;4.5 Domain Decomposition;137
6.6;4.6 Preconditioning Revisited;142
6.7;4.7 The Monodomain Model;149
6.8;4.8 The Bidomain Model;151
7;Solving Systems of ODEs;157
7.1;5.1 Simple ODE Solvers;157
7.2;5.2 Higher-Order Methods;162
7.3;5.3 Solving Nonlinear Equations;168
7.4;5.4 Automatic Time Step Control;172
7.5;5.5 The Cell Model Equations;176
8;Large-Scale Electrocardiac Simulations;182
8.1;6.1 The Electrocardiac Simulator;182
8.2;6.2 Requirements for Large-Scale Simulations;184
8.3;6.3 Introduction to Parallel Computing;188
8.4;6.4 Two Simple Examples;193
8.5;6.5 Domain-Based Parallelization;198
8.6;6.6 Explicit FDM in Parallel;204
8.7;6.7 Parallel Conjugate Gradient Iterations;208
8.8;6.8 Domain Decomposition as Parallel Preconditioners;214
8.9;6.9 Parallelizing Electrocardiac Simulations;219
8.10;6.10 Simulation on a Realistic Geometry;222
8.11;6.11 Summary;223
9;Inverse Problems;226
9.1;7.1 A Simple Example;228
9.2;7.2 The Classical Inverse Problem of Electrocardiography;245
9.3;7.3 Identifying a Simplified Source - Computing the Location and Orientation of a Dipole;260
9.4;7.4 Computing the Size and Location of a Myocardial Infarction;278
10;Color Figures;293
11;Rate Functions and Ionic Currents;303
11.1;B.1 The Hodgkin-Huxley Model;303
11.2;B.2 The Noble Model for Purkinje Cells;303
11.3;B.3 The Beeler-Reuter Model;304
12;Coefficients for the Implicit RK Solvers;306
13;Bibliography;307
14;Index;314