E-Book, Englisch, 318 Seiten
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
ISBN: 978-3-540-33437-8
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
This book describes mathematical models and numerical techniques for simulating the electrical activity in the heart. It gives an introduction to the most important models, followed by a detailed description of numerical techniques. Particular focus is on efficient numerical methods for large scale simulations on both scalar and parallel computers. The results presented in the book will be of particular interest to researchers in bioengineering and computational biology.
Autoren/Hrsg.
Weitere Infos & Material
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
