Computing the Electrical Activity in the Heart (eBook)

Joakim Sundnes, Glenn Terje Lines, Xing Cai, Bjørn Frederik Nielsen, Kent-Andre Mardal, Aslak Tveito (Autoren)

eBook Download: PDF

2007 | 2006
XII, 318 Seiten
Springer Berlin (Verlag)
978-3-540-33437-8 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 26.6.2007
• Reihe/Serie: Monographs in Computational Science and Engineering
• Reihe/Serie: Monographs in Computational Science and Engineering
• Zusatzinfo: XII, 318 p. 99 illus., 18 illus. in color.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Medizin / Pharmazie ► Medizinische Fachgebiete ► Innere Medizin
• Themenwelt: Technik
• Schlagworte: Computational Biology • heart simulations • Inverse Problems • Numerical Methods • Partial differential equations • Scientific Computing • Simulation
• ISBN-10: 3-540-33437-8 / 3540334378
• ISBN-13: 978-3-540-33437-8 / 9783540334378