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Computing the Electrical Activity in the Heart

:	Joakim Sundnes, Glenn Terje Lines, Xing Cai, Bjørn Frederik Nielsen, Kent-Andre Mardal, Aslak Tveito
:	Computing the Electrical Activity in the Heart
:	Springer-Verlag
:	9783540334378
:	1
:	CHF 97.30
:

:	Allgemeines, Lexika
:	English

:	318
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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.

	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