Mathematical models and numerical methods for the forward problem in cardiac electrophysiology

Lines, Glenn Terje; Buist, Martin L.; Grøttum, Per; Pullan, Andrew J.; Sundnes, Joakim; Tveito, Aslak

doi:10.1007/s00791-003-0101-4

Cited by 81 publications

(73 citation statements)

References 110 publications

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“…A first-order (Godunov method) and a second-order (Strang method) accurate splitting technique can be employed. For more details the reader is referred to Sundnes et al (2005), Lines, Buist, Grottum, Pullan, Sundnes & Tveito (2003); , and Weber Dos Santos et al (2003)). To reduce the computational time at each time step, parallel computing techniques are used (see Colli Franzone & Pavarino (2004), Karpoukhin et al (1995) and Weber dos Santos et al (2004)).…”

Section: Introductionmentioning

confidence: 99%

Recent Numerical Methods in Electrocardiology

Belhamadia¹

2010

New Developments in Biomedical Engineering

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Section: Introductionmentioning

confidence: 99%

Recent Numerical Methods in Electrocardiology

Belhamadia¹

2010

New Developments in Biomedical Engineering

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“…For research contributions prior to 2000, the reader may wish to consult the review by Henriquez (1993), the more recent review by Lines et al (2003a) and the papers by Panfilov & Holden (1997) and Zipes & Jalife (2000). In addition, the book by Keener & Sneyd (1998) is highly recommended as a basis for understanding the material presented herein, and a general introduction to numerical methods for the bidomain model can be found in Sundnes et al (2006).…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of the bidomain equations

Linge

Sundnes

Hanslien

et al. 2009

Phil. Trans. R. Soc. A.

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Knowledge of cardiac electrophysiology is efficiently formulated in terms of mathematical models. However, most of these models are very complex and thus defeat direct mathematical reasoning founded on classical and analytical considerations. This is particularly so for the celebrated bidomain model that was developed almost 40 years ago for the concurrent analysis of extra-and intracellular electrical activity. Numerical simulations based on this model represent an indispensable tool for studying electrophysiology. However, complex mathematical models, steep gradients in the solutions and complicated geometries lead to extremely challenging computational problems. The greatest achievement in scientific computing over the past 50 years has been to enable the solving of linear systems of algebraic equations that arise from discretizations of partial differential equations in an optimal manner, i.e. such that the central processing unit (CPU) effort increases linearly with the number of computational nodes. Over the past decade, such optimal methods have been introduced in the simulation of electrophysiology. This development, together with the development of affordable parallel computers, has enabled the solution of the bidomain model combined with accurate cellular models, on geometries resembling a human heart. However, in spite of recent progress, the full potential of modern computational methods has yet to be exploited for the solution of the bidomain model. This paper reviews the development of numerical methods for solving the bidomain model. However, the field is huge and we thus restrict our focus to developments that have been made since the year 2000.

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“…The extensive development of numerical methods and computer hardware has made the study of very complex models possible, including detailed models of cardiac muscle cells and ion channels, cardiac and non-cardiac tissues (biodomains), and the three dimensional gross anatomy of the thorax 2 . Notable examples of complex solutions to the forward problem include those of Plonsey 3 , Geselowitz 4 , Rudy 5 , Gulrajani 6 , Selvester 7 , Barr 8 , Gelernter and Swihart 9 (1964), and Miller and Geselowitz 10 .…”

Section: Introductionmentioning

confidence: 99%

“…Such approaches to solving the forward problem include dozens to hundreds of equations and thousands to hundreds of thousands of finite elements of tissue in three-dimensional space 2 . These models have become exercises in sophisticated computer science far beyond the usual domains of physiology and medicine.…”

Section: Introductionmentioning

confidence: 99%

Quantitative Prediction of Body Surface Potentials from Myocardial Action Potentials Using a Summed Dipole Model

Babbs

2009

Cardiovasc Eng

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This paper demonstrates quantitatively, using streamlined mathematics, how the transmembrane ionic currents in individual cardiac muscle cells act to produce the body surface potentials of the electrocardiogram (ECG). From fundamental principles of electrostatics, anatomy, and physiology, one can characterize the strength of apparent dipoles along a wavefront of depolarization in a local volume of myocardium. Net transmembrane flow of ionic current in actively depolarizing or repolarizing tissue induces extracellular current flow, which sets up a field of electrical potential that resembles that of a dipole. The local dipole strength depends upon the tissue cross section, the tissue resistivity, the resting membrane potential, the membrane capacitance, the volume fraction of intracellular fluid, the time rate of change of the action potential, and the cell radius. There are no unknown, "free" parameters. There are no arbitrary scale factors. Body surface potentials are a function of the summed local dipole strengths, directions, and distances from the measuring point. Calculations of body surface potentials can be made for the scenarios of depolarization (QRS complex), repolarization (T wave) and localized acute injury (ST segment shifts) and agree well with experimentally measured potentials. This simplified predictive dipole theory provides a solution to the forward problem of electrocardiography that explains from a physiological perspective how the collective depolarization and repolarization of individual cardiac muscle cells create body surface potentials in health and disease.

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Mathematical models and numerical methods for the forward problem in cardiac electrophysiology

Cited by 81 publications

References 110 publications

Recent Numerical Methods in Electrocardiology

Recent Numerical Methods in Electrocardiology

Numerical solution of the bidomain equations

Quantitative Prediction of Body Surface Potentials from Myocardial Action Potentials Using a Summed Dipole Model

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