An Unconditionally Stable Second Order Method for the Luo-Rudy 1 Model Used in Simulations of Defibrillation
Year: 2009
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 4 : pp. 627–641
Abstract
Simulations of cardiac defibrillation are associated with considerable numerical challenges. The cell models have traditionally been discretized by first order explicit schemes, which are associated with severe stability issues. The sharp transition layers in the solution call for stable and efficient solvers. We propose a second order accurate numerical method for the Luo-Rudy phase 1 model of electrical activity in a cardiac cell, which provides sequential update of each governing ODE. An a priori estimate for the scheme is given, showing that the bounds of the variables typically observed during electric shocks constitute an invariant region for the system, regardless of the time step chosen. Thus the choice of time step is left as a matter of accuracy. Conclusively, we demonstrate the theoretical result by some numerical examples, illustrating second order convergence for the Luo-Rudy 1 model.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-IJNAM-788
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 4 : pp. 627–641
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Unconditionally stable second order method maximum principle defibrillation ODE system.