AuthorsM. Hanslien, R. Artebrant, J. Sundnes and A. Tveito
TitleAn Unconditionally Stable Second Order Method for the Luo-Rudy 1 Model Used in Simulations of Defibrillation
AfilliationCenter for Biomedical Computing (SFF), Cardiac Modeling, Scientific Computing
Project(s)Center for Biomedical Computing (SFF)
StatusPublished
Publication TypeJournal Article
Year of Publication2009
JournalInternational Journal of Numerical Analysis and Modeling
Volume6
Number4
Pagination627-641
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 \textit{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.

Citation KeySimula.SC.76