Volume 6, Issue 4
An Unconditionally Stable Second Order Method for the Luo-Rudy 1 Model Used in Simulations of Defibrillation

M. Hanslien, R. Artebrant, J. Sundnes & A. Tveito

DOI:

Int. J. Numer. Anal. Mod., 6 (2009), pp. 627-641

Published online: 2009-06

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  • 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.

  • Keywords

Unconditionally stable second order method maximum principle defibrillation ODE system

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-627, author = {M. Hanslien, R. Artebrant, J. Sundnes and A. Tveito}, title = {An Unconditionally Stable Second Order Method for the Luo-Rudy 1 Model Used in Simulations of Defibrillation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {4}, pages = {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. }, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/788.html} }
TY - JOUR T1 - An Unconditionally Stable Second Order Method for the Luo-Rudy 1 Model Used in Simulations of Defibrillation AU - M. Hanslien, R. Artebrant, J. Sundnes & A. Tveito JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 627 EP - 641 PY - 2009 DA - 2009/06 SN - 6 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/ijnam/788.html KW - Unconditionally stable KW - second order method KW - maximum principle KW - defibrillation KW - ODE system AB - 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.
M. Hanslien, R. Artebrant, J. Sundnes & A. Tveito. (1970). An Unconditionally Stable Second Order Method for the Luo-Rudy 1 Model Used in Simulations of Defibrillation. International Journal of Numerical Analysis and Modeling. 6 (4). 627-641. doi:
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