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• W1805159804 abstract "Modelling in cardiac electrophysiology results in a complex system of partial differential equations (PDE) describing the propagation of the electrical wave in the heart muscle coupled with a highly nonlinear system of ordinary differential equations (ODE) describing the ionic activity in the cardiac cells. This system forms the widely accepted bidomain model or its slightly simpler version, the monodomain model. To a large extent, the stiffness of the whole model depends on the choice of the ionic model, which varies in terms of complexity and realism. These simulations require accurate and, depending on the ionic model used, possibly very stable numerical methods. At this time, solving these models numerically requires CPU time of around one day per heartbeat. Therefore, it is necessary to use the most efficient method for these simulations. This research focuses on the comparison and analysis of several time-stepping methods: explicit or semi-implicit, operator splitting, deferred correction and RushLarsen methods. The goal is to find the optimal method for the ionic model used. For our analysis, we used the monodomain model but our results apply to the bidomain model as well. We compare the methods for three ionic models of varying complexity and stiffness: the Mitchell-Schaeffer models with only 2 variables, the more realistic Beeler-Reuter model with 8 variables, and the stiff and very complex ten TuscherNoble-Noble-Panfilov (TNNP) models with 17 variables. For each method, we derived absolute stability criteria of the spatially discretized monodomain model and verified" @default.
• W1805159804 created "2016-06-24" @default.
• W1805159804 creator A5089036199 @default.
• W1805159804 date "2015-01-01" @default.
• W1805159804 modified "2023-09-27" @default.
• W1805159804 title "Time-Stepping Methods in Cardiac Electrophysiology" @default.
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• W1805159804 doi "https://doi.org/10.20381/ruor-4204" @default.
• W1805159804 hasPublicationYear "2015" @default.
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