Optimized Semi-implicit Methods for Modeling Cardiac Propagation

Computer simulation of cardiac electrophysiology is now considered a powerful tool for exploring the causes of cardiac arrhythmias Cardiac electric propagation has been studied using the monodomain model to describe wave propagation of action potential in the heart. The governing nonlinear reaction-diffusion partial differential equation is solved with the semi-implicit (implicit-explicit) method that does not have the stability limit of the explicit time-stepping scheme. Both first order and second order semi-implicit techniques for temporal discretization are considered in this paper. Second order finite difference technique is used to discretize the spatial derivatives. An explicit finite difference scheme with 512X512 nodes and 0.1 us time step is used as the benchmark for error calculation. APPSPACK, a parallel pattern search optimization software, is used to obtain the optimal semi-implicit parameters that give the lowest root-meansquare error. Results are presented for the semi-implicit techniques with or without the operator split or protective zone method. They demonstrate that the optimized second order semi-implicit method gives the best overall performance.