Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution

Abstract

The locality of solution features in cardiac electrophysiology simulations calls for adaptive methods. Due to the overhead incurred by established mesh refinement and coarsening, however, such approaches failed in accelerating the computations. Here we investigate a different route to spatial adaptivity that is based on nested subset selection for algebraic degrees of freedom in spectral deferred correction methods. This combination of algebraic adaptivity and iterative solvers for higher order collocation time stepping realizes a multirate integration with minimal overhead. This leads to moderate but significant speedups in both monodomain and cell-by-cell models of cardiac excitation, as demonstrated at four numerical examples.Keywords cell-by-celll discretization • high-order time integration • spectral deferred correction • algebraic adaptivity • multirate integration scheme

Electrograms in a Cardiac Cell-by-Cell Model

“…n represents the unit outer normal of the respective domain. The scalar conductivities of the intra-and extracellular domains were set to σ i = 0.3 S/m and σ e = 2.0 S/m in this study, while the membrane capacitance was C m = 10 −4 F/m 2 as in [5]. For the membrane dynamics, we chose the phenomenological Aliev-Panfilov model [6].…”