A parallel solver for reaction-diffusion systems in computational electrocardiology

Abstract

In this work, a parallel three-dimensional solver for numerical simulations in computational electrocardiology is introduced and studied. The solver is based on the anisotropic Bidomain %(AB) cardiac model, consisting of a system of two degenerate parabolic reaction-diffusion equations describing the intra and extracellular potentials of the myocardial tissue. This model includes intramural fiber rotation and anisotropic conductivity coefficients that can be fully orthotropic or axially symmetric around the fiber direction. %In case of equal anisotropy ratio, this system reduces to The solver also includes the simpler anisotropic Monodomain model, consisting of only one reaction-diffusion equation. These cardiac models are coupled with a membrane model for the ionic currents, consisting of a system of ordinary differential equations that can vary from the simple FitzHugh-Nagumo (FHN) model to the more complex phase-I Luo-Rudy model (LR1). The solver employs structured isoparametric $Q_1$ finite elements in space and a semi-implicit adaptive method in time. Parallelization and portability are based on the PETSc parallel library. Large-scale computations with up to $O(10^7)$ unknowns have been run on parallel computers, simulating excitation and repolarization phenomena in three-dimensional domains