Novel bidomain partitioned strategies for the simulation of ventricular fibrillation dynamics

The numerical tools to simulate the bidomain model in cardiac electrophysiology are constantly developing due to the great clinical interest and scientific advances in mathematical models and computational power. The bidomain model consists of an elliptic partial differential equation (PDE) and a non-linear parabolic PDE of reaction-diffusion type, where the reaction term is described by a set of ordinary differential equations (ODEs). We propose and analyze a suite of numerical strategies for the efficient and accurate simulation of cardiac electrophysiology, with a particular focus on ventricular fibrillation in realistic geometries. Specifically, we develop and compare a fully coupled strategy, a traditional decoupled strategy, and a novel partitioned strategy. The centerpiece of this work is a bidomain partitioned strategy enhanced with spectral deferred correction, designed to balance numerical stability and computational efficiency. To address the substantial memory requirements posed by biophysically detailed ionic models, we adopt a compile-time memory-efficient sparse matrix technique. This enables the efficient solution of the coupled nonlinear parabolic PDE and the associated large systems of ODEs that govern ionic gating and concentration dynamics. We perform comprehensive numerical experiments using the Luo-Rudy and Ten Tusscher cell models in both two- and three-dimensional geometries. In addition, we demonstrate the applicability of our approach to bidomain-bath coupling scenarios. The results confirm that the proposed partitioned strategy achieves high accuracy and efficiency compared to standard decoupled strategies. Our findings support the use of advanced partitioned strategies for large-scale simulations in cardiac electrophysiology and highlight their potential for future investigations into cardiac arrhythmias and other pathological conditions.