Novel bidomain partitioned strategies for the simulation of ventricular fibrillation dynamics
Gopika P B, Peter Bastian, Nagaiah Chamakuri
TL;DR
This work tackles the computational burden of simulating the bidomain model for ventricular fibrillation by introducing a novel partitioned strategy augmented with spectral deferred correction ($SDC$) and a memory-efficient compile-time sparse-matrix technique (CTSM). The partitioned approach couples a parabolic PDE and associated ODEs with an elliptic constraint, achieving high-order accuracy comparable to a fully coupled solver while dramatically reducing computational cost. Across LR91 and TP06 cell models in 2D, 3D, and bidomain–bath settings, the partitioned+$SDC$ method delivers accuracy on par with the fully coupled solution but speeds up runs by factors such as around $12.64\times$ over fully coupled and $3.92\times$ over the CN-RK2 scheme, enabling large-scale, long-time simulations of reentry phenomena. The framework demonstrates robust performance for spiral-wave reentry in realistic geometries and provides a scalable pathway for patient-specific, high-fidelity cardiac arrhythmia investigations.
Abstract
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.