A coupled monodomain solver with optimal memory usage for the simulation of cardiac wave propagation

The monodomain model is a common description for explaining the electrical activity of the heart. The model is nonlinear and consists of an ODE system that describes electrochemical reactions in the cardiac cells and a parabolic PDE that express the diffusion of the electrical signal. FEM approaches for the numerical solution of the monodomain equations can be classified into those that simultaneously update the state variables with respect to time by solving a coupled system and those that perform the temporal update in a decoupled manner. While coupled strategies are known to yield more accurate results, they so far have not been applied to physiological cell models due to their enormous memory requirements and computational times. In this paper, we tackle these challenges and suggest a novel computational strategy, that exploits the sparsity of local matrices in the assembly of global FEM matrices and hence features optimal usage of memory. We demonstrate the practicability of our coupled approach by employing three popular physiological cell models (Luo-Rudy phase-I, Ten Tusscher 2006 and O’Hara-Rudy 2011) and compare it with a commonly used decoupled strategy. Qualitatively different results obtained for the simulation of cardiac reentry underline the potential relevance of our work for future studies of cardiac pathology.