Numerical schemes for the simulation of three-dimensional cardiac electrical propagation in patient-specific ventricular geometries

This paper introduces different numerical strategies in computational electrophysiology, based on the Finite Element Method to handle the space discretization of the governing equations. The long-term goal is to apply these computational techniques to study the three-dimensional electrical propagation in patient-specific ventricular geometries, having in mind not only to understand the process, but also to use the simulation tools to improve the diagnosis accuracy. The electrical response of cardiac tissue is modeled by combining Bidomain (BD) and FitzHugh-Nagumo (FHN) models. The BD model uses two coupled diffusion PDEs to handle the electrical potential in the intra- and extracellular domains of cardiac tissue taking into account the anisotropic conductance of the muscle fibers. The FHN equations add a non-linear reaction term to a transient diffusion equation in order to represent the ion current flows, which drive the depolarization and repolarization processes through the intra- and extracellular domains. The FHN model also includes an ODE to account for the recovery potential contribution responsible of the excitable media repolarization. The proposed methodology is illustrated with numerical simulations both in academic simple geometries and in patient-specific cardiac ventricular. The latter have been reconstructed by using automatic three-dimensional medical image segmentation and mesh generation tools