Numerical Simulation in Electrocardiology Using an Explicit Generalized Finite Difference Method

In this paper we present a fast, accurate and conditionally stable algorithm to solve a monodomain model in 2D, which describes the electrical activity in the heart. The model consists of a parabolic anisotropic Partial Differential Equation (PDE), which is coupled to systems of Ordinary Differential Equations (ODEs) describing electrochemical reactions in the cardiac cells. The resulting system is challenging to solve numerically, because of its complexity. We propose a simple method based on operator splitting and an explicit meshless method for solving the PDE together with an adaptive method for solving the system of ODE’s for the membrane and ionic currents.