Sharp Interface and Voltage Conservation in the Phase Field Method: Application to Cardiac Electrophysiology

Abstract

We present a finite difference method for modeling the propagation of electrical waves in cardiac tissue using the cable equation with homogeneous Neumann boundary conditions. This method is novel in that it is derived by first discretizing the phase field method as described by Fenton et al. [Chaos, 15 (2005), p. 013502.] then taking a limit to recover a sharp interface. Our method provides for exact voltage conservation (up to floating point precision in application), can be used on arbitrary geometries, and can be implemented using only nearest neighbor coupling between grid points.