An Efficient Non-standard Finite Difference Scheme for an Ionic Model of Cardiac Action Potentials

Abstract

The ionic movements that generate the electrical activity in a human myocardial cell can be modeled mathematically by sets of ordinary differential equations (ODEs). The computational efficiency in solving these sets of ODEs is of paramount importance because their solution must be performed many hundreds of thousands of times over in realistic three-dimensional models of macroscopic regions of the heart such as the atria or the ventricles. In this paper, we propose a non-standard finite difference scheme for the solution of the Luo–Rudy model for ionic currents in cardiac tissue. We demonstrate that the nonstandard finite difference scheme can be as much as 25 times more efficient than standard forward Euler while maintaining an acceptable level of accuracy.