Operator splitting for the bidomain model revisited

The bidomain model is a widely used mathematical model to describe the propagation of electricity in myocardial tissue. It consists of a multi-scale system of partial differential equations coupling the electrical activity at the tissue scale with that at the cellular scale. It is common to solve the bidomain model by using a separate numerical procedure for each scale. Two well-known, first-order time-integration methods for solving the bidomain model are the semi-implicit method of Southern et al. (2009) and the Godunov operator-splitting method (as described in Sundnes et al., 2006). Both methods decouple the numerical procedure at the cellular scale from that at the tissue scale but in slightly different ways. The methods are analysed in terms of their accuracy, and their relative performance is compared on one-, two-, and three-dimensional test cases. As suggested by the analysis, the test cases show that the Godunov method is significantly faster than the semi-implicit method for the same level of accuracy, specifically, between 5 and 15 times in the cases presented.