Reducing run-times of excitable cell models by replacing computationally expensive functions with splines

Numerical simulation of muscle cells and tissue is an established tool in cardiac electrophysiology, where the electrical behavior of excitable heart muscle cells is commonly modeled as a stiff, non-linear system of ordinary differential equations. A common feature of this system’s right-hand side is the heavy use of computationally expensive univariate functions of the membrane potential. In this article, we investigate the performance benefits of replacing these functions with cubic spline approximations in an automated model simplification process. Clear performance gains were found when evaluating the right-hand side in isolation and when performing multicellular simulations using a simple forward Euler method. Single cell simulations run with an adaptive method saw smaller gains due to a higher overhead from the solver. A parallel multicellular simulation was also investigated, but the overhead of the implementation overshadowed the evaluation time of the right-hand side.