Improved Hybrid/GPU Algorithm for Solving Cardiac Electrophysiology Problems on Purkinje Networks

Cardiac Purkinje fibres provide an important pathway to the coordinated contraction of the heart. We present a numerical algorithm for the solution of electrophysiology problems across the Purkinje network that is efficient enough to be used in in-silico studies on realistic Purkinje networks with physiologically detailed models of ion exchange at the cell membrane. The algorithm is based on operator splitting and is provided with three different implementations: pure CPU, hybrid CPU/GPU, and pure GPU. Compared to our previous work, we modify the explicit gap junction term at network bifurcations in order to improve its mathematical consistency. Due to this improved consistency of the model, we are able to perform an empirical convergence study against analytical solutions. The study verified that all three implementations produce equivalent convergence rates, which shows that the algorithm produces equivalent result across different hardware platforms. Finally, we compare the efficiency of all three implementations on Purkinje networks of increasing spatial resolution using membrane models of increasing complexity. Both hybrid and pure-GPU implementations outperform the pure-CPU implementation, but their relative performance difference depends on the size of the Purkinje network and the complexity of the membrane model used.