Empirical study of an adaptive multiscale model for simulating cardiac conduction

We modify and empirically study an adaptive multiscale model for simulating cardiac action potential propagation along a strand of cardiomyocytes. The model involves microscale partial differential equations posed over cells near the action potential upstroke and macroscale partial differential equations posed over the remainder of the tissue. An important advantage of the modified model of this paper is that, unlike our original model, it does not require perfect alignment between myocytes and the macroscale computational grid. We study the effects of gap-junctional coupling, ephaptic coupling, and macroscale grid spacing on the accuracy of the multiscale model. Our simulations reveal that the multiscale method accurately reproduces both the wavespeed and the waveform, including both upstroke and recovery, of fully microscale models. They also reveal that perfect alignment between myocytes and the macroscale grid is not necessary to reproduce the dynamics of a traveling action potential. Further, our simulations suggest that the macroscale grid spacing used in an adaptive multiscale model need not be much finer than the spatial width of an action potential. These results are demonstrated to hold under high, low, and zero gap-junctional coupling regimes.