Homogenization of an electrophysiological model for a strand of cardiac myocytes with gap-junctional and electric-field coupling.

We derive a homogenized description of the electrical communication along a single strand of myocytes in the presence of gap-junctional and electric-field coupling. In the model, cells are electrically coupled through narrow clefts that are resistively connected to extracellular space. Cells are also coupled directly through gap junctions. We perform numerical simulations of this full model and its homogenization. We observe that the full and homogenized descriptions agree when gap-junctional coupling is at physiologically normal levels. When gap-junctional coupling is low, the two descriptions disagree. In this case, only the full model captures the behavior that the ephaptic mechanism can speed up action potential propagation. A strength of our homogenized description is that it is a macroscale model that can account for the preferential localization of Na+ channels at the ends of cells.