A Three Dimensional Model of Cellular Electrical Activity

We propose a three dimensional description of cellular electrophysiology which takes into account ionic concentration dynamics. The model consists of a set of partial differential equations satisfied in the intracellular and extracellular domains supplemented with dynamic nonlinear interface conditions at the membrane boundaries. After formulating the model, we perform a systematic reduction of the model to elucidate its relationship with traditional models in electrophysiology.
In so doing, we also uncover the presence of disparate time scales in the model. This "stiffness" poses interesting challenges for the construction of reliable computational schemes. We finally apply this modeling methodology to a problem in cellular cardiac
electrophysiology: electric conduction in cardiac tissue under severely reduced gap-junctional coupling