Action potential propagation in cardiac tissue is well-studied both experimentally and mathematically. The partial differential equation describing action potential propagation in one spatial dimension is known as the cable equation and in higher dimensional space the equations are known as the bidomain equations. The bidomain model is currently widely accepted as a valid model for cardiac tissue. Furthermore, our theoretical understanding of propagation is built on the premise that gap junctional coupling between cells is the most important way in which electrical coupling is accomplished.

Recent data, however, from mice with substantial gap junction depletion, has brought this view into question. In particular, there is indirect evidence that another means of coupling, called ephaptic coupling, or field effect coupling, may be extremely important. However, because ephaptic coupling is a phenomenon associated with microdomains, it has not observed experimentally or been given much mathematical attention.

In this talk, we give an overview of the study of the partial differential equations associated with cardiac action potential propagation and show some of the newly discovered features of these equations that result from consideration of microdomains and spatially inhomogeneous extracellular potential. As will be seen, the understanding of these equations is far from complete.