Analytical model of extracellular potentials in a tissue slab with a finite bath

Extracellular potentials are often used to assess the activation and repolarization of transmembrane action potentials in cardiac tissue under a variety of experimental conditions. An analytical model of the extracellular potentials arising from a planar wavefront propagating in a three-dimensional slab of cardiac tissue with a variably thick adjacent volume conductor or bath is presented. Starting with the transmembrane potential, the model yields the extracellular potentials at various points in the bath and inside tissue. The results show that the analytical model produces signal timecourses with trivial computational costs that are similar to those computed from a full reaction-diffusion bidomain model with different bath thicknesses for tissue with uniform properties and for tissue with an abrupt ionic inhomogeneity.