A planar slab propagation model for cardiac tissue

The equations needed for a theoretical study of propagation in a planar slab bidomain are given. An infinitely extending planar slab of excitable tissue lying in an infinite, homogeneous extracellular bath is considered. The slab comprises coupled parallel fibers. Using the bidomain approach, the intracellular and interstitial space bundles are treated as continua, occupying the same volume, and coupled everywhere by a distributed membrane. Planar activation along the z direction is assumed to eliminate one dimension (i.e. the x direction). Thus any (y, z) cross section is representative. The tissue is characterized by macroscopic bidomain conductivities in the y (depth) and z (axial) directions. It is shown that the planar geometry is useful for investigations involving both transverse and longitudinal conduction and represents the first step toward a fully three-dimensional model.