Mathematical modeling of the excitation process in myocardial tissue: influence of fiber rotation on wavefront propagation and potential field

Abstract

In our macroscopic model the heart tissue is represented as a bidomain coupling the intra- and extracellular media. Owing to the fiber structure of the myocardium, these media are anisotropic, and their conductivity tensors have a principal axis parallel to the local fiber direction. A reaction-diffusion system is derived that governs the distribution and evolution of the extracellular and transmembrane potentials during the depolarization phase of the heart beat. To investigate frontlike solutions, the system is rescaled and transformed into a system dependent on a small parameter. Subsequently a perturbation analysis is carried out that yields zero- and first-order approximations called eikonal equations. The effects of the transmural fiber rotation on wavefront propagation and the corresponding potential field, elicited by point stimulations, are investigated by means of numerical simulations.