Mathematical model of signal propagation in excitable media

Abstract

This article deals with a model of signal propagation in excitable media based on a system of reaction-diffusion equations. Such media have the ability to exhibit a large response in reaction to a small deviation from the rest state. An example of such media is the nerve tissue or the heart tissue. The first part of the article briefly describes the origin and the propagation of the cardiac action potential in the heart. In the second part, the mathematical properties of the model are discussed. Next, the numerical algorithm based on the finite difference method is used to obtain computational studies in both a homogeneous and heterogeneous medium with an emphasis on interactions of the propagating signals with obstacles in the medium.

On Diffusion and Transport Acting on Parameterized Moving Closed Curves in Space

“…A closed simple curve can also represent a 2D cut through the myocardum surface, the heart muscle operated by electric signal broadcasted by the sino-atrial node [17]. This signal is represented by ions located along the cell membrane, their potential together with the ability of cell membranes to allow the motion of ions [23] are the scalar variables appearing in the FitzHugh-Nagumo reaction-diffusion model [22] on the curved myocardum-surface curve. Thin liquid pathways occur between grains and ice during soil freezing and mediate mass transport responsible for mechanical effects such as the frost heave (see e.g.…”