Simulation of Action Potential Propagation in Cardiac Ventricular Tissue Using an Efficient PDE Model

Abstract

Signal transmission in the form of propagating waves of electrical excitation is a fast type of communication and coordination between cells that is known in cardiac tissue as the action potential.In this article we used an efficient model of cardiac ventricular cell that is based on partial differential equations(PDE).After that a computational algorithm for action potential propagation was represented that according to this algorithm and proposed efficient model, We demonstrated action potential propagation in one-dimensional (1D) and two-dimensional (2D) space lattices using the central finite-difference method.In addition we investigated the effect of obstacles on the propagation of normal action potential using represented 2D excitable medium.Our results show that proposed efficient model, represented algorithm and excitable media are suitable for simulation of action potential propagation in cardiac tissue. Traveling waves transmit information through space and always an excitable medium serves to promote propagation. an excitable medium is typically comprised of a continuous set of locally excitable regions,which can be both inde- pendently stimulated and inhibited.these media exhibit a sensitivity threshold blow which the media persist undis- turbed at a stable resting state.while subthreshold perturba- tions are rapidly diminished, greater than threshold signals induce an abrupt local transformation within a portion of the medium. shortly after this change occurs, the region becomes transiently refractory to further perturbation, after which it relaxes to the resting state. The bioelectric activity of cardiac cells results from the transport processes of ionic species across the membrane through voltage-gated ion channels. The ion channels act as gates that regulate the permeabilities of sodium, potassium and calcium ions. At rest, the cell maintains a constant, negative transmembrane voltage, called the resting potential. However, if a strong enough depolarizing current is passed through the membrane, the cell departs from equilibrium and responds with a sharp change in the transmembrane voltage followed by a return to the resting state. This rapid course of the transmembrane voltage is called action poten- tial (AP) that is the fastest form of communications in the cardiac excitable tissue. Conduction of AP in the heart occurs by electrotonic mechanisms, in which the local