The Curie effect incorporation in the monodomain equation describing the action potential dynamics in cardiac tissue

Abstract

In their in-depth study on cardiac tissue modeling, Clayton and Panfilov [1] present several monodomain or bidomain approaches for the mathematical description of the cardiac tissue action potential dynamics. For simulation of wave propagation in the cardiac tissue, the monodomain descriptions which use integer order derivatives reproduce many of the phenomena that are observed experimentally and are thus an appropriate analysis tool. The main objection concerning the monodomain approaches is that the electrical circuit capacitor, appearing in these descriptions, is considered ideal (the space between the capacitor plates is vacuum) and the Curie effect is ignored. The Curie effect consists of the fact that in case of a dielectric material, if at a moment of time a constant external voltage is applied, due to the capacitance of the capacitor and the properties of the dielectric, a supplementary electrical current is produced, besides the ohmic current. This supplementary contribution cannot be neglected in some cases. In this paper, the Curie effect, describing the action potential dynamics in cardiac tissue, assumed isotropic, is incorporated in the monodomain equation. The novelty is that this approach does not use fractional order derivatives and the obtained mathematical description with these equations is objective.