Study of Action Potential Propagation in Cardiac Tissues Using Cable Theory

The goal of the present paper is to study the propagation of action potential in cardiac tissue using the cable equation. The paper discusses one-dimensional models of continuously coupled myocytes. Electrical behavior in cardiac tissue is averaged over many cells. Therefore, the transmembrane potential behavior for a single cell is studied. Using the monodomain model, in the absence of current at the beginning and end of the cable (cell), the initial boundary problem is posed and solved analytically. The paper also discusses a one-dimensional mathematical model of conduction in discretely coupled myocytes. The electrical behavior in the tissue is studied in individual myocytes, each of which is modeled as a continuum connected through conditions at the cell boundaries, which represent gap junctions. A stationary passive problem with Dirichlet boundary conditions is stated and solved analytically using the bidomain model. The problems are solved by the method of separation of variables. Numerical modeling of transmembrane potential propagation is performed using MATLAB software. Transmembrane isopotential contours, and 2D and 3D graphs corresponding to the obtained numerical results are presented.