Mathematical Modeling of the Distribution of Electrotonic Potential in Three-Dimensional Anisotropic RC Media

Abstract

Myocardium is a complex three-dimensional anisotropic syncytial structure formed of separate cells connected in between by intercellular contacts. As the passive electric properties of myocardium cannot be measured directly, for the purpose the mathematical models of anisotropic ohmic-capacitive (RC) media have been developed. The analysis of simplified cases with a point-shaped source of current made it possible to discover one of regularities of the distribution of electrotonic potential in the one- and two-dimensional RC media: time T_1/2 during which electrotonic potential reaches half of its stationary amplitude is in linear dependence on the distance R between the point-shaped source of current and the electrotonic potential recording site: T_1/2=R/2+const. It has been found by mathematical modeling that in the three-dimensional anisotropic RC medium of finite thickness (D) the dependence T_1/2=f(R,D) is not linear in close proximity to the source of current of finite size.