Theoretical aspects of evaluation of the plasma membrane time constant in myocardial tissue using a model of three-dimensional RC-medium of finite thickness

Abstract

An analytical solution of the differential equation describing the distribution of the electrotonic potential in the three-dimensional RC-medium of finite thickness when the current source is hemispheric was obtained. Computerized programs were developed, and families of curves of T1/2 (time during which the electrotonic potential reaches half of the stationary amplitude) dependence on the size of current electrode (R0), the distance between the current electrode and the potential recording site (R), and medium thickness (D) were established. It is shown that function T1/2 = f(R) is not linear in close vicinity of the current electrode, and the application of linear dependence T1/2 = R/2 + const for the determination of the plasmic membrane time constant (taum) in myocardial tissue would lead to errors of -70% / +20%.