The potential in the gap between two abutting cardiac muscle cells. A closed solution

Abstract

An approximate differential equation is developed describing the potential in the gap (intercalated disc) between two closely abutting, coaxial cylindrical cardiac muscle cells. This permits approximate calculation of the degree of current spread from an active to an inactive cell. The equation has a closed solution in terms of the zero-order Bessel function I(0)(x). This result is different from one given by Woodbury and Crill (1961). The source of the original mistake is given and the magnitude of the error estimated. The new solution is compared with the exact, series solution to this problem given by Heppner and Plonsey (1970) in the preceding paper. It is shown analytically that our approximate solution differs negligibly from the series solution for the parameter values chosen. The closed solution not only considerably simplifies calculations but yields additional insights into the nature of the coupling resistances R and r used by Heppner and Plonsey in their detailed analysis of the cell-to-cell transmission process.