Effective boundary conditions for syncytial tissues

Abstract

This study derives effective boundary conditions for potentials and currents on the interface between syncytial tissue and a surrounding volume conductor. The derivation is based on an idealized representation of the syncytium as a network of interconnected cells arranged periodically in space. The microscopic model of an interface assumes that the extracellular fluid is in direct contact with the outside volume conductor and that the inside of the cells is separated from the outside by the membrane. From this microscopic model, a homogenization process and boundary layer analysis derive effective boundary conditions applicable to macroscopic volume-averaged potentials. These effective boundary conditions call for the extracellular potential and current density to be continuous with the potential and current density in the volume conductor, and for the intracellular current to vanish. Hence, the long-debated appropriate boundary conditions for the bidomain model are established.