Current flow and potential in a three-dimensional syncytium

Analytical solutions are obtained describing the spread of potential in a continuous syncytium which is the three-dimensional analogue of the “cable” and “thin sheet” models. Two discrete (finite-element) models are also developed and their behaviour shown to agree with that of the continuous model. All three models are able to account for the peculiarities of passive responses to intracellular current injection in tissues such as cardiac and smooth muscle. The time course and spread of junction potentials in electrically coupled tissues is discussed.