Surface capacity of electrically syncytial tissues

An exact geometry-independent formula is derived that gives the total surface membrane capacity of an electrical syncytium in terms of its input resistance (RIN) and the phase angle (phi) of its complex admittance. The formula strips off the effects of resistance in the extracellular space and exposes the true capacity of the external surface of preparations such as skeletal muscle fibers, cardiac Purkinje fibers, or spherical cardiac aggregates. The shape, extent, and resistivity of the extracellular space may be arbitrary and need not be measured. The medium in this space may have an arbitrary and nonuniform resistivity. It is assumed that the tissue is impaled with current and voltage electrodes, so that the intracellular resistance between the electrodes and membranes is negligible or can de dealth with by theoretical calculations. Under these circumstances the total surface membrane capacity at high frequency is determined exactly by RIN and a frequency domain integral over phi. The method is tested with synthetic data for RIN and phi generated by the "disk" model of skeletal muscle fibers and the "pie" model of cardiac Purkinje fibers. The formula allows the "inversion" of these data and the deduction of the correct value of the total surface membrane capacity