Modeling the effects of electric fields on nerve fibers: determination of excitation thresholds.

We have developed a method to predict excitation of axons based on the response of passive models. An expression describing the transmembrane potential induced in passive models to an applied electric field is presented. Two terms were found to drive the polarization of each node. The first was a source term described by the activating function at the node, and the other was an ohmic term resulting from redistribution of current from sources at other nodes. A total equivalent driving function including both terms was then defined. We found that the total equivalent driving function can be used to provide accurate predictions of excitation thresholds for any applied field. The method requires only knowledge of the intracellular strength-duration relationship of the axon, the passive step response of the axon to an intracellular current, and the values of the extracellular potentials. Excitation thresholds for any given applied field can then be calculated using a simple algebraic expression. This method eliminates the errors associated with use of the activating function alone, and greatly reduces the computation required to determine fiber response to applied extracellular fields.