A Model for the Propagation of Action Potentials in Nonuniform Axons

摘要

This paper presents a method to mathematically analyze the nerve impulse propagation in nonuniform axons. Starting from the general, nonlinear one-dimensional cable equations with spatially varying cable diameter, the problem is shown to be equivalent (under some variable transformations) to the case of uniform axons Characterized by the same normal form, six functions for analytically treatable axon diameter variations are determined. For this class of nonunifbim axons, exact solutions describing the propagation of the front of the action potential are derived. The results are used to evaluate the impact of geometric non-uniformity on the properties of propagating action potentials.