High-frequency signals: a comparison between the cable equation and telegrapher's equations in nerves.

Abstract

Transmission of electrical impulses along axons is commonly modelled with the cable equation, which neglects the inductive effects that have been measured in nerves. By using the telegrapher's equations, it is possible to incorporate inductive effects and compare with the non-inductive case. Although both of these approaches have been extensively studied, the question remains as to which of these provides a more accurate model of human physiology. Many of the electrical properties of nerves are frequency-dependent, a fact which is not very relevant in a low-frequency domain, but which becomes salient when higher frequencies are considered, and necessitates the exploration of the magnitude of their effects. We compare the effects of both inductance and other variable parameters across a wide frequency range using both the cable equation and the telegrapher's equations, demonstrating that it is possible for axons to transmit high-frequency signals much more effectively than might be expected, especially in the absence of an action potential. This implies that the high-frequency domain necessitates use of the more complete model.