Generalized cable theory for neurons in complex and heterogeneous media

TL;DR

This paper extends classical cable theory to account for complex extracellular media with properties like polarization and ionic diffusion, revealing significant effects on neuronal voltage attenuation and filtering.

Contribution

It introduces a generalized cable theory applicable to complex media, expanding beyond traditional resistive assumptions to include phenomena like ionic diffusion.

Findings

Complex media significantly affect voltage attenuation.

Generalized equations recover traditional cable theory in resistive media.

Numerical comparisons show notable differences in cable properties.

Abstract

Cable theory has been developed over the last decades, usually assuming that the extracellular space around membranes is a perfect resistor. However, extracellular media may display more complex electrical properties due to various phenomena, such as polarization, ionic diffusion or capacitive effects, but their impact on cable properties is not known. In this paper, we generalize cable theory for membranes embedded in arbitrarily complex extracellular media. We outline the generalized cable equations, then consider specific cases. The simplest case is a resistive medium, in which case the equations recover the traditional cable equations. We show that for more complex media, for example in the presence of ionic diffusion, the impact on cable properties such as voltage attenuation can be significant. We illustrate this numerically always by comparing the generalized cable to the traditional cable. We conclude that the nature of intracellular and extracellular media may have a strong influence on cable filtering as well as on the passive integrative properties of neurons.