Neuronal cable equations derived from the hydrodynamic motion of charged particles

TL;DR

This paper derives neuronal cable equations from hydrodynamic principles of charged particle motion, revealing nonlinear fluid interactions that could influence neuronal integration, offering a novel perspective beyond traditional electrical analogues.

Contribution

It introduces a new derivation of neuronal cable equations based on hydrodynamics, highlighting nonlinear fluid effects absent in classical models.

Findings

Cable equations include nonlinear fluid dynamic contributions

Hydrodynamic derivation offers alternative insights into neuronal behavior

Potential impact on understanding neuronal integration and signal processing

Abstract

Neuronal cable theory is usually derived from an electric analogue of the membrane, which contrasts with the slow movement of ions in aqueous media. We show here that it is possible to derive neuronal cable equations from a different perspective, based on the laws of hydrodynamic motion of charged particles (Navier-Stokes equations). This results in similar cable equations, but with additional contributions arising from nonlinear interactions inherent to fluid dynamics, and which may shape the integrative properties of the neurons.