Neuronal Cable Equations Derived from the Hydrodynamic Motion of Charged Particles

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. The model recovers the classic cable equations as a particular case, when the fluid is assumed to be linear.