On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation

Abstract EN

We deal with the transmembrane sodium diffusion in a nerve.

We study a mathematical model of a nerve fibre in response to an imposed extracellular stimulus.

The presented model is constituted by a diffusion-drift vectorial equation in a bidomain, that is, two parabolic equations defined in each of the intra- and extra-regions.

This system of partial differential equations can be understood as a reduced three-dimensional Poisson-Nernst-Planck model of the sodium concentration.

The representation of the membrane includes a jump boundary condition describing the mechanisms involved in the excitation-contraction couple.

Our first novelty comes from this general dynamical boundary condition.

The second one is the three-dimensional behaviour of the extracellular stimulus.

An analytical solution to the mathematical model is proposed depending on the morphology of the excitation.