On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation

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.

Abstract licence: CC BY

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