On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation

Luisa Consiglieri and Ana Rute Domingos

International Journal of Mathematics and Mathematical Sciences, 2011, vol. 2011, 1-19

Abstract:

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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:862813

DOI: 10.1155/2011/862813

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