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On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation

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  • Luisa Consiglieri
  • Ana Rute Domingos

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.

Suggested Citation

  • Luisa Consiglieri & Ana Rute Domingos, 2011. "On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-19, July.
    • Handle: RePEc:hin:jijmms:862813
    DOI: 10.1155/2011/862813
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