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 t...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/862813 |
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| _version_ | 1849306188393480192 |
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| author | Luisa Consiglieri Ana Rute Domingos |
| author_facet | Luisa Consiglieri Ana Rute Domingos |
| author_sort | Luisa Consiglieri |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-38d4683d2cad488daca4fde42c231c8a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-38d4683d2cad488daca4fde42c231c8a2025-08-20T03:55:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/862813862813On the Sodium Concentration Diffusion with Three-Dimensional Extracellular StimulationLuisa Consiglieri0Ana Rute Domingos1Departamento de Matemática e CMAF, Faculdade de Ciências da Universidade de Lisboa, 1749-016 Lisboa, PortugalDepartamento de Matemática e CMAF, Faculdade de Ciências da Universidade de Lisboa, 1749-016 Lisboa, PortugalWe 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.http://dx.doi.org/10.1155/2011/862813 |
| spellingShingle | Luisa Consiglieri Ana Rute Domingos On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation International Journal of Mathematics and Mathematical Sciences |
| title | On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation |
| title_full | On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation |
| title_fullStr | On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation |
| title_full_unstemmed | On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation |
| title_short | On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation |
| title_sort | on the sodium concentration diffusion with three dimensional extracellular stimulation |
| url | http://dx.doi.org/10.1155/2011/862813 |
| work_keys_str_mv | AT luisaconsiglieri onthesodiumconcentrationdiffusionwiththreedimensionalextracellularstimulation AT anarutedomingos onthesodiumconcentrationdiffusionwiththreedimensionalextracellularstimulation |