Sensitivity analysis of the Poisson Nernst–Planck equations: a finite element approximation for the sensitive analysis of an electrodiffusion model
| Autor: | Ibrahima Dione, Jean Deteix, Nicolas Doyon |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Finite Element Analysis
Models Neurological Sensitive analysis System of linear equations Poisson distribution 01 natural sciences 010305 fluids & plasmas Diffusion 03 medical and health sciences symbols.namesake Ranvier's Nodes 0103 physical sciences Animals Computer Simulation Nernst equation Poisson Distribution Statistical physics Sensitivity (control systems) Planck 030304 developmental biology Physics 0303 health sciences Ion Transport Applied Mathematics Computational Biology Mathematical Concepts Agricultural and Biological Sciences (miscellaneous) Finite element method Electrophysiological Phenomena Modeling and Simulation symbols Electric potential |
| Zdroj: | Journal of Mathematical Biology. 78:21-56 |
| ISSN: | 1432-1416 0303-6812 |
| DOI: | 10.1007/s00285-018-1266-2 |
| Popis: | Biological structures exhibiting electric potential fluctuations such as neuron and neural structures with complex geometries are modelled using an electrodiffusion or Poisson Nernst-Planck system of equations. These structures typically depend upon several parameters displaying a large degree of variation or that cannot be precisely inferred experimentally. It is crucial to understand how the mathematical model (and resulting simulations) depend on specific values of these parameters. Here we develop a rigorous approach based on the sensitivity equation for the electrodiffusion model. To illustrate the proposed methodology, we investigate the sensitivity of the electrical response of a node of Ranvier with respect to ionic diffusion coefficients and the membrane dielectric permittivity. |
| Databáze: | OpenAIRE |
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