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J Math Biol. 2019 Jan;78(1-2):21-56. doi: 10.1007/s00285-018-1266-2. Epub 2018 Sep 5.

Sensitivity analysis of the Poisson Nernst-Planck equations: a finite element approximation for the sensitive analysis of an electrodiffusion model.

Author information

1
Département de mathématiques et statistique/Groupe Interdisciplinaire de Recherche en Éléments Finis (GIREF), Université Laval, Pavillon Vachon, 1045 Avenue de la médecine, Québec, QC, Canada.
2
Département de mathématiques et statistique/Groupe Interdisciplinaire de Recherche en Éléments Finis (GIREF), Université Laval, Pavillon Vachon, 1045 Avenue de la médecine, Québec, QC, Canada. jean.deteix@mat.ulaval.ca.

Abstract

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.

KEYWORDS:

Electrodiffusion; Finite elements; Ionic concentrations; Node of Ranvier; Sensitivity equation method

PMID:
30187223
DOI:
10.1007/s00285-018-1266-2

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