Journal of Mathematical Biology

, Volume 78, Issue 1–2, pp 21–56 | Cite as

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

  • Ibrahima Dione
  • Nicolas Doyon
  • Jean DeteixEmail author


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.


Electrodiffusion Finite elements Ionic concentrations Node of Ranvier Sensitivity equation method 

Mathematics Subject Classification

92B05 35Q92 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Département de mathématiques et statistique/Groupe Interdisciplinaire de Recherche en Éléments Finis (GIREF)Université LavalQuébecCanada

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