Dione Ibrahima, Doyon Nicolas, Deteix Jean
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.
J Math Biol. 2019 Jan;78(1-2):21-56. doi: 10.1007/s00285-018-1266-2. Epub 2018 Sep 5.
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.
使用电扩散或泊松能斯特 - 普朗克方程组对表现出电势波动的生物结构进行建模，比如具有复杂几何形状的神经元和神经结构。这些结构通常取决于几个参数，这些参数显示出很大程度的变化，或者无法通过实验精确推断。了解数学模型（以及由此产生的模拟）如何依赖于这些参数的特定值至关重要。在此，我们基于电扩散模型的灵敏度方程开发了一种严格的方法。为了说明所提出的方法，我们研究了郎飞结的电响应相对于离子扩散系数和膜介电常数的灵敏度。
