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

Sensitivity of the electrical response of a node of Ranvier model to alterations of the myelin sheath geometry

Nodes of Ranvier play critical roles in the generation and transmission of action potentials. Alterations in node properties during pathology and/or development are known to affect the speed and quality of electrical transmission. From a modelling standpoint, nodes of Ranvier are often described by systems of ordinary differential equations neglecting or greatly simplifying their geometric structure. These approaches fail to accurately describe how fine scale alteration in the node geometry or in myelin thickness in the paranode region will impact action potential generation and transmission. Here, we rely on a finite element approximation to describe the three dimensional geometry of a node of Ranvier. With this, we are able to investigate how sensitive is the electrical response to alterations in the myelin sheath and paranode geometry. We could in particular investigate irregular loss of myelin, which might be more physiologically relevant than the uniform loss often described through simpler modelling approaches.