Spatio-temporal modeling of saltatory conduction in neurons using Poisson-Nernst-Planck treatment and estimation of conduction velocity

Abstract

Action potential propagation along the axons and across the dendrites is the foundation of the electrical activity observed in the brain and the rest of the central nervous system. Theoretical and numerical modeling of this action potential activity has long been a key focus area of electro-chemical neuronal modeling. Specifically, considering the presence of nodes of Ranvier along the myelinated axon, single-cable models of the propagation of action potential have been popular. Building on these models, and considering a secondary electrical conduction pathway below the myelin sheath, the double-cable model has been proposed. Such cable theory based treatments have inherent limitations in their lack of a representation of the spatio-temporal evolution of the neuronal electro-chemistry. In contrast, a Poisson-Nernst-Planck (PNP) based electro-diffusive framework accounts for the underlying spatio-temporal ionic concentration dynamics and is a more comprehensive treatment. In this work, a high-fidelity implementation of the PNP model is demonstrated. This model is shown to produce results similar to the cable theory based electrical models, and in addition, the rich spatio-temporal evolution of the underlying ionic transport is captured. Novel to this work is the extension of PNP model to axonal geometries with multiple nodes of Ranvier and multiple variants of the electro-diffusive model - PNP without myelin, PNP with myelin, and PNP with the myelin sheath and peri-axonal space. Further, we apply this spatio-temporal model to numerically estimate conduction velocity in a rat axon. Specifically, saltatory conduction due to the presence of myelin sheath and the peri-axonal space is investigated.