A Computation Based Approach for Modeling the Efficacy of Neurostimulation Therapies on Neural Functioning

Abstract

Neurostimulation demonstrates success as a medical treatment for patients suffering from neurodegenerative diseases and psychiatric disorders. Despite promising clinical results, the cellular-level processes by which they achieve these favorable outcomes are not completely understood. Specifically, the neuronal mechanisms by which neurostimulation impacts ion channel gating and transmembrane ionic flux are unknown. To help elucidate these mechanisms, we have developed a novel mathematical model that integrates the Poisson-Nernst-Planck system of PDEs and Hodgkin-Huxley based ODEs to model the effects of this neurotherapy on transmembrane voltage, ion channel gating, and ionic mobility. Using a biologically-inspired domain, in silico simulations are used to assess the impact of TES and DBS on neuronal electrodynamics. Results show that an instantaneous polarization of the membrane’s resting potential occurs in a location specific manner, where the type and degree of polarization depends on the position on the membrane. This polarization in turn leads ion channel gating and transmembrane ionic flux to change in a site specific fashion. In addition, results show differences in polarization, membrane voltage, and transmembrane ion mobility resulting from highly distinct forms of neurostimulation, namely tran-scranial electrical stimulation and deep brain stimulation.