Multiscale modeling via split-step methods in neural firing

TL;DR

This paper introduces a multiscale model combining stochastic ion channel gating with action potential propagation, using a split-step numerical method, and discusses extending it with Maxwell's equations for extracellular potential modeling.

Contribution

It presents a novel split-step numerical method for coupling stochastic ion channel dynamics with neuronal signal propagation, extending to extracellular space modeling.

Findings

Feasibility demonstrated for the split-step coupling method

Potential extension with Maxwell's equations outlined

Multiscale modeling enhances understanding of neuronal activity

Abstract

Neuronal models based on the Hodgkin-Huxley equation form a fundamental framework in the field of computational neuroscience. While the neuronal state is often modeled deterministically, experimental recordings show stochastic fluctuations, presumably driven by molecular noise from the underlying microphysical conditions. In turn, the firing of individual neurons gives rise to an electric field n extracellular space, also thought to affect the firing pattern of nearby neurons. We develop a multiscale model which combines a stochastic ion channel gating process taking place on the neuronal membrane, together with the propagation of an action potential along the neuronal structure. We also devise a numerical method relying on a split-step strategy which effectively couples these two processes and we experimentally test the feasibility of this approach. We finally also explain how the approach can be extended with Maxwell's equations to allow the potential to be propagated in extracellular space.