A Computational Approach for the inverse problem of neuronal conductances determination

TL;DR

This paper presents a computational iterative method to determine non-uniform neuronal conductances from voltage data, addressing the challenges of experimental measurement and heterogeneity in neurons.

Contribution

It introduces a novel iterative scheme using Landweber iteration to recover spatially and temporally varying conductances from voltage data in a simplified cable model.

Findings

Method accurately recovers conductances from voltage data.

Effective even with noisy data.

Applicable to single branches and neuronal trees.

Abstract

The derivation by Alan Hodgkin and Andrew Huxley of their famous neuronal conductance model relied on experimental data gathered using neurons of the giant squid. It becomes clear that determining experimentally the conductances of neurons is hard, in particular under the presence of spatial and temporal heterogeneities. Moreover it is reasonable to expect variations between species or even between types of neurons of a same species. Determining conductances from one type of neuron is no guarantee that it works across the board. We tackle the inverse problem of determining, given voltage data, conductances with non-uniform distribution computationally. In the simpler setting of a cable equation, we consider the Landweber iteration, a computational technique used to identify non-uniform spatial and temporal ionic distributions, both in a single branch or in a tree. Here, we propose and (numerically) investigate an iterative scheme that consists in numerically solving two partial differential equations in each step. We provide several numerical results showing that the method is able to capture the correct conductances given information on the voltages, even for noisy data.