Dynamical mean-field theory of noisy spiking neuron ensembles: Application to the Hodgkin-Huxley model

TL;DR

This paper extends a dynamical mean-field approximation to noisy spiking neuron ensembles, including Hodgkin-Huxley models, enabling efficient analysis of noise, coupling, and size effects on neural responses with results matching direct simulations.

Contribution

The paper introduces a generalized DMA for complex noisy neuron ensembles, reducing high-dimensional stochastic DEs to deterministic equations involving means and moments, applicable to Hodgkin-Huxley neurons.

Findings

DMA accurately predicts noise and coupling effects on neuron responses

Results agree well with direct simulation data

Analysis includes ensemble size impact on neural dynamics

Abstract

A dynamical mean-field approximation (DMA) previously proposed by the present author [H. Hasegawa, Phys. Rev E {\bf 67}, 041903 (2003)] has been extended to ensembles described by a general noisy spiking neuron model. Ensembles of $N$-unit neurons, each of which is expressed by coupled $K$-dimensional differential equations (DEs), are assumed to be subject to spatially correlated white noises. The original $KN$-dimensional {\it stochastic} DEs have been replaced by $K(K+2)$-dimensional {\it deterministic} DEs expressed in terms of means and the second-order moments of {\it local} and {\it global} variables: the fourth-order contributions are taken into account by the Gaussian decoupling approximation. Our DMA has been applied to an ensemble of Hodgkin-Huxley (HH) neurons (K=4), for which effects of the noise, the coupling strength and the ensemble size on the response to a single-spike input have been investigated. Results calculated by DMA theory are in good agreement with those obtained by direct simulations.