Nonequilibrium Green's functions for functional connectivity in the brain

TL;DR

This paper introduces a nonequilibrium Green's function framework to model the nonlinear, time-dependent functional connectivity in the brain, linking theoretical constructs to measurable neural responses.

Contribution

It extends Green's function methods to nonlinear, dynamic neural systems, providing a new approach to analyze brain connectivity.

Findings

Green's functions relate to measurable neural responses.

Numerical examples demonstrate the framework's applicability.

Model inspired by C. elegans neural data.

Abstract

A theoretical framework describing the set of interactions between neurons in the brain, or functional connectivity, should include dynamical functions representing the propagation of signal from one neuron to another. Green's functions and response functions are natural candidates for this but, while they are conceptually very useful, they are usually defined only for linear time-translationally invariant systems. The brain, instead, behaves nonlinearly and in a time-dependent way. Here, we use nonequilibrium Green's functions to describe the time-dependent functional connectivity of a continuous-variable network of neurons. We show how the connectivity is related to the measurable response functions, and provide two illustrative examples via numerical calculations, inspired from $\textit{C. elegans}$.