Dynamic Brain Networks with Prescribed Functional Connectivity

TL;DR

This paper models whole-brain resting-state dynamics using stochastic linear systems, showing how a skew-symmetric matrix influences stability, excitability, and responsiveness to inputs, linking functional connectivity to dynamic properties.

Contribution

It introduces a parametrization of brain network dynamics with a skew-symmetric matrix, revealing its role in modulating stability and responsiveness.

Findings

Large skew-symmetric matrix enhances stability.

Skew-symmetric matrix increases system excitability.

System becomes more responsive to high-frequency inputs.

Abstract

In this paper, we consider stable stochastic linear systems modeling whole-brain resting-state dynamics. We parametrize the state matrix of the system (effective connectivity) in terms of its steady-state covariance matrix (functional connectivity) and a skew-symmetric matrix $S$. We examine how the matrix $S$ influences some relevant dynamic properties of the system. Specifically, we show that a large $S$ enhances the degree of stability and excitability of the system, and makes the latter more responsive to high-frequency inputs.