# The role of node dynamics in shaping emergent functional connectivity patterns in the brain

## TL;DR

This study uses mathematical and computational models of neural mass nodes to explore how local node dynamics influence the relationship between structural and functional connectivity in the brain, revealing conditions under which structure strongly shapes function.

## Contribution

It introduces a combined simulation and analytical framework to understand the structure-function relationship, emphasizing the impact of local dynamics near bifurcations on functional connectivity patterns.

## Key findings

- Functional connectivity is strongly inherited from structure near Hopf bifurcations.
- Near false bifurcations, structure weakly influences functional connectivity.
- Linear stability analysis can predict modular FC structures.

## Abstract

The contribution of structural connectivity to functional brain states remains poorly understood. We present a mathematical and computational study suited to assess the structure--function issue, treating a system of Jansen--Rit neural-mass nodes with heterogeneous structural connections estimated from diffusion MRI data provided by the Human Connectome Project. Via direct simulations we determine the similarity of functional (inferred from correlated activity between nodes) and structural connectivity matrices under variation of the parameters controlling single-node dynamics, highlighting a non-trivial structure--function relationship in regimes that support limit cycle oscillations. To determine their relationship, we firstly calculate network instabilities giving rise to oscillations, and the so-called `false bifurcations' (for which a significant qualitative change in the orbit is observed, without a change of stability) occurring beyond this onset. We highlight that functional connectivity (FC) is inherited robustly from structure when node dynamics are poised near a Hopf bifurcation, whilst near false bifurcations, structure only weakly influences FC. Secondly, we develop a weakly-coupled oscillator description to analyse oscillatory phase-locked states and, furthermore, show how the modular structure of FC matrices can be predicted via linear stability analysis. This study thereby emphasises the substantial role that local dynamics can have in shaping large-scale functional brain states.