A mathematical perspective on edge-centric brain functional connectivity

TL;DR

This paper establishes the mathematical basis for edge-centric brain connectivity analysis, critiques existing methods, and emphasizes the importance of dynamic measures over static null models in neuroimaging studies.

Contribution

It provides a mathematical framework for edge-centric analysis, critiques current approaches, and demonstrates the significance of temporal dynamics in brain connectivity.

Findings

High-amplitude cofluctuations drive node functional connectivity.

Most variation in edge FC can be explained by nFC.

Dynamic measures reveal temporal structure not captured by static models.

Abstract

Edge time series are increasingly used in brain functional imaging to study the node functional connectivity (nFC) dynamics at the finest temporal resolution while avoiding sliding windows. Here, we lay the mathematical foundations for the edge-centric analysis of neuroimaging time series, explaining why a few high-amplitude cofluctuations drive the nFC across datasets. Our exposition also constitutes a critique of the existing edge-centric studies, showing that their main findings can be derived from the nFC under a static null hypothesis that disregards temporal correlations. Testing the analytic predictions on functional MRI data from the Human Connectome Project confirms that the nFC can explain most variation in the edge FC matrix, the edge communities, the large cofluctuations, and the corresponding spatial patterns. We encourage the use of dynamic measures in future research, which exploit the temporal structure of the edge time series and cannot be replicated by static null models.