Dynamic Functional Connectivity as a complex random walk: Definitions and the dFCwalk toolbox

Abstract

Functional Connectivity, describing the interaction between brain regions beyond their anatomical interconnection, is highly dynamic even when no task is performed (“resting state”) and it remains a methodological challenge to properly describe its changes in time without strong assumptions. We have developed a framework to describe the dynamics of Functional Connectivity (dFC) estimated from brain activity time-series as a as a smooth reconfiguration process, combining “liquid” and “coordinated” aspects. Our framework considers dFC as a complex random walk in the space of possible functional networks. Unlike other previous approaches, our method does not require the explicit extraction of discrete connectivity states but tracks changes in a continuous time fashion. • We introduced several dFC random walk metrics. First, dFC speed analyses extract the distribution of the time-resolved rate of reconfiguration of FC along time. These distributions have a clear peak (typical dFC speed, that can already serve as a biomarker) and fat tails (denoting deviations from Gaussianity that can be detected by suitable scaling analyses of FC network streams). • Second, meta-connectivity (MC) analyses identify groups of functional links whose fluctuations co-vary in time and that define veritable dFC modules organized along specific dFC meta-hub controllers (differing from conventional FC modules and hubs). The decomposition of whole-brain dFC by MC allows performing dFC speed analyses separately for each of the detected dFC modules. • We present here blocks and pipelines for dFC random walk analyses that are made easily available through a dedicated MATLABⓇ toolbox (dFCwalk), openly downloadable. Although we applied such analyses mostly to fMRI resting state data, in principle our methods can be extended to any type of neural activity (from Local Field Potentials to EEG, MEG, fNIRS, etc.) or even non-neural time-series.

Keywords

• dFC random walk analyses