DySCo: a general framework for dynamic Functional Connectivity

A crucial challenge in neuroscience involves characterising brain dynamics from high-dimensional brain recordings. Dynamic Functional Connectivity (dFC) is an analysis paradigm that aims to address this challenge. dFC consists of a time-varying matrix (dFC matrix) expressing how pairwise interactions across brain areas change with time. However, the main dFC approaches have been developed and applied mostly empirically, lacking a unifying theoretical framework, a general interpretation, and a common set of measures to quantify the dFC matrices properties. Moreover, the dFC field has been lacking ad-hoc algorithms to compute and process the matrices efficiently. This has prevented the field to show its full potential with high-dimensional datasets and/or real time applications. With this paper, we introduce the Dynamic Symmetric Connectivity Matrix analysis framework (DySCo), with its associated repository. DySCo is a unifying approach that allows the study of brain signals at different spatio-temporal scales, down to voxel level, that is computationally ultrafast. DySCo unifies in a single theoretical framework the most employed dFC matrices, which share a common mathematical structure. Doing so it allows: 1) A new interpretation of dFC that further justifies its use to capture the spatiotemporal patterns of data interactions in a form that is easily translatable across different imaging modalities. 2) The introduction of the the Recurrence Matrix EVD to compute and store the eigenvectors and eigenvalues of all types of dFC matrices in an efficent manner that is orders of magnitude faster than naive algorithms, and without loss of information. 3) To simply define quantities of interest for the dynamic analyses such as: the amount of connectivity (norm of a matrix) the similarity between matrices, their informational complexity. The methodology developed here is validated on both a synthetic dataset and a rest/N-back task experimental paradigm - the fMRI Human Connectome Project dataset. We demonstrate that all the measures proposed are highly sensitive to changes in brain configurations. To illustrate the computational efficiency of the DySCo toolbox, we perform the analysis at the voxel-level, a computationally very demanding task which is easily afforded by the RMEVD algorithm.