Time-varying Graphs: A Method to Identify Abnormal Integration and Disconnection in Functional Brain Connectivity with Application to Schizophrenia

Objective: A graph theoretical approach provides a powerful framework for discovering potential biomarkers of psychotic disorders. Comparing the brain graphs of the control and patient groups can help us to discover changes in mental disorders in a more convenient way. In this paper, we propose a novel tool to identify missing links associated with blocked paths (segregation) and new links associated with additional paths (abnormal integration) in estimated patient group’s time-varying graphs. We highlight the approach in an example application to the resting-state functional magnetic resonance imaging (fMRI) data of schizophrenia (SZ) patients. Methods: We first estimated whole-brain functional connectivity dynamics using a combination of spatial independent component analysis (ICA), sliding time window, and k-means clustering of windowed correlation matrices on resting-state fMRI data. The clusters are regarded as functional connectivity states, and each of them includes time intervals exhibiting similar connectivity patterns. We then estimated a Gaussian graphical model (GGM) for each state for both groups. To evaluate this approach, we compared different paths between brain components (nodes) of SZ and control groups’ graphs within each state by using the concept of connected components in graph theory. Results: We identified missing edges associated with disconnectivity (disconnectors) and showed there are additional edges in the SZ group graph that contribute to creating new paths in brain graphs. Conclusion: The proposed approach provides a tool for extracting time-varying graphs and identifying disconnectors associated with disconnectivity (absence of paths) and also connectors associated with abnormal integration (additional paths) in patient group graphs. Significance: We detected several missing links in SZ, both within and between functional domains, in particular within the subcortical (3 links) and somatomotor (4 links) domains. Interestingly, our proposed method identified new links within the somatomotor domain which may be related to a compensatory response in patients that warrants future study.