A Riemannian Framework for Longitudinal Analysis of Resting-State Functional Connectivity

Even though the number of longitudinal resting-state-fMRI studies is increasing, accurately characterizing the changes in functional connectivity across visits is a largely unexplored topic. To improve characterization, we design a Riemannian framework that represents the functional connectivity pattern of a subject at a visit as a point on a Riemannian manifold. Geodesic regression across the ‘sample’ points of a subject on that manifold then defines the longitudinal trajectory of their connectivity pattern. To identify group differences specific to regions of interest (ROI), we map the resulting trajectories of all subjects to a common tangent space via the Lie group action. We account for the uncertainty in choosing the common tangent space by proposing a test procedure based on the theory of latent p-values. Unlike existing methods, our proposed approach identifies sex differences across 246 subjects, each of them being characterized by three rs-fMRI scans.