Testing Stationarity of Brain Functional Connectivity Using Change-Point Detection in fMRI Data

Mengyu Dai, Zhengwu Zhang, Anuj Srivastava

Abstract: This paper studies two questions: (1) Does the functional connectivity (FC) in a human brain remain stationary during performance of a task? (2) If it is non-stationary, how can one evaluate and estimate dynamic FC? The framework presented here relies on pre-segmented brain regions to represent instantaneous FC as symmetric, positive-definite matrices (SPDMs), with entries denoting covariances of fMRI signals across regions. The time series of such SPDMs is tested for change point detection using two important ideas: (1) a convenient Riemannian structure on the space of SPDMs for calculating geodesic distances and sample statistics, and (2) a graph-based approach, for testing similarity of distributions, that uses pairwise distances and a minimal spanning tree. This hypothesis test results in a temporal segmentation of observation interval into parts with stationary connectivity and an estimation of graph displaying FC during each such interval. We demonstrate these ideas using fMRI data from HCP database.