Dynamic Topological Data Analysis for Functional Brain Signals

We propose a novel dynamic topological data analysis (TDA) framework that builds persistent homology over a time series of 3D functional brain images. The proposed method encodes the time series as a time-ordered sequence of Vietoris-Rips complexes and their corresponding barcodes in studying dynamically changing topological patterns. The method is applied to the resting-state functional magnetic resonance imaging (fMRI) of the human brain. We demonstrate that the dynamic-TDA can capture the topological patterns that are consistently observed across different time points in the resting-state fMRI.