Persistent Homology of Time Varying and Spatially Varying Brain Networks

Brain connectivity, particularly based on resting-state fMRI data has been the subject of intense study for over a decade, stimulated by growing evidence of network involvement in brain diseases. But such study needs methods of analysis that can compare networks with differing numbers of nodes and links and provide results that are stable over different spatial and temporal data resolutions, as well as time varying networks. Topology provides a toolset that can address these issues.

In this work we discuss: network interpretation and comparison of sparsely and densely connected brain networks; multi-scale (spatial and temporal) network analyses; data quality diagnostics, defining of a core brain architecture; and differences in time varying persistent homology between a new approach for network construction and traditional time varying correlation networks.