A new hierarchical brain parcellation method based on discrete morse theory for functional MRI data

Parcellation of the brain into functionally meaningful regions is a crucial step in studies of brain connectivity using complex network analysis methods based on resting-state functional MRI (rs-fMRI). With the recent development of fast acquisition sequences at ultra-high-field (7T), high-spatial-resolution rs-fMRI can now be collected from the whole-brain with sufficient temporal resolution to capture the slow haemodynamic fluctuations underlying functional brain connectivity. A method for obtaining individual brain parcel-lations based on rs-fMRI has recently been proposed, which grows a set of stable seeds into an initial detailed parcellation that is further clustered using a hierarchical approach that enforces spatial contiguity of the parcels. Smoothing is performed to remove spurious features before the growing step, which precludes the exploration of the ultra-high spatial resolution of our data. In this paper, we propose an approach for brain parcellation that takes advantage of the topological structure present in the spatial organization exhibited by rs-fMRI data, using methods based on discrete Morse theory and persistent homology. This framework provides a region importance measure derived from local functional homogeneity and a topologically-informed simplification procedure that enables the analysis of high resolution rs-fMRI data at different levels of detail.