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The brain structural connectome is generated by a collection of white matterfiber bundles constructed from diffusion weighted MRI (dMRI), acting ashighways for neural activity. There has been abundant interest in studying howthe structural connectome varies across individuals in relation to theirtraits, ranging from age and gender to neuropsychiatric outcomes. Afterapplying tractography to dMRI to get white matter fiber bundles, a key questionis how to represent the brain connectome to facilitate statistical analysesrelating connectomes to traits. The current standard divides the brain intoregions of interest (ROIs), and then relies on an adjacency matrix (AM)representation. Each cell in the AM is a measure of connectivity, e.g., numberof fiber curves, between a pair of ROIs. Although the AM representation isintuitive, a disadvantage is the high-dimensionality due to the large number ofcells in the matrix. This article proposes a simpler tree representation of thebrain connectome, which is motivated by ideas in computational topology andtakes topological and biological information on the cortical surface intoconsideration. We demonstrate that our tree representation preserves usefulinformation and interpretability, while reducing dimensionality to improvestatistical and computational efficiency. Applications to data from the HumanConnectome Project (HCP) are considered and code is provided for reproducingour analyses.

Tree Representations of Brain Structural Connectivity via Persistent Homology