  The brain structural connectome is generated by a collection of white matter
fiber bundles constructed from diffusion weighted MRI (dMRI), acting as
highways for neural activity. There has been abundant interest in studying how
the structural connectome varies across individuals in relation to their
traits, ranging from age and gender to neuropsychiatric outcomes. After
applying tractography to dMRI to get white matter fiber bundles, a key question
is how to represent the brain connectome to facilitate statistical analyses
relating connectomes to traits. The current standard divides the brain into
regions of interest (ROIs), and then relies on an adjacency matrix (AM)
representation. Each cell in the AM is a measure of connectivity, e.g., number
of fiber curves, between a pair of ROIs. Although the AM representation is
intuitive, a disadvantage is the high-dimensionality due to the large number of
cells in the matrix. This article proposes a simpler tree representation of the
brain connectome, which is motivated by ideas in computational topology and
takes topological and biological information on the cortical surface into
consideration. We demonstrate that our tree representation preserves useful
information and interpretability, while reducing dimensionality to improve
statistical and computational efficiency. Applications to data from the Human
Connectome Project (HCP) are considered and code is provided for reproducing
our analyses.
