Altered Topological Structure of the Brain White Matter in Maltreated Children through Topological Data Analysis.

Childhood maltreatment may adversely affect brain development and consequently behavioral, emotional, and psychological patterns during adulthood. In this study, we propose an analytical pipeline for modeling the altered topological structure of brain white matter structure in maltreated and typically developing children. We perform topological data analysis (TDA) to assess the alteration in global topology of the brain white-matter structural covariance network for child participants. We use persistent homology, an algebraic technique in TDA, to analyze topological features in the brain covariance networks constructed from structural magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI). We develop a novel framework for statistical inference based on the Wasserstein distance to assess the significance of the observed topological differences. Using these methods in comparing maltreated children to a typically developing sample, we find that maltreatment may increase homogeneity in white matter structures and thus induce higher correlations in the structural covariance; this is reflected in the topological profile. Our findings strongly demonstrates that TDA can be used as a baseline framework to model altered topological structures of the brain.