  Childhood maltreatment may adversely affect brain development and
consequently influence 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 in maltreated and typically
developing children. We perform topological data analysis (TDA) to assess the
alteration in the global topology of the brain white-matter structural
covariance network among children. 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 control group, 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 suggest that TDA can be a valuable framework to
model altered topological structures of the brain. The MATLAB codes and
processed data used in this study can be found at
https://github.com/laplcebeltrami/maltreated.
