Abstract
We present a novel persistent homological sparse network analysis framework for characterizing white matter abnormalities in tensor-based morphometry (TBM) in magnetic resonance imaging (MRI). Traditionally TBM is used in quantifying tissue volume change in each voxel in a massive univariate fashion. However, this obvious approach cannot be used in testing, for instance, if the change in one voxel is related to other voxels. To address this limitation of univariate-TBM, we propose a new persistent homological approach to testing more complex relational hypotheses across brain regions. The proposed methods are applied to characterize abnormal white matter in maltreated children. The results are further validated using fractional anisotropy (FA) values in diffusion tensor imaging (DTI).