Exploiting Hidden Persistent Structures in Multivariate Tensor-Based Morphometry and Its Application to Detecting White Matter Abnormality in Maltreated Children

We present novel multivariate tensor-based morphometry (TBM) for characterizing white matter abnormalities. Traditionally TBM is used in quantifying tissue volume changes in a massive univariate fashion. At each voxel, the Jacobian determinant obtained from TBM is used as the response variable in a general linear model (GLM) and a test statistic is constructed. 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 novel multivariate framework for more complex relational hypotheses across brain regions. To develop multivariate-TBM, it is necessary to regularize ill-conditioned covariance matrix by incorporating sparse penalty. Unfortunately, most sparse models like compressed sensing, sparse likelihood and LASSO cause a serious computational bottleneck. The computational bottleneck can be bypassed by exploiting hidden persistent structures in the sparse models. The proposed methods are applied to quantify abnormal white matter in maltreated children to show multivariate-TBM combined with persistent homology can extract additional information that cannot be obtained in univariate-TBM.