Varying Coefficient Models for Modeling Diffusion Tensors Along White Matter Bundles

This paper develops a functional data analysis framework to model diffusion tensors along fiber bundles as functional responses with a set of covariates of interest, such as age, diagnostic status and gender. This framework has a wide range of clinical applications including the characterization of normal brain development, the neural bases of neuropsychiatric disorders, and the joint effects of environmental and genetic factors on white matter fiber bundles. A challenging statistical issue is how to appropriately handle diffusion tensors along fiber bundles as functional data in a Riemannian manifold. We propose a statistical model with varying coefficient functions,called VCTF to characterize the dynamic association between functional SPD matrix-valued responses and covariates. We calculate a weighted least squares estimation of the varying coefficient functions under the Log-Euclidean metric in the space of SPD matrices. We also develop a global test statistic to test specific hypotheses about these coefficient functions. Simulated data are further used to examine the finite sample performance of VCTF . We apply our VCTF to study potential gender differences and find statistically significant aspect of the development of diffusion tensors along the right internal capsule tract in a clinical study of neurodevelopment.