Varying Coefficient Model for Modeling Diffusion Tensors Along White Matter Bundles

• Activity Number: 31
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ying Yuan*+ and Hongtu Zhu and Martin Styner and John H. Gilmore and Steve Marron
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina
• Keywords: Confidence band ; Diffusion tensor imaging ; Global test statistic ; Varying coefficient model ; Log-Euclidean metric ; Symmetric positive matrix

Abstract

Diffusion tensor imaging (DTI) provides important information on tissue structure and orientation of major fiber bundles in brain white matter in vivo. It results in a three dimensional grid of tensors, which are 3 × 3 symmetric positive definite (SPD) matrices. 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.