Varying coefficient model for modeling diffusion tensors along white matter tracts

TL;DR

This paper introduces a novel statistical framework for modeling diffusion tensors along brain white matter tracts as functional data on a Riemannian manifold, incorporating covariates like age and gender.

Contribution

It develops a varying coefficient model for SPD matrices using the log-Euclidean metric, including hypothesis testing and confidence bands, advancing analysis of diffusion tensor imaging data.

Findings

Identified significant gender differences in diffusion tensors along the right internal capsule.

Demonstrated the model's effectiveness through simulations and real neurodevelopmental data.

Provided a new methodology for analyzing tensor-valued functional data in neuroimaging.

Abstract

Diffusion tensor imaging provides important information on tissue structure and orientation of fiber tracts in brain white matter in vivo. It results in diffusion tensors, which are $3\times3$ symmetric positive definite (SPD) matrices, along fiber bundles. This paper develops a functional data analysis framework to model diffusion tensors along fiber tracts as functional data in a Riemannian manifold with a set of covariates of interest, such as age and gender. We propose a statistical model with varying coefficient functions to characterize the dynamic association between functional SPD matrix-valued responses and covariates. We calculate weighted least squares estimators of the varying coefficient functions for 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 and construct their simultaneous confidence bands. Simulated data are further used to examine the finite sample performance of the estimated varying coefficient functions. We apply our model to study potential gender differences and find a statistically significant aspect of the development of diffusion tensors along the right internal capsule tract in a clinical study of neurodevelopment.