## The Annals of Applied Statistics

### Varying coefficient model for modeling diffusion tensors along white matter tracts

#### 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.

#### Article information

Source
Ann. Appl. Stat., Volume 7, Number 1 (2013), 102-125.

Dates
First available in Project Euclid: 9 April 2013

https://projecteuclid.org/euclid.aoas/1365527192

Digital Object Identifier
doi:10.1214/12-AOAS574

Mathematical Reviews number (MathSciNet)
MR3086412

Zentralblatt MATH identifier
06171265

#### Citation

Yuan, Ying; Zhu, Hongtu; Styner, Martin; Gilmore, John H.; Marron, J. S. Varying coefficient model for modeling diffusion tensors along white matter tracts. Ann. Appl. Stat. 7 (2013), no. 1, 102--125. doi:10.1214/12-AOAS574. https://projecteuclid.org/euclid.aoas/1365527192

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