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March 2013 Varying coefficient model for modeling diffusion tensors along white matter tracts
Ying Yuan, Hongtu Zhu, Martin Styner, John H. Gilmore, J. S. Marron
Ann. Appl. Stat. 7(1): 102-125 (March 2013). DOI: 10.1214/12-AOAS574


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.


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Ying Yuan. Hongtu Zhu. Martin Styner. John H. Gilmore. J. S. Marron. "Varying coefficient model for modeling diffusion tensors along white matter tracts." Ann. Appl. Stat. 7 (1) 102 - 125, March 2013.


Published: March 2013
First available in Project Euclid: 9 April 2013

zbMATH: 06171265
MathSciNet: MR3086412
Digital Object Identifier: 10.1214/12-AOAS574

Keywords: Confidence band , Diffusion tensor imaging , global test statistic , log-Euclidean metric , symmetric positive matrix , varying coefficient model

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.7 • No. 1 • March 2013
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