Varying coefficient model for modeling diffusion tensors along white matter tracts. (English) Zbl 1454.62425

Yuan, Ying; Zhu, Hongtu; Styner, Martin; Gilmore, John H.; Marron, J. S.

Ann. Appl. Stat. 7, No. 1, 102-125 (2013).

Summary: 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 \(3\times 3\) 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.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
62G08	Nonparametric regression and quantile regression
62G07	Density estimation
62G20	Asymptotic properties of nonparametric inference
62H12	Estimation in multivariate analysis
62H35	Image analysis in multivariate analysis
62R10	Functional data analysis

Keywords:

confidence band; diffusion tensor imaging; global test statistic; varying coefficient model; log-Euclidean metric; symmetric positive matrix

Software:

KernSmooth; fda (R)

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