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Varying Coefficient Model for Modeling Diffusion Tensors along White Matter Tracts

University of North Carolina at Chapel Hill, NC, USA.
Publication Date:
Ann Appl Stat
Volume Number:
Issue Number:
Ann Appl Stat. 2013 Mar;7(1):102-25.
PubMed ID:
Confidence band, Diffusion tensor imaging, Global test statistic, Log-Euclidean metric, Symmetric positive matrix, Varying coefficient model
Appears in Collections:
KL2 RR025746/RR/NCRR NIH HHS/United States
P01 CA142538/CA/NCI NIH HHS/United States
P30 HD003110/HD/NICHD NIH HHS/United States
P50 MH064065/MH/NIMH NIH HHS/United States
R01 CA074015/CA/NCI NIH HHS/United States
R01 GM070335/GM/NIGMS NIH HHS/United States
R01 HD053000/HD/NICHD NIH HHS/United States
R01 MH070890/MH/NIMH NIH HHS/United States
R01 MH086633/MH/NIMH NIH HHS/United States
TL1 RR025745/RR/NCRR NIH HHS/United States
U54 EB005149/EB/NIBIB NIH HHS/United States
UL1 RR025747/RR/NCRR NIH HHS/United States
Generated Citation:
Yuan Y., Zhu H., Styner M., Gilmore J.H., Marron J.S. Varying Coefficient Model for Modeling Diffusion Tensors along White Matter Tracts. Ann Appl Stat. 2013 Mar;7(1):102-25. PMID: 24533040. PMCID: PMC3922407.
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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 3×3 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 co-efficient 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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