Yuan Ying, Zhu Hongtu, Styner Martin, Gilmore John H, Marron J S
University of North Carolina at Chapel Hill.
Ann Appl Stat. 2013 Mar;7(1):102-125. 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 3×3 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.
扩散张量成像能够在活体状态下提供关于脑白质中组织结构和纤维束方向的重要信息。它会沿着纤维束生成扩散张量，这些扩散张量是3×3对称正定（SPD）矩阵。本文开发了一个功能数据分析框架，将沿着纤维束的扩散张量建模为具有一组感兴趣的协变量（如年龄和性别）的黎曼流形中的功能数据。我们提出了一个具有变系数函数的统计模型，以刻画功能SPD矩阵值响应与协变量之间的动态关联。我们计算了SPD矩阵空间中对数欧几里得度量下变系数函数的加权最小二乘估计量。我们还开发了一个全局检验统计量来检验关于这些系数函数的特定假设，并构建它们的同时置信带。模拟数据进一步用于检验估计的变系数函数的有限样本性能。我们将我们的模型应用于研究潜在的性别差异，并在一项神经发育临床研究中发现沿着右侧内囊束的扩散张量发育在统计上有显著差异。
