Schwartzman Armin, Dougherty Robert F, Taylor Jonathan E
Department of Statistics, Stanford University, Stanford, California, USA.
Magn Reson Med. 2005 Jun;53(6):1423-31. doi: 10.1002/mrm.20503.
Diffusion tensor imaging (DTI) data differ fundamentally from most brain imaging data in that values at each voxel are not scalars but 3 x 3 positive definite matrices also called diffusion tensors. Frequently, investigators simplify the data analysis by reducing the tensor to a scalar, such as fractional anisotropy (FA). New statistical methods are needed for analyzing vector and tensor valued imaging data. A statistical model is proposed for the principal eigenvector of the diffusion tensor based on the bipolar Watson distribution. Methods are presented for computing mean direction and dispersion of a sample of directions and for testing whether two samples of directions (e.g., same voxel across two groups of subjects) have the same mean. False discovery rate theory is used to identify voxels for which the two-sample test is significant. These methods are illustrated in a DTI data set collected to study reading ability. It is shown that comparison of directions reveals differences in gross anatomic structure that are invisible to FA.
扩散张量成像（DTI）数据与大多数脑成像数据有着根本区别，即每个体素的值不是标量，而是3×3正定矩阵，也称为扩散张量。通常，研究人员通过将张量简化为标量，如分数各向异性（FA），来简化数据分析。需要新的统计方法来分析向量和张量值成像数据。基于双极沃森分布，提出了一种针对扩散张量主特征向量的统计模型。给出了计算方向样本的平均方向和离散度以及检验两个方向样本（例如，两组受试者的相同体素）是否具有相同均值的方法。错误发现率理论用于识别两样本检验具有显著性的体素。这些方法在为研究阅读能力而收集的DTI数据集中得到了说明。结果表明，方向比较揭示了FA无法察觉的大体解剖结构差异。
