Cross‐subject comparison of principal diffusion direction maps

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.