Voxel-Based Inference for Eigenvalues and Eigenvectors in Group Diffusion Tensor Imaging Studies

• Activity Number: 356
• Type: Topic Contributed
• Date/Time: Tuesday, August 4, 2009 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Armin Schwartzman*+ and Robert F. Dougherty and Jonathan Taylor
• Companies: Harvard School of Public Health and Stanford University and Stanford University
• Keywords: random matrix ; likelihood ratio test ; manifold-valued data ; multiple testing ; empirical null ; false discovery rate

Abstract

Diffusion tensor images (DTI) differ from most medical images in that values at each voxel are not scalars, but 3×3 positive definite matrices called diffusion tensors (DTs). We consider the problem of testing whether two groups of DTIs are equal at each voxel in terms of the DT's eigenvalues or eigenvectors. Because eigen-decompositions are highly nonlinear, existing likelihood ratio statistics for these tests assume a simple orthogonally invariant covariance between the DT entries. We derive new approximations to the true distributions of these statistics when the covariance between the DT entries is arbitrary. The approximations are chi-square mixture distributions, obtained from approximate likelihood ratios computed at the tangent space to the eigenvalue/eigenvector parameter manifolds. Inference using these methods is illustrated in a DTI group comparison of boys vs. girls.