Statistical artifacts in diffusion tensor MRI (DT-MRI) caused by background noise

This work helps elucidate how background noise introduces statistical artif acts in the distribution of the sorted eigenvalues and eigenvectors in diff usion tensor MRI (DT-MRI) data, Although it was known that sorting eigenval ues (principal diffusivities) by magnitude introduces a bias in their sampl e mean within a homogeneous region of interest (ROI), here it is shown that magnitude sorting also introduces a significant bias in the variance of th e sample mean eigenvalues. New methods are presented to calculate the mean and variance of the eigenvectors of the diffusion tensor, based on a dyadic tensor representation of eigenvalue-eigenvector pairs. Based on their use it is shown that sorting eigenvalues by magnitude also introduces a bias in the mean and the variance of the sample eigenvectors (principal directions ), This required the development of new methods to calculate the mean and v ariance of the eigenvectors of the diffusion tensor, based on a dyadic tens or representation of eigenvalue-eigenvector pairs. Moreover, a new approach is proposed to order these pairs within an ROI, To do this, a corresponden ce between each principal axis of the diffusion ellipsoid, an eigenvalue-ei genvector pair, and a dyadic tensor constructed from it is exploited, A mea sure of overlap between principal axes of diffusion ellipsoids in different voxels is defined that employs projections between these dyadic tensors, T he optimal eigenvalue assignment within an ROI maximizes this overlap. Bias in the estimate of the mean and of the variance of the eigenvalues and of their corresponding eigenvectors is reduced in DT-MRI experiments and in Mo nte Carlo simulations of such experiments. Improvement is most significant in isotropic regions, but some is also observed in anisotropic regions. Thi s statistical framework should enhance our ability to characterize microstr ucture and architecture of healthy tissue, and help to assess its changes i n development, disease, and degeneration. Mitigating these artifacts should also improve the characterization of diffusion anisotropy and the elucidat ion of fiber-tract trajectories in the brain and in other fibrous tissues. Published 2000 Wiley-Liss, Inc.(dagger).