Consistent realignment of 3D diffusion tensor MRI eigenvectors

Diffusion tensor MR image data gives at each voxel in the image a symmetric, positive definite matrix that is denoted as the diffusion tensor at that voxel location. The eigenvectors of the tensor represent the principal directions of anisotopy in water diffusion. The eigenvector with the largest eigenvalue indicates the local orientation of tissue fibers in 3D as water is expected to diffuse preferentially up and down along the fiber tracts. Although there is no anatomically valid positive or negative direction to these fiber tracts, for many applications, it is of interest to assign an artificial direction to the fiber tract by choosing one of the two signs of the principal eigenvector in such a way that in local neighborhoods the assigned directions are consistent and vary smoothly in space. We demonstrate here an algorithm for realigning the principal eigenvectors by flipping their sign such that it assigns a locally consistent and spatially smooth fiber direction to the eigenvector field based on a Monte-Carlo algorithm adapted from updating clusters of spin systems. We present results that show the success of this algorithm on 11 available unsegmented canine cardiac volumes of both healthy and failing hearts.