Nicholas Lange1,2, Peter J. Basser3
1Departments of Psychiatry & Biostatistics, Harvard University, Boston, MA, United States; 2Neurostatistics Laboratory, McLean Hospital, Belmont, MA, United States; 3PPITS, STBB, NICHD, National Institutes of Health, Bethesda, MD, United States
More biological information may already be contained in diffusion tensors measured typically by standard protocols run on clinical scanners in addition to that conveyed by their first-order size (e.g., mean, axial and radial diffusivity), second-order shape (e.g., FA) and third-order shape (skewness) coefficients. An enriched understanding of the size and shape of a tensor can be obtained by close inspection of its associated covariance tensor. This tensor takes on a variety of patterns whose complexity depends on the tissues unknown symmetry class, which can be determined by statistical methods, that may provide new insights in typical and disordered brain circuitry.