Orientation-independent diffusion imaging without tensor diagonalization: Anisotropy definitions based on physical attributes of the diffusion ellipsoid

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Abstract
Diffusion tensor imaging can provide a complete description of the diffusion process in tissue. However, this description is not unique but is orientation dependent, and, to quantify properly the intrinsic orientation-independent diffusion properties of the tissue, a set of three rotationally invariant quantities is needed. Instead of using the tensor eigenvalues for this, we define a new set consisting of scaled invariants that have the proper magnitude of actual diffusion constants and that are directly related to the physical attributes of the diffusion ellipsoid, namely, its average radius, surface, and volume. Using these three physical invariants, a new family of anisotropy measures is defined that are normalized between zero (isotropic) and one (completely anisotropic). Because rotational invariants are used, this approach does not require tensor diagonalization and eigenvalue determination and is therefore not susceptible to potential artifacts induced during these number manipulations. The relationship between the new anisotropy definitions and existing orientation-independent anisotropy indices obtained from eigenvalues is discussed, after which the new approach is evaluated for a group of healthy volunteers. J. Magn. Reson. Imaging 1999;9:804–813.