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

Diffusion tensor imaging can provide a complete description of the diffusio n process in tissue. However, this description Is not unique but is orienta tion dependent, and, to quantify properly the intrinsic orientation-indepen dent diffusion properties of the tissue, a set of three rotationally invari ant quantities is needed. Instead of using the tensor eigenvalues for this, we define a new set consisting of scaled invariants that have the proper m agnitude 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 (isotrop ic) and one (completely anisotropic). Because rotational invariants are use d, this approach does not require tensor diagonalization and eigenvalue det ermination and is therefore not susceptible to potential artifacts induced during these number manipulations. The relationship between the new anisotr opy definitions and existing orientation-independent anisotropy indices obt ained from eigenvalues is discussed, after which the new approach is evalua ted for a group of healthy volunteers. (C) 1999 Wiley-Liss, Inc.