Retrospective measurement of the diffusion tensor eigenvalues from diffusion anisotropy and mean diffusivity in DTI

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Abstract
A simple theoretical framework to compute the eigenvalues of a cylindrically symmetric prolate diffusion tensor (D) from one of the rotationally‐invariant diffusion anisotropy indices and average diffusivity is presented and validated. Cylindrical or axial symmetry assumes a prolate ellipsoid shape (λ∥ = λ1 > λ⟂ = (λ2 + λ3)/2; λ2 = λ3). A prolate ellipsoid with such symmetry is largely satisfied in a number of white matter (WM) structures, such as the spinal cord, corpus callosum, internal capsule, and corticospinal tract. The theoretical model presented is validated using in vivo DTI measurements of rat spinal cord and human brain, where eigenvalues were calculated from both the set of diffusion coefficients and a tensor analysis. This method was used to retrospectively analyze literature data that reported tensor‐derived average diffusivity, anisotropy, and eigenvalues, and similar eigenvalue measurements were obtained. The method provides a means to retrospectively reanalyze literature data that do not report eigenvalues. Other potential applications of this method are also discussed. Magn Reson Med, 2006.