Two-step anomalous diffusion tensor imaging.

We extend the formalism of anomalous diffusion imaging to include directional anisotropy of fitted parameters. The resulting technique is termed anomalous diffusion tensor imaging (aDTI), and allows the directional properties of the distributed diffusion coefficient (α) and the anomalous diffusion exponent, (γ) to be analysed using the same analytical techniques as regular diffusion tensor imaging (DTI). Together, these parameters quantify the rate of diffusion (α) and the complexity of the diffusion environment (γ). We generated tensor images for the anomalous exponent tensor (Γ) and distributed diffusivity tensor (A) from in vivo human brain data and present images of eigenvalues, eigenvectors, Trace/3 (Tr), fractional anisotropy (FA) and tensor shape measures. In white matter, A is found to have a median Tr = 0.56 × 10(- 3) mm(2) s(- 1), FA = 0.58 and Γ Tr = 0.69, FA = 0.13. We observed that white matter shows a similar anisotropic geometry for the distributed diffusion tensor as for the regular diffusion tensor, whereas the anomalous exponent tensor exhibits a different shape characteristic which may be informative of tissue microstructure.