Anisotropy in high-resolution diffusion-weighted MRI and anomalous diffusion.
It is shown below that complex diffusion anisotropy observed in diffusion-weighted MRI can be fully accounted for by allowing for non-locality of the spatial operator in the diffusion equation. The anisotropy is represented by a distribution over directions on a sphere. It allows recognition of fiber tracts crossing at arbitrary angles. A simple generalization of the Stejskal-Tanner equation for the determination of the ODF is presented. Furthermore, an explicit solution of the Bloch-Torrey equation for an anisotropic time-fractional diffusion equation is obtained in terms of a generalized Mittag-Leffler type function.
ul. M.Grzegorzewskiej 6 m. 70, 02-778 Warszawa, Poland. ajhbergen@yahoo.com
A
A
Hanyga
M
M
Seredyńska
D000465:Algorithms; D016880:Anisotropy; D016477:Artifacts; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity