Dmitry S. Novikov1, Els Fieremans1,
Jens H. Jensen1, Joseph A. Helpern2
1Radiology, NYU School of
Medicine, New York, NY, United States; 2Radiology &
Radiological Science, Medical University of South Carolina, Charleston, SC,
United States
Diffusion coefficient in tissues is known to depend on the diffusion time. The short-time limit, while useful in probing surface-to-volume ratio of restrictions, is challenging in the clinical DWI. Here we focus on the opposite, long-time limit, and argue that the way the diffusivity approaches its tortuosity asymptote reveals quantitative information about the long-range order in tissues. We show that both diffusivity and kurtosis decrease with time with the same power law exponent that distinguishes a periodic arrangement from a disordered one. Our results agree with numerical simulations and can be applied to characterize tissue composition over large diffusion lengths.