Time-Dependent Diffusion & Kurtosis as a Probe of Tissue Structure

Dmitry S. Novikov¹, Els Fieremans¹, Jens H. Jensen¹, Joseph A. Helpern²

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.