Structural universality class from time-dependent diffusion
In plain words
How quickly the measured water mobility settles as observation time increases depends on how the tissue structure is arranged at large scales. Which arrangement class each tissue belongs to is not established.
Precise statement
For the diffusion coefficient $D(t)$ in tissue approaching its long-time value as D(t) - D_inf ~ t^(-theta), with $\theta = (p + d)/2$ where d is the spatial dimension of the relevant disorder and p the structural exponent of its density correlations at long wavelengths, measure $\theta$ and assign p for white matter along and across axons, grey matter and muscle. An answer is a classification of tissues by p with measured exponents and uncertainty.
What would settle it
Oscillating and pulsed-gradient measurements over diffusion times spanning at least a decade, fitted against the competing power laws with model-selection statistics.
Status in the literature
Short-range disorder along axons ($p = 0, \theta = 1/2$ in one dimension) has support in brain and muscle data, while assignments for grey matter and transverse diffusion remain debated.