In vivo observation and biophysical interpretation of time-dependent diffusion in human cortical gray matter

Abstract

The dependence of the diffusion MRI signal on the diffusion time \(t\) is a hallmark of tissue microstructure at the scale of the diffusion length. Here we measure the time-dependence of the mean diffusivity \(D(t)\) and mean kurtosis \(K(t)\) in cortical gray matter and in 25 gray matter sub-regions, in 10 healthy subjects. Significant diffusivity and kurtosis time-dependence is observed for \(t=21.2\)-100 ms, and is characterized by a power-law tail \(\sim t^{-\vartheta}\) with dynamical exponent \(\vartheta\). To interpret our measurements, we systematize the relevant scenarios and mechanisms for diffusion time-dependence in the brain. Using effective medium theory formalisms, we derive an exact relation between the power-law tails in \(D(t)\) and \(K(t)\). The estimated power-law dynamical exponent \(\vartheta\simeq1/2\) in both \(D(t)\) and \(K(t)\) is consistent with one-dimensional diffusion in the presence of randomly positioned restrictions along neurites. We analyze the short-range disordered statistics of synapses on axon collaterals in the cortex, and perform one-dimensional Monte Carlo simulations of diffusion restricted by permeable barriers with a similar randomness in their placement, to confirm the \(\vartheta=1/2\) exponent. In contrast, the K\"arger model of exchange is less consistent with the data since it does not capture the diffusivity time-dependence, and the estimated exchange time from \(K(t)\) falls below our measured \(t\)-range. Although we cannot exclude exchange as a contributing factor, we argue that structural disorder along neurites is mainly responsible for the observed time-dependence of diffusivity and kurtosis. Our observation and theoretical interpretation of the \(t^{-1/2}\) tail in \(D(t)\) and \(K(t)\) alltogether establish the sensitivity of a macroscopic MRI signal to micrometer-scale structural heterogeneities along neurites in human gray matter in vivo.