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 ∼ t ^{− ϑ} with dynamical exponent ϑ. 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 ϑ ≃ 1/2 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 ϑ = 1/2 exponent. In contrast, the Kärger 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.