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

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### 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.

### Author and article information

###### Journal
17 January 2020
###### Article
2001.06529