人大脑皮质灰质时间依赖性弥散的活体观察和生物物理学解释
In vivo observation and biophysical interpretation of time-dependent diffusion in human cortical gray matter
摘要：
扩散MRI信号对扩散时间$t$的依赖性是扩散长度尺度下组织微结构的标志。在这里，我们测量的时间依赖性的平均扩散率$D(t)$和平均峰度$K(t)$在皮质灰质和25个灰质子区域，在10名健康受试者。对于$t=21.2$ ~ 100 ms，观察到显著的扩散率和峰度时间依赖性，其特征在于具有动力学指数$\vartheta$的幂律尾部$\sim t^{-\vartheta}$。为了解释我们的测量结果，我们系统化了大脑中扩散时间依赖性的相关场景和机制。利用有效介质理论，我们推导出了$D(t)$和$K(t)$中幂律尾之间的精确关系。估计的幂律动力学指数$\vartheta\simeq1/2$在$D(t)$和$K(t)$是一致的一维扩散中存在的随机定位的限制沿神经突。我们分析了皮层轴突侧支突触的短程无序统计，并进行了一维蒙特卡罗模拟扩散限制的渗透性障碍与类似的随机性，在他们的位置，以确认$\vartheta=1/2$指数。相比之下，Kärger交换模型与数据不太一致，因为它没有捕获扩散率时间依赖性，并且从$K(t)$估计的交换时间低于我们测量的$t$范围。虽然我们不能排除交换作为一个贡献因素，我们认为，沿神经突的结构紊乱主要是负责观察到的扩散率和峰度的时间依赖性。我们对$D(t)$和$K(t)$中的$t^{-1/2}$尾的观察和理论解释共同建立了宏观MRI信号对体内人类灰质中沿神经突的微米级结构异质性的敏感性。
英文摘要：
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 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.
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