论文标题
人类皮质灰质中时间依赖性扩散的体内观察和生物物理解释
In vivo observation and biophysical interpretation of time-dependent diffusion in human cortical gray matter
论文作者
论文摘要
扩散MRI信号对扩散时间$ t $的依赖性是扩散长度尺度上组织微观结构的标志。在这里，我们在10个健康受试者中衡量平均扩散率$ d（t）$和平均峰度$ k（t）$的时间依赖性。观察到$ t = 21.2 $ -100毫秒的显着扩散性和峰度时间依赖性，其特征是幂律尾巴$ \ sim t^{ - \ vartheta} $，带有动态指数$ \ vartheta $。为了解释我们的测量值，我们将相关的情景和机制系统化，以扩散时间依赖大脑的时间。使用有效的媒介理论形式主义，我们得出了$ d（t）$和$ k（t）$中的幂律尾巴之间的确切关系。 $ d（t）$和$ k（t）$中估计的动力学动态指数$ \ vartheta \ simeq1/2 $在存在随机定位沿神经突的限制的情况下，与一维扩散一致。我们分析了皮质中轴突抵押品上突触的短距离无序统计，并进行一维蒙特卡洛模拟，该蒙特卡罗模拟受到渗透性障碍的限制，其放置的随机性相似，以确认$ \ vartheta = 1/2 $指数。相比之下，Kärger交换模型与数据不一致，因为它没有捕获扩散性时间依赖性，并且估计的交换时间从$ k（t）$降至我们测量的$ t $范围以下。尽管我们不能排除交换为促成因素，但我们认为沿着神经突的结构性疾病主要导致观察到的扩散性和峰度的时间依赖性。我们对$ t^{ - 1/2} $ tail的观察和理论解释在$ d（t）$和$ k（t）$ alltogether中建立了宏观MRI信号对人类灰质物中神经素养的层级结构异质性的宏观MRI信号。
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.
