Magin Richard L, Ingo Carson, Colon-Perez Luis, Triplett William, Mareci Thomas H
Department of Bioengineering, University of Illinois at Chicago, Chicago, IL USA 60607.
Microporous Mesoporous Mater. 2013 Sep 15;178:39-43. doi: 10.1016/j.micromeso.2013.02.054.
In this high-resolution magnetic resonance imaging (MRI) study at 17.6 Tesla of a fixed rat brain, we used the continuous time random walk theory (CTRW) for Brownian motion to characterize anomalous diffusion. The complex mesoporus structure of biological tissues (membranes, organelles, and cells) perturbs the motion of the random walker (water molecules in proton MRI) introducing halts between steps (waiting times) and restrictions on step sizes (jump lengths). When such waiting times and jump lengths are scaled with probability distributions that follow simple inverse power laws (, ||) non-Gaussian motion gives rise to sub- and super- diffusion. In the CTRW approach, the Fourier transform yields a solution to the generalized diffusion equation that can be expressed by the Mittag-Leffler function (MLF), (- ||Δ). We interrogated both white and gray matter regions in a 1 slice of a fixed rat brain (190 μ in plane resolution) with diffusion weighted MRI experiments using -values up to 25,000 /, by independently varying and Δ. When fitting these data to our model, the fractional order parameters, α and β, and the entropy measure, [Formula: see text], were found to provide excellent contrast between white and gray matter and to give results that were sensitive to the type of diffusion experiment performed.
在这项针对固定大鼠脑的17.6特斯拉高分辨率磁共振成像（MRI）研究中，我们使用布朗运动的连续时间随机游走理论（CTRW）来表征反常扩散。生物组织（膜、细胞器和细胞）复杂的中孔结构扰乱了随机游走者（质子MRI中的水分子）的运动，在步长之间引入了停顿（等待时间）并对步长大小（跳跃长度）施加了限制。当这些等待时间和跳跃长度用遵循简单反幂律（，||）的概率分布进行缩放时，非高斯运动会导致亚扩散和超扩散。在CTRW方法中，傅里叶变换给出了广义扩散方程的一个解，该解可以用米塔格 - 莱夫勒函数（MLF），（ - ||Δ）来表示。我们通过独立改变和Δ，使用高达25,000 /的 值进行扩散加权MRI实验，对固定大鼠脑的1个切片（平面分辨率为190 μ）中的白质和灰质区域进行了研究。当将这些数据拟合到我们的模型时，发现分数阶参数α和β以及熵度量[公式：见正文]在白质和灰质之间提供了出色的对比度，并且给出了对所执行的扩散实验类型敏感的结果。
