Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY 10016, USA.
NMR Biomed. 2010 Aug;23(7):682-97. doi: 10.1002/nbm.1584.
Living tissues and other heterogeneous media generally consist of structural units with different diffusion coefficients and NMR properties. These blocks, such as cells or clusters of cells, can be much smaller than the imaging voxel, and are often comparable with the diffusion length. We have developed a general approach to quantify the medium heterogeneity when it is much finer than the sample size or the imaging resolution. The approach is based on the treatment of the medium statistically in terms of the correlation functions of the local parameters. The diffusion-weighted signal is explicity found for the case in which the local diffusivity varies in space, in the lowest order in the diffusivity variance. We demonstrate how the correlation length and the variance of the local diffusivity contribute to the time-dependent diffusion coefficient and the time-dependent kurtosis. Our results are corroborated by Monte Carlo simulations of diffusion in a two-dimensional heterogeneous medium.
活组织和其他不均匀介质通常由具有不同扩散系数和 NMR 性质的结构单元组成。这些块，如细胞或细胞簇，可以比成像体素小得多，并且通常与扩散长度相当。当介质的不均匀性比样品尺寸或成像分辨率小得多时，我们已经开发出了一种定量描述介质不均匀性的通用方法。该方法基于根据局部参数的相关函数对介质进行统计学处理。在局部扩散率随空间变化的情况下，明确找到了扩散加权信号，其扩散率方差的最低阶。我们展示了局部扩散率的相关长度和方差如何影响时变扩散系数和时变峰度。我们的结果得到了在二维不均匀介质中扩散的蒙特卡罗模拟的证实。
