The displacement correlation tensor: Microstructure, ensemble anisotropy and curving fibers
The displacement correlation tensor: Microstructure, ensemble anisotropy and curving fibers
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DOI：
10.1016/j.jmr.2010.10.003
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发表时间：
2011-01-01
影响因子：
2.2
通讯作者：
Buhl, Niels
中科院分区：
文献类型：
--
作者：
Jespersen, Sune Norhoj;Buhl, Niels
已知多个扩散波矢量的实验比标准扩散实验携带更多的信息。在这里，我们考虑这类脉冲序列的一个特殊情况，双波矢扩散实验，并使用信号的累积展开引入位移相关张量。我们讨论了它的物理解释和属性，特别注意到，它的短时间的行为允许确定的孔隙空间的表面体积比。我们提出了位移相关张量的一般表达式，并提供了几个模型的几何形状的显式表达式。然后，我们表明，散射矩阵表征的取向分布的合奏的圆柱体是简单的位移相关张量。这一结果被推广到具有任意形状的孔系综，允许在高斯相位近似的双波矢量扩散信号的微观结构和系综各向异性的影响的精确制定。最后，作为双波矢量扩散信号的一个新的应用，我们分析了它在弯曲纤维中的行为，并建议位移相关张量可以用来估计亚体素纤维曲率和偏转角。计算机模拟证实了理论结果。(C)2010年爱思唯尔公司All rights reserved.
Experiments with multiple diffusion wave vectors are known to carry more information than what is available from standard diffusion experiments. Here we consider a special case of this class of pulse sequences, the double wave vector diffusion experiment, and use the cumulant expansion of the signal to introduce the displacement correlation tensor. We discuss its physical interpretation and properties, noting in particular that its short time behavior allows determination of the surface to volume ratio of the pore space. We present a general expression for the displacement correlation tensor, and provide explicit expressions for a few model geometries. We then show that the scatter matrix characterizing the orientation distribution of an ensemble of cylinders is simply related to the displacement correlation tensor. This result is generalized to ensembles of pores with arbitrary shapes allowing a precise formulation of the influence of microstructural and ensemble anisotropy on the double wave vector diffusion signal in the Gaussian phase approximation. Finally, as a new application of the double wave vector diffusion signal, we analyze its behavior in a curving fiber, and suggest that the displacement correlation tensor may be used to estimate sub-voxel fiber curvature and deflection angle. The theoretical results are corroborated by computer simulations. (C) 2010 Elsevier Inc. All rights reserved.