Effect of impermeable boundaries on diffusion-attenuated MR signal
Effect of impermeable boundaries on diffusion-attenuated MR signal
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DOI：
10.1016/j.jmr.2005.12.005
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发表时间：
2006-04-01
影响因子：
2.2
通讯作者：
Kiselev, VG
中科院分区：
文献类型：
--
作者：
Frohlich, AF;Ostergaard, L;Kiselev, VG
扩散加权信号（In S）的对数与b值(b)之间的非线性依赖关系通常被解释为两个物理上不同的间隔的表现，从而导致信号的双指数形式。该模型适合实验数据，然而，未能产生真实的隔室大小，严重危及DWI在细胞水平上推断结构信息的使用。据推测，双指数行为可归因于限制扩散在单个物理隔间的限制边界的影响。这种解释是基于对存在不渗透界面的扩散的分析，这种扩散时间很短，与整个隔室的尺寸相比，受边界影响的扩散层很薄。从扩散加权信号的累积展开式的角度分析该模型系统，该展开式导致in S的b次方的泰勒展开式。将该展开式终止为多项式形式，对于小b因子提供了极好的精度，但对于大b因子，该级数发散。研究了该级数的收敛性。产生大范围的b值，其中在第二项终止序列的绝对误差相对于没有扩散加权的信号幅度保持小于1%。在此精度下，研究模型中的信号可以描述为in S近似于-A中心点bD + B中心点（bD）(2)，其中参数A和B可以用分子速度的相关函数表示。这些参数对精确信号的拟合比双指数函数的三个参数更稳定。这种描述不适用于大b，因为它的累积展开是发散的。在更大的b值下，信号分别与一维、二维和三维系统中的1/b、1/b（3/2）和1/b(2)成正比。(c) 2005爱思唯尔公司版权所有。
The nonlinear dependence between the logarithm of the diffusion weighted signal, In S, and the b-value, b, has often been interpreted as a manifestation of two physically distinct compartments, resulting in a biexponential form of the signal. This model fits to experimental data, however, has failed to yield realistic compartment sizes, severely jeopardizing the use of DWI to infer structural information on a cellular level. It has been hypothesized that the biexponential behavior can be attributed to the effect of confining boundaries that restrict diffusion in individual physical compartments. This interpretation is based on the analysis of diffusion in the presence of impermeable interfaces for short diffusion times such that the layer in which diffusion is affected by the boundary is thin as compared with the dimensions of the whole compartment. This model system is analyzed from the point of view of the cumulant expansion of the diffusion-weighted signal that results in a Taylor expansion of In S in powers of b. Termination of this expansion to a polynomial form provides an excellent accuracy for small b-factors, but the series diverges for large b. The convergence of the series is studied, yielding a large range of b-values in which the absolute error of terminating the series at the second term remains smaller than 1% relative to the signal magnitude without diffusion weighting. With this accuracy, the signal in the studied model can be described as In S approximate to -A center dot bD + B center dot (bD)(2), where the parameters A and B can be expressed in terms of correlation functions of molecular velocity. Fitting of these parameters to the exact signal is more stable than for the three parameters of the biexponential function. This description fails for large b, for which the cumulant expansion diverges. The signal at even larger b-values is proportional to 1/b, 1/b(3/2), and 1/b(2) in one-, two-, and three-dimensional systems, respectively. (c) 2005 Elsevier Inc. All rights reserved.