标题： 各向异性扩散的取向平均扩散衰减磁共振信号 显示英文标题

标题： Orientationally-averaged diffusion-attenuated magnetic resonance signal for locally-anisotropic diffusion

摘要： 扩散衰减的磁共振信号对于异质介质已被表示为各向异性高斯子区域信号的总和。 任何宏观（全局或集合）各向异性对信号的影响可以通过平均不同取向实验方案得到的信号值来消除。 所得的平均信号与如果微区是各向同性（例如，随机）分布时所得到的结果相同，这在“粉末”样品中是常见的情况。 当微区由可能具有三个不同特征值的一般扩散张量表征时，我们提供了通过一般梯度波形获得的取向平均信号的精确表达式。 由于这两个领域在数学上的相似性，我们的结果预计不仅在多维扩散磁共振中而且在固态核磁共振光谱学中都将是有用的。 显示英文摘要

摘要： Diffusion-attenuated MR signal for heterogeneous media has been represented as a sum of signals from anisotropic Gaussian sub-domains. Any effect of macroscopic (global or ensemble) anisotropy in the signal can be removed by averaging the signal values obtained by differently oriented experimental schemes. The resulting average signal is identical to what one would get if the micro-domains are isotropically (e.g., randomly) distributed, which is the case for "powdered" specimens. We provide exact expressions for the orientationally-averaged signal obtained via general gradient waveforms when the microdomains are characterized by a general diffusion tensor possibly featuring three distinct eigenvalues. Our results are expected to be useful in not only multidimensional diffusion MR but also solid-state NMR spectroscopy due to the mathematical similarities in the two fields.