Dept. of Radiology, Medical Physics, Medical Center, Faculty of Medicine, University of Freiburg, Freiburg, Germany.
J Magn Reson. 2019 Feb;299:168-175. doi: 10.1016/j.jmr.2018.12.008. Epub 2018 Dec 15.
High-precision signal phase measurements ignited an ongoing discussion of the microstructural correlates of the Larmor frequency shift of water in biological tissues. In a broader context, this is the question about the averaged precession frequency in magnetically heterogenous, in particular, porous media. In this study, the Larmor frequency shift is found analytically for water filling connected pore space between NMR-invisible magnetized inclusions with a constant magnetic susceptibility tensor. The magnetic microstructure that encompasses the inclusions' shape and their spatial arrangement is arbitrary as well as the inclusions' magnetic susceptibility tensor. The result is limited to the case of effectively fast diffusion of water molecules. In this limit, the effect of magnetic microstructure on the Larmor frequency shift is represented by only five relevant parameters in the general case and by a single parameter in the case of axially symmetric microstructure. This single parameter enters the dependence of the Larmor frequency on the sample orientation relative to the main magnetic field in the previously performed experiments. The result can help interpreting known experimental data and developing realistic models of biological tissues.
高精度信号相位测量引发了一场关于生物组织中水分子拉莫尔频率移动的微观结构相关性的持续讨论。更广泛地说，这就是关于在磁性不均匀、特别是多孔介质中平均进动频率的问题。在这项研究中，对于充满 NMR 不可见的磁化夹杂物之间的连通孔隙空间的水，我们通过分析找到了拉莫尔频率移动，这些夹杂物的磁各向异性张量是常数。包含夹杂物形状及其空间排列的磁微观结构是任意的，夹杂物的磁各向异性张量也是任意的。该结果仅限于水分子有效快速扩散的情况。在这个极限下，磁微观结构对拉莫尔频率移动的影响在一般情况下仅由五个相关参数表示，而在轴对称微观结构的情况下仅由一个参数表示。这个单一参数进入了先前进行的实验中样品相对于主磁场的取向对拉莫尔频率的依赖关系。该结果有助于解释已知的实验数据并开发生物组织的现实模型。
