Bergman D J, Dunn K J, LaTorraca G A
School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Israel.
Magn Reson Imaging. 1996;14(7-8):853-5. doi: 10.1016/s0730-725x(96)00215-9.
Magnetic field inhomogeneity can arise either because of an externally applied field gradient or because of spatial variations in magnetic susceptibility. The latter are most important when the solid matrix includes paramagnetic substances and when the uniform applied field, and, consequently, also the Larmor precession frequency are very large. Both types of field inhomogeneity add extra phase shifts to the precessing spins. These phase shifts vary with time and position in a complex and random fashion as a result of the diffusive motion of the spins. We have studied these effects by performing detailed calculations for the case of a fluid filled porous medium with a periodic microstructure. Special attention was devoted to the question of whether the statistical distribution of the phase shifts encountered in a Hahn spin echo experiment or in a Carr-Purcell-Meiboom-Gill (CPMG) spin-echo train can be approximated as a Gaussian. The mean square phase shift is measured in such experiments as an enhanced relaxation rate of the precessing transverse magnetization. We determine this mean square phase shift for periodic composites from the diffusion eigenstates, which were calculated using a previously developed Fourier expansion method. The enhanced relaxation rate depends on the echo spacing time tau in a way that can be correlated with important length scales of the porous microstructure. Those correlations can be extended also to disordered microstructures, like the ones that are found in natural rocks. We compare these theoretically predicted correlations with CPMG measurements performed on protons in laboratory samples of brine saturated sandstone.
磁场不均匀性可能由于外部施加的场梯度或由于磁化率的空间变化而产生。当固体基质包含顺磁性物质时，以及当均匀施加的场，进而拉莫尔进动频率非常大时，后者最为重要。这两种类型的场不均匀性都会给进动的自旋增加额外的相移。由于自旋的扩散运动，这些相移会随时间和位置以复杂且随机的方式变化。我们通过对具有周期性微观结构的充满流体的多孔介质情况进行详细计算来研究这些效应。特别关注的问题是，在哈恩自旋回波实验或卡尔 - 珀塞尔 - 梅博姆 - 吉尔（CPMG）自旋回波序列中遇到的相移的统计分布是否可以近似为高斯分布。在这样的实验中，均方相移被测量为进动横向磁化强度的增强弛豫率。我们从扩散本征态确定周期性复合材料的这种均方相移，扩散本征态是使用先前开发的傅里叶展开方法计算的。增强的弛豫率以一种可以与多孔微观结构的重要长度尺度相关的方式取决于回波间隔时间τ。这些相关性也可以扩展到无序微观结构，比如天然岩石中发现的那些。我们将这些理论预测的相关性与在盐水饱和砂岩的实验室样品中对质子进行的CPMG测量结果进行比较。
