Sukstanskii Alexander L, Yablonskiy Dmitriy A
Biomedical MR Lab, Mallinckrodt Institute of Radiology, Washington University, St. Louis, MO 63110, USA.
J Magn Reson. 2003 Aug;163(2):236-47. doi: 10.1016/s1090-7807(03)00131-9.
A detailed theoretical analysis of the free induction decay (FID) and spin echo (SE) MR signal formation in the presence of mesoscopic structure-specific magnetic field inhomogeneities is developed in the framework of the Gaussian phase distribution approximation. The theory takes into account diffusion of nuclear spins in inhomogeneous magnetic fields created by arbitrarily shaped magnetized objects with permeable boundaries. In the short-time limit the FID signal decays quadratically with time and depends on the objects' geometry only through the volume fraction, whereas the SE signal decays as 5/2 power of time with the coefficient depending on both the volume fraction of the magnetized objects and their surface-to-volume ratio. In the motional narrowing regime, the FID and SE signals for objects of finite size decay mono-exponentially; a simple general expression is obtained for the relaxation rate constant deltaR2. In the case of infinitely long cylinders in the motional narrowing regime the theory predicts non-exponential signal decay lnS approximately -tlnt in accordance with previous results. For specific geometries of the objects (spheres and infinitely long cylinders) exact analytical expressions for the FID and SE signals are given. The theory can be applied, for instance, to biological systems where mesoscopic magnetic field inhomogeneities are induced by deoxygenated red blood cells, capillary network, contrast agents, etc.
在高斯相位分布近似框架下，对存在介观结构特定磁场不均匀性时自由感应衰减（FID）和自旋回波（SE）磁共振信号形成进行了详细的理论分析。该理论考虑了核自旋在由具有可渗透边界的任意形状磁化物体产生的非均匀磁场中的扩散。在短时间极限下，FID信号随时间呈二次衰减，且仅通过体积分数依赖于物体的几何形状，而SE信号随时间呈5/2次幂衰减，其系数取决于磁化物体的体积分数及其表面积与体积比。在运动窄化区域，有限尺寸物体的FID和SE信号呈单指数衰减；得到了弛豫速率常数deltaR2的一个简单通用表达式。在运动窄化区域中无限长圆柱体的情况下，该理论根据先前的结果预测信号呈非指数衰减lnS≈ -tlnt。对于物体的特定几何形状（球体和无限长圆柱体），给出了FID和SE信号的精确解析表达式。例如，该理论可应用于由脱氧红细胞、毛细血管网络、造影剂等引起介观磁场不均匀性的生物系统。
