Ziener C H, Kampf T, Schlemmer H-P, Buschle L R
German Cancer Research Center DKFZ, E010 Radiology, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany. University Hospital Heidelberg, Neuroradiology, Im Neuenheimer Feld 400, 69120 Heidelberg, Germany.
J Phys Condens Matter. 2019 Apr 17;31(15):155101. doi: 10.1088/1361-648X/aafe21. Epub 2019 Jan 14.
The spin echo signal from vessels in Krogh's capillary model as well in the random distribution vessel model are studied by numerically solving the Bloch-Torrey equation. A comparison is made with the Gaussian local phase approximation, the Gaussian phase approximation and the strong-collision approximation. Differences between the Gaussian local phase approximation and the Gaussian phase approximation are explained. In the intermediate diffusion regime, the full numerical solution shows oscillations which are absent in any of the approximate solutions. In the limit of large diffusion coefficients, where the approximations become exact, the signal shows a linear-exponential decay governed by a single parameter. The features of the exact numerical solution can be explained by an analytically solvable discrete two-level model. There is a one-to-one correspondence between the different diffusion regimes and the three cases of the damped harmonic oscillator.
通过对布洛赫 - 托里方程进行数值求解，研究了克罗格毛细血管模型以及随机分布血管模型中血管的自旋回波信号。将其与高斯局部相位近似、高斯相位近似和强碰撞近似进行了比较。解释了高斯局部相位近似和高斯相位近似之间的差异。在中间扩散区域，完整的数值解显示出振荡，而任何近似解中都不存在这种振荡。在大扩散系数的极限情况下，近似变得精确，信号呈现出由单个参数控制的线性指数衰减。精确数值解的特征可以通过一个可解析求解的离散双能级模型来解释。不同的扩散区域与阻尼谐振子的三种情况之间存在一一对应关系。
