Schwartz L M, Bergman D J, Dunn K J, Mitra P P
Schlumberger-Doll Research, Ridgefield, CT 06877-4108, USA.
Magn Reson Imaging. 1996;14(7-8):737-43. doi: 10.1016/s0730-725x(96)00158-0.
Random walk computer simulations are an important tool in understanding magnetic resonance measurements in porous media. In this paper we focus on the description of pulsed field gradient spin echo (PGSE) experiments that measure the probability, P(R,t), that a diffusing water molecule will travel a distance R in a time t. Because PGSE simulations are often limited by statistical considerations, we will see that valuable insight can be gained by working with simple periodic geometries and comparing simulation data to the results of exact eigenvalue expansions. In this connection, our attention will be focused on (1) the wavevector, k, and time dependent magnetization, M(k, t); and (2) the normalized probability, Ps(delta R, t), that a diffusing particle will return to within delta R of the origin after time t.
随机游走计算机模拟是理解多孔介质中磁共振测量的重要工具。在本文中，我们重点描述脉冲场梯度自旋回波（PGSE）实验，该实验测量扩散水分子在时间t内移动距离R的概率P(R,t)。由于PGSE模拟常常受到统计因素的限制，我们将看到，通过研究简单的周期性几何结构并将模拟数据与精确本征值展开的结果进行比较，可以获得有价值的见解。在这方面，我们将关注：（1）波矢k和随时间变化的磁化强度M(k,t)；（2）扩散粒子在时间t后返回原点的δR范围内的归一化概率Ps(δR,t)。
