Codd SL, Callaghan PT
Institute of Fundamental Sciences-Physics, Massey University, Palmerston North, 11222, New Zealand
J Magn Reson. 1999 Apr;137(2):358-372. doi: 10.1006/jmre.1998.1679.
A simple matrix formalism presented by Callaghan [J. Magn. Reson. 129, 74-84 (1997)], and based on the multiple propagator approach of Caprihan et al. [J. Magn. Reson. A 118, 94-102 (1996)], allows for the calculation of the echo attenuation, E(q), in spin echo diffusion experiments, for practically all gradient waveforms. We have extended the method to the treatment of restricted diffusion in parallel plate, cylindrical, and spherical geometries, including the effects of fluid-surface interactions. In particular, the q-space coherence curves are presented for the finite-width gradient pulse PGSE experiment and the results of the matrix calculations compare precisely with published computer simulations. It is shown that the use of long gradient pulses (delta approximately a2/D) create the illusion of smaller pores if a narrow pulse approximation is assumed, while ignoring the presence of significant wall relaxation can lead to both an underestimation of the pore dimensions and a misidentification of the pore geometry. Copyright 1999 Academic Press.
卡拉汉提出的一种简单矩阵形式（《磁共振杂志》129卷，74 - 84页，1997年），基于卡普里汉等人的多重传播子方法（《磁共振杂志A》118卷，94 - 102页，1996年），能够计算自旋回波扩散实验中几乎所有梯度波形下的回波衰减E(q)。我们已将该方法扩展到处理平行板、圆柱和球形几何结构中的受限扩散，包括流体 - 表面相互作用的影响。特别地，给出了有限宽度梯度脉冲PGSE实验的q空间相干曲线，并且矩阵计算结果与已发表的计算机模拟结果精确匹配。结果表明，如果采用窄脉冲近似，使用长梯度脉冲（δ约为a2/D）会造成孔隙较小的假象，而忽略显著的壁弛豫会导致孔隙尺寸估计偏低以及孔隙几何形状误判。版权所有1999年，学术出版社。
