Callaghan PT
Department of Physics, Massey University, Palmerston North, New Zealand.
J Magn Reson. 1997 Nov;129(1):74-84. doi: 10.1006/jmre.1997.1233.
A simple mathematical formalism is presented which allows closed form expressions for the echo attenuation, E(q), in spin echo diffusion experiments, for practically all gradient waveforms and for the case of restricted diffusion in enclosing pores, with or without wall relaxation. The method, which derives from the multiple propagator approach of A. Caprihan et al. (1996, J. Magn. Reson. A 118, 94), depends on the representation of the gradient waveform by a succession of sharp gradient impulses. It leads to E(q) being expressed as a product of matrix operators corresponding quite naturally to the successive sandwich of phase evolution and Brownian migration events. Simple expressions are given for the case of the finite width gradient pulse PGSE experiment, the CPMG pulse train used in frequency-domain modulated gradient spin echo NMR, and the case of a sinusoidal waveform. The finite width gradient pulse PGSE and CPMG pulse trains are evaluated for the case of restricted diffusion between parallel reflecting planes. The former results agree precisely with published computer simulations while the latter calculation provides useful insight regarding the spectral density approach to impeded Brownian motion. Copyright 1997 Academic Press. Copyright 1997Academic Press
本文提出了一种简单的数学形式，它可以给出自旋回波扩散实验中回波衰减E(q)的封闭形式表达式，适用于几乎所有的梯度波形，以及在有或没有壁弛豫的封闭孔隙中受限扩散的情况。该方法源自A. Caprihan等人（1996年，《磁共振杂志A》118卷，94页）的多重传播子方法，它依赖于用一系列尖锐的梯度脉冲来表示梯度波形。这使得E(q)可以表示为矩阵算子的乘积，这些矩阵算子与相位演化和布朗迁移事件的连续夹心相当自然地对应。对于有限宽度梯度脉冲PGSE实验、频域调制梯度自旋回波核磁共振中使用的CPMG脉冲序列以及正弦波形的情况，都给出了简单的表达式。对于平行反射平面之间受限扩散的情况，对有限宽度梯度脉冲PGSE和CPMG脉冲序列进行了评估。前者的结果与已发表的计算机模拟结果精确一致，而后者的计算为受阻布朗运动的谱密度方法提供了有用的见解。版权所有1997年学术出版社。版权所有1997年学术出版社
