A simple matrix formalism for spin echo analysis of restricted diffusion under generalized gradient waveforms
A simple matrix formalism for spin echo analysis of restricted diffusion under generalized gradient waveforms
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DOI：
10.1006/jmre.1997.1233
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发表时间：
1997-11-01
影响因子：
2.2
通讯作者：
Callaghan, PT
中科院分区：
文献类型：
--
作者：
Callaghan, PT
一个简单的数学形式主义，它允许封闭的形式表达式的回波衰减，E（q），在自旋回波扩散实验中，几乎所有的梯度波形和限制扩散的情况下，在封闭的孔隙，有或没有壁松弛，该方法，它来自多个传播的方法A，Caprihan等人。（1996，J.Magn.Reson，A 118，94），取决于梯度波形通过一系列尖锐梯度脉冲的表示。它导致E（q）被表示为矩阵算子的乘积，很自然地对应于相位演化和布朗迁移事件的连续夹层。给出了有限宽度梯度脉冲PGSE实验、频域调制梯度自旋回波NMRI中使用的CPMG脉冲列和正弦波形的情况下的简单表达式。有限宽度梯度脉冲PGSE和CPMG脉冲序列的情况下，平行反射面之间的限制扩散进行了评估。前者的结果与发表的计算机模拟完全一致，而后者的计算提供了有用的见解，关于谱密度方法阻碍布朗运动。(C)?中国科学出版社.
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 ct 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 NMRI 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. (C) ?Academic Press.