Diffusional Attenuation During Soft Pulses: a Zangger-Sterk Pure Shift iDOSY Experiment

Diffusion-ordered spectroscopy experiments in which existing delays in a parent pulse sequence are used for diffusion encoding – iDOSY experiments – are potentially attractive because of their simplicity and sensitivity. However the calculation of diffusional attenuation in Zangger-Sterk pure shift iDOSY experiments is a very difficult problem to attack analytically, and is more easily approached numerically. Numerical simulations show that for typical experimental conditions, the dependence of diffusional attenuation on diffusion-encoding gradient amplitude is well represented by a shifted Gaussian function. The shift in gradient can be calculated analytically for the limiting case where the selective pulse is replaced by a hard 180° pulse at its midpoint; numerical simulations show that the effect of using different shapes of selective pulse is to scale down this limiting gradient shift by a constant factor that depends on the pulse shape used. The practical consequence is that under the experimental conditions appropriate for small molecules, the pure shift iDOSY method should allow good diffusion coefficient measurements to be made if appropriate allowance is made for the change in effective diffusion-encoding gradient. Parallel sets of numerical simulations and experiments are presented, and a practical application of a Zangger-Sterk pure shift iDOSY experiment to a simple test mixture is illustrated. Files provided: Data ==== Figs. 2 to 4 and S1 to S4 Figure 6a Oneshot-45 Figure 6b ZS-iDOSY Code ==== Mathematica code MGC analysis and figures.nb Process simulated / experimental data for figs. 2 to 5 and S1 to S4 Matlab code gradient_shift_analysis.m gradient_shift_test.m idosyzs.m Simulate data for figs. 2 to 4 and S1 to S4 Sequence code gmmgc Fig. 1c, for figs. 2 to 4 and S1 to S4 kp_ifZS-iDOSY_03 Fig. 1a, for fig. 6b ZS-iDOSY kp_oneshot45_02 Fig. 1d, for fig. 6a Oneshot-45 N.B. The definition of d20 has been corrected to match the diffusion delay in these sequences, correcting errors in the sequences used for acquisition of, and found in, the data directories “Figs. 2 to 4 and S1 to S4” and “Figure 6b ZS-iDOSY” VnmrJ macros GMgshift Calculate and apply gradient value shift GMPKBrukerNUG Calculate and apply amplitude and diffusion coefficient correction for gradient non-uniformity GMprocPK22 Produce Fig. 6a GMprocPK1002 Produce Fig. 6b以母脉冲序列中固有延迟时段作为扩散编码的扩散有序波谱实验——即iDOSY实验——因其简洁性与高灵敏度而极具应用潜力。然而，针对赞格-斯特克（Zangger-Sterk）纯位移iDOSY实验中的扩散衰减计算，解析求解难度极高，更适合通过数值方法处理。 数值模拟结果表明，在典型实验条件下，扩散衰减对扩散编码梯度幅值的依赖关系可通过位移高斯函数进行良好拟合。对于选择性脉冲中点被硬180°脉冲替代的极限情况，梯度位移可通过解析方法求解；数值模拟显示，采用不同形状的选择性脉冲时，该极限梯度位移会被一个依赖于脉冲形状的常数因子缩放降低。 实际应用中，在适用于小分子的实验条件下，若对有效扩散编码梯度的变化做出适当校正，纯位移iDOSY方法可实现精准的扩散系数测量。 本文展示了多组并行的数值模拟与实验结果，并演示了赞格-斯特克纯位移iDOSY实验在简单测试混合物中的实际应用。 提供的文件如下： 数据文件：图2至图4、补充图S1至S4；图6a：Oneshot-45；图6b：ZS-iDOSY 代码文件： Mathematica代码：MGC analysis and figures.nb（用于处理图2至图5及补充图S1至S4的模拟/实验数据） Matlab代码：gradient_shift_analysis.m、gradient_shift_test.m、idosyzs.m（用于模拟图2至图4及补充图S1至S4的实验数据） 序列代码： gmmgc（对应图1c、图2至图4及补充图S1至S4） kp_ifZS-iDOSY_03（对应图1a、图6b ZS-iDOSY） kp_oneshot45_02（对应图1d、图6a Oneshot-45） 注意：已修正d20的定义以匹配这些序列中的扩散延迟时段，纠正了"Figs. 2 to 4 and S1 to S4"和"Figure 6b ZS-iDOSY"数据目录中所用采集序列的原有错误。 VnmrJ宏命令： GMgshift：计算并应用梯度位移校正 GMPKBrukerNUG：计算并应用梯度不均匀性导致的幅值与扩散系数校正 GMprocPK22：生成图6a GMprocPK1002：生成图6b