Stimulated echo diffusion sequence

Diffusion-relaxation correlation has been utilized to study biological tissues, e.g., compartmentalization in tissues [32-35]. In many reports, a sequence that combines a stimulated echo-type sequence with a pulsed field gradient and a CPMG as a detection has been described [35]. Other pulses sequences have also been used to study the diffusion-relaxation correlation, e.g., Ref. [36]. 

In an experiment, tcp is to be varied systematically to obtain the 2D data matrix. For the spin-echo and stimulated-echo based sequences, molecular diffusion causes signal decay in the first segment, thus both are called diffusion-editing sequences. 

Figure 9.24. Solvent signal suppiession by a diffusion filter. The sample is 1 mM lysozyme in 50 50 H20 D20 and suppression in (a) was achieved using a H stimulated-echo-based sequence employing a diffusion delay A of 50 ms, bipolar gradient pairs of 4 ms total duration ( ) and gradient strengths of 0.43 Tm. The standard spectrum is shown in (b).

Figure 9 (a) Stimulated echo pulse sequence with length of gradient pulse S and diffusion time A longimdinal and transverse relaxation takes place within the time intervals as indicated, (b) Stimulated echo sequence with longimdinal prerelaxation. 

Pulsed field gradient spin echo NMR is generally the method of choice for diffusion measurements on liquid samples (see Section 5.1 in this chapter). With modem high field instruments, however, severe problems can arise when it is applied to samples with very high proton concentrations because of the presence of radiation damping. Connel et al reduced the problems by a suitable choice of experimental parameters, in particular the use of modified stimulated echo pulse sequences with a reduced flip angle for the first pulse. 

Fig. 2.7.2 Diffusion-relaxation correlation se- The detection (2nd) segment for both is a quences using pulsed field gradients, (a) The CPMG pulse train that is similar to that in first segment is a spin-echo with the echo Figure 2.7.1. The amplitude or the duration of appearing at a time 2tcpi after the first pulse, the gradient pairs in both sequences is (b) The first segment is a stimulated echo incremented to vary the diffusion effects, appearing at a time tcpi after the third pulse.

The reference scan is to measure the decay due to spin-lattice relaxation. Compared with the corresponding stimulated echo sequence, the reference scan includes a jt pulse between the first two jt/2 pulses to refocus the dephasing due to the internal field and the second jt/2 pulse stores the magnetization at the point of echo formation. Following the diffusion period tD, the signal is read out with a final detection pulse. The phase cycling table for this sequence, including 2-step variation for the first three pulses, is shown in Table 3.7.2. The output from this pair of experiments are two sets of transients. A peak amplitude is extracted from each, and these two sets of amplitudes are analyzed as described below. 

Fig. 4.5.5 Pulsed field gradient sequences to obtain velocity and diffusion data (a) spin-echo (PGSE) and (b) stimulated-echo (PGSTE). The application of imaging gradients C Gy and Gz allows the measurement of velcocity maps and spatially-resolved diffusion coefficients and size distribution in emulsions.

Fig. 1. LED pulse sequence for the measurement of stimulated echoes attenuated by diffusion. Typical values for delays and pulse widths are 5 ms for the gradient pulse widths tg, 2-3 ms for the recovery time tr, 0.1 s for the diffusion time td, and 5 ms for the storage time...

Tanner [49] measured diffusion coefficients of water in three different types of frog muscle cells. He used a variety of magnetic field gradient techniques so as to cover a wide range of diffusion times A= 1 ms to 1 s. The time dependence of the diffusion coefficient was analyzed to obtain the intracellular diffusion coefficients and estimates of the permeability of the cell membranes. In restricted diffusion studies three 90 degree r.f. pulse sequences (stimulated echo) are often used which provides PG-NMR experiments with long diffusion times to explore the dependence of diffusion time on the echo attenuation [49]. 

In multidimensional NMR studies of organic compounds, 2H, 13C and 31P are suitable probe nuclei.3,4,6 For these nuclei, the time evolution of the spin system is simple due to 7 1 and the strengths of the quadrupolar or chemical shift interactions exceed the dipole-dipole couplings so that single-particle correlation functions can be measured. On the other hand, the situation is less favorable for applications on solid-ion conductors. Here, the nuclei associated with the mobile ions often exhibit I> 1 and, hence, a complicated evolution of the spin system requires elaborate pulse sequences.197 199 Further, strong dipolar interactions often hamper straightforward analysis of the data. Nevertheless, it was shown that 6Li, 7Li and 9Be are useful to characterize ion dynamics in crystalline ion conductors by means of 2D NMR in frequency and time domain.200 204 For example, small translational diffusion coefficients D 1 O-20 m2/s became accessible in 7Li NMR stimulated-echo studies.201... 

Figure 27 Pulse sequence for stimulated echo PGSE diffusion spectroscopy...

The stimulated echo (STE) diffusion pulse sequence is depicted in Fig. 6.Id [12], The signal intensity of the STE diffusion experiment, for rectangular pulse gradients, is given by Eq. (6.11),... 

Fig. 6.25. Simulation of the effect of the diffusion time on the normalized signal decay for the two site exchange model as a function of the diffusion time (A) in a stimulated echo-based diffusion sequence. (Reproduced with permission from ref. [11c]. Copyright 2005 Wiley-VCH.)...

The Hahn and the stimulated echo are used to study molecular self-diffusion in fluids with field gradients which are active during the pulse sequence [Cal2, Karl, Kiml, Stil]. These gradients can be static [Hahl] or pulsed [Stel]. For a static gradient of known magnitude G the self-diffusion constant D can be determined from the amplitude Hahn echo as a function of the echo time t [Hahl, Carl],... 

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