Stimulated echoes

The longest diffusion time (which is essentially given by A) that can be probed with the Hahn echo methods is limited by the transverse relaxation time T2. As a consequence, the echo attenuation achievable in this time limit may not be sufficient for very slow diffusion even for the strongest field gradients technically feasible. Also, in the case of anomalous diffusion it may 

The total attenuation of the stimulated echo in liquids after two free-evo-lution intervals Ti and the grating storage interval T2 is given by 

A-diff represents any of the formulas given in Eqs. 13-16 and Eq. 20 for the respective limits. If Ti T2 Ti T2, the maximum diffusion time can be adjusted much longer than in the Hahn echo case. 

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Flaase A and Frahm J 1985 Multiple chemical-shift-selective NMR imaging using stimulated echoes J. Magn. Reson. 64 94-102... 

Figure Bl.15.11. Fomiation of electron spin echoes. (A) Magnetization of spin packets i,j, /rand / during a two-pulse experiment (rotating frame representation). (B) The pulse sequence used to produce a stimulated echo. In addition to this echo, which appears at r after the third pulse, all possible pairs of the tluee pulses produce primary echoes. These occur at times 2x, 2(x+T) and (x+2T).

The main advantage of tlie tln-ee-pulse ESEEM experiment as compared to the two-pulse approach lies m the slow decay of the stimulated echo intensity detemiined by T, which is usually much longer than the phase memory time Ty that limits the observation of the two-pulse ESE. 

Muns ENDOR mvolves observation of the stimulated echo intensity as a fimction of the frequency of an RE Ti-pulse applied between tlie second and third MW pulse. In contrast to the Davies ENDOR experiment, the Mims-ENDOR sequence does not require selective MW pulses. For a detailed description of the polarization transfer in a Mims-type experiment the reader is referred to the literature [43]. Just as with three-pulse ESEEM, blind spots can occur in ENDOR spectra measured using Muns method. To avoid the possibility of missing lines it is therefore essential to repeat the experiment with different values of the pulse spacing Detection of the echo intensity as a fimction of the RE frequency and x yields a real two-dimensional experiment. An FT of the x-domain will yield cross-peaks in the 2D-FT-ENDOR spectrum which correlate different ENDOR transitions belonging to the same nucleus. One advantage of Mims ENDOR over Davies ENDOR is its larger echo intensity because more spins due to the nonselective excitation are involved in the fomiation of the echo. 

He, Q Johnson, CS, Stimulated Echo Electrophoretic NMR, Journal of Magnetic Resonance 85, 181, 1989. 

Another approach to obtain spatially selective chemical shift information is, instead of obtaining the entire image, to select only the voxel of interest of the sample and record a spectrum. This method called Volume Selective spectroscopY (VOSY) is a ID NMR method and is accordingly fast compared with a 3D sequence such as the CSI method displayed in Figure 1.25(a). In Figure 1.25(b), a VOSY sequence based on a stimulated echo sequence is displayed, where three slice selective pulses excite coherences only inside the voxel of interest. The offset frequency of the slice selective pulse defines the location of the voxel. Along the receiver axis (rx) all echoes created by a stimulated echo sequence are displayed. The echoes V2, VI, L2 and L3 can be utilized, where such multiple echoes can be employed for signal accumulation. 

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]. 

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.

For the case of the stimulated echo for diffusion weighting, the full kernel can be written as... 

They also showed that a spin-echo segment with two it pulses improves the echo signal due to the inclusion of a stimulated-echo coherence pathway. 

The stimulated echo diffusion-relaxation experiment exhibits a kernel that is similar to that of the one with the pulsed field gradients ... 

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. 

K. J. Packer, J. J. Tessier 1996, (The characterization of fluid transport in a porous solid by pulsed gradient stimulated echo NMR), Mol. Phys. 87, 267. 

R M. Cotts, M. J. R. Hoch, T. Sun, J.T. Markert 1989, (Pulsed field stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems), J. Magn. Reson. 83, 252. 

The DDIF experiment consists of a stimulated echo pulse sequence [50] and a reference scan to measure and separate the effect of spin-lattice relaxation. The pulse diagrams for these two are shown in Figure 3.7.2. Details of the experiments have been discussed in Ref. [51] and a brief description will be presented here. 

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. 4.1.5 A stimulated-echo sequence for detecting spin displacements. This sequence detects spin displacements along the Zt direction. TM is mixing time.

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. 5.3.4 (A) Stimulated echo dynamic NMR microscopy pulse sequence. The first field gradient pulse (g,) of duration 8 serves to encode spatial positions of spins and the second field gradient pulse has a refocusing effect.

A second imaging gradient (Gy) is added in order to obtain a spatial map of the displacements. A notable feature of the stimulated echo protocol is that during the flow encoding time, A, the magnetization is stored along the z axis and is subject to the longitudinal... 

This experiment has two limitations (a) nuclei with short T2 are difficult to be detected and (b) multiplets produce a distorted signal phase after n pulse which inverts the coupled spin states. Both limitations are partially overcome by the stimulated echo experiment (STE).64,65 The main difference with the experiment previously described is that the echo attenuation due to the diffusion competes with Tx rather than with T2. The equation analogous to Equation (13) is now ... 

Fig. 12. Sequences for volume selective single voxel spectroscopy. Both techniques work with three slice-selective RF-pulses. (a) The Point RESolved Spectroscopy (PRESS) sequence generates a volume selective double spin-echo. The entire time delay between the initial 90° excitation and the echo is sensitive to transverse relaxation, (b) The Stimulated Echo Acquisition Mode (STEAM) sequence generates a stimulated echo. Maximal signal intensity (without relaxation effects) is only half the signal intensity of PRESS under comparable conditions, but slice profiles are often better (only 90° pulses instead of 180° pulses) and the TM interval is not susceptible to transverse relaxation, (c) The recorded echo signal is only generated in a volume corresponding to the intersection of all three slices.

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