Spin echo formation

SPIN-ECHO FORMATION IN HOMONUCLEAR AND HETERONUCLEAR SYSTEMS... 

Spin-Echo Formation in Homonuclear and Heteronuclear Systems... 

Figure 3. Spin echo formation with (a-b) non-inverted and (c) inverted 90° pulse.

N. Gelman, R.F. Code, A simple model of F spin-echo formation in polycrystalline fluorapatite, J. Magn. Res. A 107 (1994) 185-193. 

Consider the free procession signal acquired as a function of time t after the spin-echo formation at time t. We shall presume that the sole term acting in the Hamiltonian after the echo center is due to the Larmor precession at frequency in the uniform field, where the use of the subscript i allows for the range of chemical shifts in the NMR spectrum. This precession contributes an evolution operator exp(iWo,t ->, ) to the density matrix so that we can rewrite Eq. (39) as... 

We now consider the simple case of a spin echo in which two rectangular linear gradient pulses are applied as shown in Fig. 1. In this pulsed gradient spin-echo (PGSE) experiment, the time t used in Eq. (41) will refer to the position of the spin-echo formation. In analyzing this experiment, we will assume the weak inhomogeneous field limit and the uniform... 

Mansfieid P 1977 Muiti-pianar image formation using NMR spin echoes J. Rhys. C Solid State Rhys. 10 L55-L58... 

Another 2D homonuclear shift-correlation experiment that provides the coupling information in a different format is known as SECSY (spin-echo correlation spectroscopy). It is of particular use when the coupled nuclei lie in a narrow chemical shift range and nuclei with large chemical shift differences are not coupled to one another. The experiment differs... 

Fig. 1.22 RARE sequence. Here the formation of the first spin echo is conventional. The CPMG form of spin echo is used to avoid the accumulation of flip angle errors over the echo train. However, before the second echo can be acquired, the phase-encoding has to be rewound to undo the dephasing of the spins. Therefore, a phase encoding step of equal...

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. 2.1 Spin history leading to the formation of the spin-echo. Longitudinally polarized neutrons enter from the left. Upper part spin motion. Lower part NSE setup, Ti/2-flipper between belonging current rings, primary main precession solenoid l symmetry scan...

The solvent mobility in atactic polystyrene-toluene solutions has been studied as a function of temperature using NMR. The local reorientation of the solvent was studied using deuterium NMR relaxation times on the deuterated solvent. Longer range motions were also probed using the pulsed-gradient spin-echo NMR method for the measurement of diffusion coefficients on the protonated solvent. The measurements were taken above and below the gel transition temperatures reported by Tan et al. (Macromolecules, 1983. 16, 28). It was found that both the relaxation time measurements and the diffusion coefficients of the solvent varied smoothly through the reported transition temperature. Consequently, it appears that in this system, the solvent dynamics are unaffected by gel formation. This result is similar to that found in other chemically crossed-linked systems. 

Figure 6 Typical pulse sequence used in experiments with a signal-enhancement scheme (which can involve DFS, RAPT or application of adiabatic pulses) placed before the CT excitation and detection, with formation of a spin-echo.

Because the induced NMR signal after switching off the 90° RF pulse decays so rapidly as mentioned above, spin echoes are often detected in many practical pulse sequences for MRI visualization. Spin echo is formed by an additional RF pulse applied to the sam-ple.The additional RF pulse is applied after an evolution period, r. This RF pulse that gives rise to inversion of the magnetization components causes the spins to rephrase and is thus referred to the 180° RF pulse as shown in Fig. 2. This rephrasing process contributes to recover the transverse magnetization which had lost in dephasing process and results in the formation of an echo . We detected the echo by the receiver coil. The time from when the 90° RF pulse is applied to when the echo forms is referred to as the echo time , TE and is equal to twice the time between the 90° and 180° pulses, i.e. 2r. 

In this section, we provide an outline of the theoretical and practical aspects of diffusometry NMR experiments that are the core of chrom-NMR. This issue has been reviewed at large38,39 and thus only the key and most relevant aspects will be mentioned below. The displacement of a given molecular tracer is followed by a classical Stejskal-Tanner experiment. In this, pulses of magnetic field gradients are used to label the initial position of the tracer, and to follow its displacement along the direction of the gradient, Az. Indeed, in a spin-echo experiment, any displacement corresponds to a reduction of the efficiency of the echo formation. 

Fig. 5.20a-d. Subacute thrombus formation in a large fusiforme aneurysm of the basilar artery. Parts of the thrombus are still isoin-tense to brain, while others are moderately hyperintense on spin echo Tl-weighted image (a). Residual flow within the vessel is outlined against thrombus much better on post-contrast Tl-weighted spin echo (c) and post-contrast TOF-MRA (d) than on unenhanced TOF-MRA (b)... 

Figure 2 shows the code for the spin-echo pulse sequence. In lines 1-7, NMR object variables are declared. In lines 9-16, these objects are assigned values or specific NMR operations. A lactate spin system is read in from a file using a standard GAMMA text file format. Lines 20-24 are the code for the actual 90°Y-delay-180°Y-delay-acquire pulse sequence. In line 26, the density matrix is parsed into a transition table for the specified observation operator. And the "write results" function in line 27 converts the GAMMA transition table into three arrays of ppm, area and phase values one value for each line found in the transition table. This is a fairly trivial example, and the use of ideal pulses is often not sufficient to account for real-world artefacts in a simulation, but it shows how the object-oriented style of coding results in short amounts of code that is easy to read and comprehend. When compiled with the Visual Studio C++ compiler on a... 

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