Two-Dimensional spin-echo multiple-quantum transitions in strongly coupled spin systems. Calculation of spectra

A general method for computation of two-dimensional spin-echo multiple-quantum spectra of strongly coupled spin systems is presented. It has been demonstrated that the 180° pulse can severely modify the multiple-quantum spectra of strongly coupled spins and explicit spectral details are given for the spin systems of types AB, ABX, and AB₂. In addition to the modified frequencies and additional transitions, it is found that such spectra possess additional frequency symmetry with respect to the center of each multiple-quantum order, even though the multiple-quantum spectrum without the 180° pulse may not be symmetric. The ABX spin system is treated in detail and the behavior of the homonuclear and heteronuclear multiple-quantum transitions in the presence of selective or nonselective 180° pulses is discussed. It has been demonstrated that strong coupling allows transfer of magnetization from abundant spins to a coupled rare spin even in the absence of excitation pulses on abundant spins. The amplitudes of various coherences created by selective and nonselective pulses and the nature of spin-echo zero-quantum transitions of strongly coupled spins are discussed in appendices.     

Oscillations of echo amplitude in glasses in a magnetic field induced by nuclear dipole-dipole interaction

The influence of a magnetic field on the dipole echo amplitude in glasses (at temperatures of about 10 mK) induced by the dipole-dipole interaction of nuclear spins has been theoretically studied. It has been shown that a change in the mutual position of nuclear spins at tunneling and the Zeeman energy E _H of their interaction with the external magnetic field lead to a nonmonotonic magnetic-field dependence of the dipole echo amplitude. The approximation that the nuclear dipole-dipole interaction energy E _d is much smaller than the Zeeman energy has been found to be valid in the experimentally important cases. It has been shown that the dipole echo amplitude in this approximation may be described by a simple universal analytic function independent of the microscopic structure of the two-level systems. An excellent agreement of the theory with the experimental data has been obtained without fitting parameters (except for the unknown echo amplitude).     

Stimulated spin echo upon excitation with pseudorandom pulses

Different regimes of excitation of a stimulated spin echo by pseudorandom pulses and short coherent delta-shaped pulses are considered. Radio pulses phase-shifted by a 127-element M sequence are used as pseudorandom signals. The shape of the complex envelope of the stimulated echo is simulated in linear and nonlinear regimes with respect to the phase-shifted pulses. It is demonstrated that the excitation pulses can be described by correlation functions. Appropriate conditions are determined under which the amplitude of the stimulated echo can be greater than the amplitude corresponding to the classical algorithm used for exciting a stimulated echo by three delta-shaped pulses. The results obtained can be used for analyzing the formation of a stimulated photon echo.     

Large angle spin-echo imaging

A study was undertaken to assess the use of excitation flip angles greater than 90° for T₁ weighted spin-echo (SE) imaging with a single 180° refocusing pulse and short TR values. Theoretical predictions of signal intensity for SE images with excitation pulse angles of 90–180° were calculated based on the Bloch equations and then measured experimentally from MR images of MnCl₂ phantoms of various concentrations. Liver signal-to-noise ratios (SNR) and liver-spleen contrast-to-noise ratios (CNR) were measured from breathhold MR images of the upper abdomen in 16 patients using 90 and 110° excitation flip angles. The theoretical predictions showed significant improvements in SNR with excitation flip angles >90°, which were more pronounced at small TR values. The phantom studies showed reasonably good agreement with the theoretical predictions in correlating the excitation pulse angle with signal intensity. In the human imaging studies, the 110° excitation pulse angle resulted in a 7.4% (p < .01) increase in liver SNR and an 8.2% (p = .2) increase in liver-spleen CNR compared to the 90° pulse angle at TR = 275 ms. Increased signal intensity resulting from the use of large flip angle excitation pulses with a single echo SE pulse sequence was predicted and confirmed experimentally in phantoms and humans.     

Conventional and collision photon echo in ytterbium vapor

The polarization properties of the photon echo generated by two linearly polarized pulses of resonant radiation at the (6s6p)³ P ₁ ? (6s ²)¹ S ₀ transition of ¹⁷⁴Yb are investigated. A complicated polarization behavior of the photon echo versus an angle between the polarization vectors of the excitation pulses is revealed in a mixture of ytterbium vapor with inert gas. For the angles ranging from 0° to 75°, a conventional echo with its linear polarization coinciding with the second excitation pulse dominates and the echo amplitude decreases with an increasing angle. For the angles ranging from 75° to 89°, the photon echo is elliptically polarized. Finally, for an angle of 90°, the conventional echo disappears and the collision echo becomes linearly polarized along the first excitation pulse.     

Generalized MAGSTE with bipolar diffusion-weighting gradient pulses

The generalized magic asymmetric gradient stimulated echo (generalized MAGSTE) sequence compensates background gradient cross-terms and can be adjusted to asymmetric timing boundary conditions which for instance are present in echo-planar MR imaging. However, its efficiency is not optimal because one of the two diffusion-weighting gradients applied in each interval usually must have a reduced amplitude to ensure the desired cross-term compensation. In this work, a modification of generalized MAGSTE is investigated where this gradient pulse is replaced by two gradient pulses with full amplitude but opposite polarities. It is shown that with these bipolar gradients (i) the sequence retains the cross-term compensation capability for an appropriate choice of the gradient pulse durations and (ii) the diffusion-weighting efficiency is improved, i.e. higher k and b values can be achieved without prolonging the echo time. These results are confirmed in MR imaging experiments on phantoms and in vivo in the human brain at 3 T using spin-echo and echo-planar MR imaging. In the examples shown, the b value could be increased between about 30% and 200% when using the bipolar gradient pulses. Thus, bipolar gradients may help to improve the applicability of the generalized MAGSTE sequence.     

Measurement and correction of stimulated echo contamination in T2-based iron quantification

The purpose of this study was to characterize the effects of stimulated echo contamination on MR-based iron measurement derived from quantitative T₂ images and develop a method for retrospective correction. Two multiple spin-echo (MSE) pulse sequences were implemented with different amounts of stimulated echo contamination. Agarose-based phantoms were constructed that simulate the relaxation and susceptibility properties of tissue with different concentrations of dispersed (ferritin-like) and aggregated (hemosiderin-like) iron. Additionally, myocardial iron was assessed in nine human subjects with transfusion iron overload. These data were used to determine the influence of stimulated echoes on iron measurements made by an MR-based iron quantification model that can separately measure dispersed and aggregated iron. The study found that stimulated echo contamination caused an underestimation of dispersed (ferritin-like) iron and an overestimation of aggregated (hemosiderin-like) iron when applying this model. The relationship between the measurements made with and without stimulated echo appears to be linear. The findings suggest that while it is important to use MSE sequences with minimal stimulated echo in T₂-based iron quantification, it appears that data acquired with sub-optimal sequences can be retrospectively corrected using the methodology described here.     

Calculation of Double-Quantum-Coherence Two-dimensional Spectra: Distance Measurements and Orientational Correlations

The double-quantum-coherence (DQC) echo signal for two coupled nitroxides separated by distances ?10 Å, is calculated rigorously for the six-pulse sequence. Successive application of six pulses on the initial density matrix, with appropriate inter-pulse time evolution and coherence pathway selection leaves only the coherent pathways of interest. The amplitude of the echo signal following the last π pulse can be used to obtain a one-dimensional (1D) dipolar spectrum (Pake doublet), and the echo envelope can be used to construct the 2D DQC spectrum. The calculations are carried out using the product space spanned by the two electron-spin magnetic quantum numbers m ₁, m ₂ and the two nuclear-spin magnetic quantum numbers M ₁, M ₂, describing, e.g. two coupled nitroxides in bilabeled proteins. The density matrix is subjected to a cascade of unitary transformations taking into account dipolar and electron exchange interactions during each pulse and during the evolution in the absence of a pulse. The unitary transformations use the eigensystem of the effective spin Hamiltonians obtained by numerical matrix diagonalization. Simulations are carried out for a range of dipolar interactions, D, and microwave magnetic field strength B ₁ for both fixed and random orientations of the two ¹⁴N (and ¹⁵N) nitroxides. Relaxation effects were not included. Several examples of 1D and 2D Fourier transforms of the time-domain signals versus dipolar evolution and spin-echo envelope time variables are shown for illustration. Comparisons are made between 1D rigorous simulations and analytical approximations. The rigorous simulations presented here provide insights into DQC electron spin resonance spectroscopy, they serve as a standard to evaluate the results of approximate theories, and they can be employed to plan future DQC experiments.     

Displacement power spectrum measurement by CPMG in constant gradient

The modulation of spin phase produced by Carr-Purcell-Meiboom-Gill (CPMG) sequence in combination with constant magnetic field gradient is appropriate to probe the displacement power spectrum (DPS). The spin-echo attenuation is directly proportional to the DPS value at the applied modulation frequency. Relaxation and selective excitation effects can be factored out while probing the DPS. The modulation frequency is adjusted by varying the pulse separation time while the gradient strength and the time of acquisition are kept constant. In designing the experiment gradient strength limitations, imposed by off-resonance effects, as well as limitations arising from using Gaussian phase approximation must be considered. An effective experimental strategy is presented, supported by experimental results for free and restricted diffusion.     

What Are the Conditions for Exponential Time-Cubed Echo Decays?

Diffusion of precessing spins through a constant field gradient is well-known to produce two distinctive features: an exp(-bt(3)) decay of the echo amplitude in response to two pulses and a much slower decay of the Carr-Purcell echo train. These features will appear whenever the spin frequency is described by a continuous random-walk. The present work shows that this may also occur in the presence of motions with long correlation times tau(c)-continuous Gaussian frequency noise with an exponential autocorrelation has the correct properties over time durations smaller than tau(c). Thus, time-cubed echo decays will occur in situations other than physical diffusion. The decay rate of the Carr-Purcell echo train is shown to vary with the pulse spacing tau whenever the correlation time tau(c) is long; the slower Carr-Purcell decay compared to the two-pulse echo decay is not unique to diffusion. Simulations are presented that display time-cubed decays. The simulations confirm two important criteria: the echo time must be less than tau(c) and the frequency noise must consist of nearly continuous variations, as opposed to step-like changes. These criteria define the range of physical parameters for which time-cubed decays will be observable.     

Magnetic field-mapping by multi-slice MAGNEX

A magnetic field-mapping multi-slice sequence and its application on phantoms andin vivo is described. The sequence used consists of a slice and frequency selective two pulse excitation with a subsequent spin-echo imaging part. The pattern of these lines reflects the inhomogeneity homogeneity of the internal magnetic-flux density.     

Electron spin-echo experiments in photo-excited triplet states in an external magnetic field

Electron spin-echo experiments in the photo-excited triplet states of quinoxaline-d₆ and naphthalene-d₈ at 1·2 K in an external magnetic field are presented. These include two-pulse Hahn echoes, three-pulse stimulated echoes and Carr-Purcell pulse-echo trains. The decay of the Hahn and stimulated echoes as a function of pulse interval yields measures of the spin relaxation times. Furthermore, the Hahn echo is used to obtain E.P.R. line shapes and the dynamics of the triplet sublevel populations. The angular dependence of the Hahn echo is also investigated. The Hahn echo decay time and decay modulation suggest the kind of role played by nuclear spins in the loss of electron spin phase coherence. Some promising characteristics of the pulse method are discussed.     

Use of composite refocusing pulses to form spin echoes

The radiofrequency pulses used in NMR are subject to a number of imperfections such as those caused by inhomogeneity of the radiofrequency (B(1)) field and an offset of the transmitter frequency from precise resonance. The effect of these pulse imperfections upon a refocusing pulse in a spin-echo experiment can be severe. Many of the worst effects, those that distort the phase of the spin echo, can be removed completely by selecting the echo coherence pathway using either the "Exorcycle" phase cycle or magnetic field gradients. It is then tempting to go further and try to improve the amplitude of the spin-echo signal by replacing the simple refocusing pulse with a broadband composite 180° pulse that compensates for the relevant pulse imperfection. We show here that all composite pulses with a symmetric or asymmetric phase shift scheme will reintroduce phase distortions into the spin echo, despite the selection of the echo coherence pathway. In contrast, all antisymmetric composite pulses yield no phase distortion whatsoever, both on and off resonance, and are therefore the correct symmetry of composite refocusing pulse to use. These conclusions are verified using simulations and (31)P MAS NMR spin-echo experiments performed on a microporous aluminophosphate.     

Velocity selective radiofrequency pulse trains

The incorporation of velocity-encoding gradient pulses in RF-pulse trains is proposed and examined. Velocity selective perturbation is shown to be analogous in many respects to the well established use of trains of short RF-pulses for chemical shift selective perturbation. Velocity selective perturbation is viable in a biomedical setting only if additional RF refocusing pulses are inserted between the individual RF-pulse elements. Aspects of velocity selective excitation saturation and inversion are examined, and new inversion pulse trains proposed. The selective perturbation of both flowing and stationary spins is demonstrated in phantoms and possible biomedical applications of these pulse trains are discussed.     

Spin-echo attenuation by diffusion in nonuniform field gradients

The diffusion-dependent decay of spin-echo signals from samples distributed over non-uniform field gradients is analyzed. This decay deviates from the linear semilogarithmic dependencies on t³ or t obtained, respectively, in Hahn spin-echo or Carr-Purcell echo trains from spins in constant field gradients. It is demonstrated here that when the average diffusion distance is small compared to the spatial variation of the gradient, the spin-echo decay can be modeled by a simple superposition of signals from a large number of microdomains, each characterized by a different gradient. This is illustrated by two examples, a water sample in a deliberately created quadratic variation of the external field, and a saturated water/ sand mixture with large internal field gradients.     

Determination of quadrupole parameters with a composite pulse for spurious signal suppression

Spurious signals such as the piezoelectric signal from a ferroelectric crystal or the ringing signal from the NMR probe head tuned for low gyromagnetic ratio nuclei are often observed in pulsed NMR. Both signals are cancelled using the Hahn echo sequence with appropriate phase cyclings. The present paper applies a composite-pulse sequence to cancel the ringing signal. The main advantage of this sequence over the Hahn echo sequence is in the simplicity of optimizing the line intensity: the optimization of only one pulse duration for this sequence but of two pulse durations and the interpulse delay for the Hahn echo sequence. We are interested in half-integer quadrupole spins (I = 3/2, 5/2, 7/2, and 9/2), which means that we must consider the first-order quadrupole interaction during the pulses. For simplicity, we deal mainly with spin I = 3/2 nuclei. Since the central-line intensity depends on the ratio of the quadrupole coupling constant (QCC) to the amplitude of the RF pulse, we can determine the QCC from a featureless lineshape by fitting the variation of the experimental central-line intensity for increasing pulse duration with theoretical results. Contrary to the one-pulse sequence where the central-line intensity is proportional to the pulse duration if the latter is short, there is no such condition with the composite-pulse sequence. In other words, this sequence does not allow us to quantify the relative spin populations in powders. The size of the sample must be much smaller than that of the RF coil in order for the RF magnetic field to become homogeneous for the sample. We used (87)Rb (I = 3/2) in an aqueous solution of RbCl and in RbNb2O5F powder, (131)Xe (I = 3/2) of xenon gas physisorbed in Na-Y zeolite, and (23)Na (I = 3/2) in two well-known powders (NaNO3 and NaNO2) to support our theoretical result.     

Algorithmic treatment of the spin-echo effect

We analyze the apparent increase in entropy in the course of the spin-echo effect using algorithmic information theory. We show that although the state of the spins quickly becomes algorithmically complex, then simple again during the echo, the overall complexity of spins together with the magnetic field grows slowly, as the logarithm of the elapsed time. This slow increase in complexity is reflected in an increased difficulty in taking advantage of the echo pulse. Our discussion illustrates the fundamental role of algorithmic information content in the formulation of statistical physics, including the second law of thermodynamics, from the viewpoint of the observer.     

Improved Spin-Echo-Edited NMR Diffusion Measurements

The need for simple and robust schemes for the analysis of ligand-protein binding has resulted in the development of diffusion-based NMR techniques that can be used to assay binding in protein solutions containing a mixture of several ligands. As a means of gaining spectral selectivity in NMR diffusion measurements, a simple experiment, the gradient modified spin-echo (GOSE), has been developed to reject the resonances of coupled spins and detect only the singlets in the (1)H NMR spectrum. This is accomplished by first using a spin echo to null the resonances of the coupled spins. Following the spin echo, the singlet magnetization is flipped out of the transverse plane and a dephasing gradient is applied to reduce the spectral artifacts resulting from incomplete cancellation of the J-coupled resonances. The resulting modular sequence is combined here with the BPPSTE pulse sequence; however, it could be easily incorporated into any pulse sequence where additional spectral selectivity is desired. Results obtained with the GOSE-BPPSTE pulse sequence are compared with those obtained with the BPPSTE and CPMG-BPPSTE experiments for a mixture containing the ligands resorcinol and tryptophan in a solution of human serum albumin.     

On the nuclear electric resonance in ferroelectric KNbO<Subscript>3</Subscript>

The pulse electric excitation of nuclear spins in the KNbO₃ crystal and the electric polarization response caused by the nuclear spin precession were theoretically studied. Equations for a 90-degree exciting pulse and the amplitude of the nuclear response are derived, and numerical evaluations are performed.     

Volume selective detection by weighted averaging of constant tip angle scans

We propose a method to improve the sensitivity in volume selective detection based on the CARVE excitation sequence (I. Sersa and S. Macura, J. Magn. Reson. 135, 466-477 (1998)) which consists of signal acquisition with constant tip angle excitation and a short phase-encoding gradient pulse. Volume selectivity is achieved using the weighted average of a number of scans whose weights and gradient steps are determined by the shape of the excitation profile. The method is particularly useful for broadband volume selective detection of insensitive spins where the volume selection can be merged with the standard signal averaging process, without compromising the excitation bandwidth or sensitivity.