On the application of magic echo cycles for quadrupolar echo spectroscopy of spin-1 nuclei

Magic echo cycles are introduced for performing quadrupolar echo spectroscopy of spin-1 nuclei. An analysis is performed via average Hamiltonian theory showing that the evolution under chemical shift or static field inhomogeneity can be refocused simultaneously with the quadrupolar interaction using these cycles. Due to the higher convergence in the Magnus expansion, with sufficient RF power, magic echo based quadrupolar echo spectroscopy outperforms the conventional two pulse quadrupolar echo in signal to noise. Experiments highlighting a signal to noise enhancement over the entire bandwidth of the quadrupolar pattern of a powdered sample of deuterated polyethelene are shown.     

Triple-quantum-filtered (23)Na NMR spectroscopy of subcutaneously implanted 9l gliosarcoma in the rat in the presence of TmDOTP(5-1)

The utility of triple-quantum (TQ)-filtered (23)Na NMR spectroscopy for discriminating between intra- and extracellular Na(+)(Na(i)(+) and Na(e)(+), respectively) in a solid tumor in vivo was evaluated using TmDOTP(5-) as a (23)Na shift reagent. Infusion of 80 mM TmDOTP(5-) without added Ca(2+) produced baseline-resolved Na(i)(+) and Na(e)(+) peaks in both single-quantum (SQ) and TQ-filtered (23)Na spectra. The Na(i)(+) signal represented 22+/-4% of the SQ spectrum, but 59+/-10% of the TQ-filtered spectrum. Therefore, the Na(i)(+) contribution in TQ-filtered spectra is much higher than in SQ spectra. Both SQ and TQ-filtered Na(i)(+) signals increased by about 75% 1 h after sacrificing the animal. The TQ-filtered relaxation times did not change during this time, indicating that changes observed in TQ-filtered spectra collected with a preparation time of 3 ms represent changes in the concentration of sodium ions contributing to the TQ-filtered signal. Similar experiments were conducted without TmDOTP(5-) to determine changes in the Na(e)(+) signal in the absence of the shift reagent. The changes in total SQ and TQ-filtered signals 1 h after sacrificing the animal showed that the SQ Na(e)(+) signal decreased by approximately 35%, while the TQ-filtered Na(e)(+) signal did not change significantly. This demonstrates that the TQ-filtered (23)Na signal is relatively insensitive to changes in Na(e)(+) content. To our knowledge, this work represents the first evaluation of multiple-quantum-filtered (23)Na spectroscopy to discriminate between intra- and extracellular Na(+) in a solid tumor in vivo.     

Multi-quantum echoes in GdAl2 zero-field high-resolution NMR

In this paper we present a series of high-resolution zero-field NMR spectra of the polycrystalline intermetallic compound GdAl₂. The spectra were obtained with the sample at 4.2 K in the ordered magnetic state and in the absence of an external static magnetic field. Using a sequence composed of two RF pulses, we obtained up to five multi-quantum echoes for the ²⁷Al nuclei, which were used to construct the zero-field NMR spectra. The spectra obtained from the FID observed after the second pulse and the even echoes exhibited higher resolution than the odd ones. In order to explain such behavior, we propose a model in which there are two regions inside the sample with different inhomogeneous spectral-line broadenings. Moreover, with the enhanced resolution from the FID signal, we were able to determine quadrupolar couplings with great precision directly from the respective spectra. These results were compared with those obtained from the quadrupolar oscillations of the echo signals, and showed good agreement. Similar data were also obtained from ¹⁵⁵Gd and ¹⁵⁷Gd nuclei.     

Stray-field imaging of quadrupolar nuclei of half integer spin in solids

A report is presented on the observation of Hahn echoes from the following quadrupolar nuclei of half integer spin (I) in polycrystalline solids in the large static magnetic field gradient (37.5 T/m) which exists in the fringe field of a superconducting solenoid: ⁷Li, ²³Na, ¹¹B, ⁶⁵Cu (I = 3/2); ²⁷Al (I = 5/2); ⁵¹V, ⁵⁹Co (I = 7/2); and ¹¹⁵In (I = 9/2). ²³Na echo-trains from NaCl (with non-selective excitation) and from Na₂SO₄ (with selective excitation) are compared quantitatively for two different RF pulse sequences: 90_x-(τ-90_y-τ-echo-)_n and 90_x-(τ-90_x-τ-echo-)_n. The signals obtained from RF pulses corresponding to non-selective 90 ° pulses were shown to be quantitative, whereas in the selective case smaller signals were obtained since only the central transition contributed. The loss of signal from this cause can be distinguished from small signals resulting from low density of nuclei by use of the second sequence. A ⁷Li image obtained from LiF in a cylindrical glass-vial is shown.     

2H T2rho relaxation dynamics and double-quantum filtered NMR studies

In this study 2H T2rho DQF NMR spectra of water in MCM-41 were measured. The T2rho double-quantum filtered (DQF) NMR signal is generated by applying a radio frequency (RF) field for various durations and then observed after a monitor RF pulse. It was found that the transfer between different quantum coherences by the couplings during long-duration RF fields (i.e., soft pulses) and that residual quadrupolar interaction dominates the signal decay. Knowledge of coherence transfer during long-RF pulses has special significance for the development of sophisticated multi-quantum NMR experiments especially multi-quantum MRI applications.     

Radio frequency field intensity mapping using a composite spin-echo sequence

A novel radio frequency (RF) field intensity mapping or imaging method using a composite NMR spin-echo sequence is proposed. A composite spin-echo RF pulse with 90 degrees y-180 degrees x-90 degrees y sequence makes phase change in the final image depending on the RF field intensity on the object. The resultant phase change or phase map can be used to obtain the actual RF flip-angle map for a given condition which includes the status of tuning and RF inhomogeneity, etc. Bloch equation has been solved numerically to obtain the effects of the RF field intensity as well as the main magnetic field inhomogeneity and the results are used for the mapping (imaging) of the RF field intensity. Phantom studies have been performed using a 1.5 Tesla whole body MRI system and the results are presented.     

Radiofrequency magnetic field gradient echoes have reduced sensitivity to susceptibility gradients

The amplitudes of gradient-echoes produced using static field gradients are sensitive to diffusion of tissue water during the echo evolution time. Gradient-echoes have been used to produce MR images in which image intensity is proportional to the self-diffusion coefficient of water. However, such measurements are subject to error due to the presence of background magnetic field gradients caused by variations in local magnetic susceptibility. These local gradients add to the applied gradients. The use of radiofrequency (RF) gradients to produce gradient-echoes may avoid this problem. The RF magnetic field is orthogonal to the offset field produced by local magnetic susceptibility gradients. Thus, the effect of the local gradients on RF gradient-echo amplitude is small if the RF field is strong enough to minimize resonance offset effects. The effects of susceptibility gradients can be further reduced by storing magnetization longitudinally during the echo evolution period. A water phantom was used to evaluate the effects of background gradients on the amplitudes of RF gradient-echoes. A surface coil was used to produce an RF gradient of between 1.3 and 1.6 gauss/cm. Gradient-echoes were detected with and without a 0.16 gauss/cm static magnetic field gradient applied along the same direction as the RF gradient. The background static field gradient had no significant effect on the decay of RF gradient-echo amplitude as a function of echo evolution time. In contrast, the effect of the background gradient on echoes produced using a 1.6 gauss/cm static field gradient is calculated to be significant. This analysis suggests that RF gradient-echoes can produce MR images in which signal intensity is a function of the self-diffusion coefficient of water, but is not significantly affected by background gradients.     

Simultaneous Acquisition of Quadrupolar Order and Double-QuantumNa Signals

Na⁺with both residual quadrupolar coupling and biexponential relaxation contributes to the signal acquired from DQF-4, while only Na⁺with residual quadrupolar coupling contributes to the signal acquired with the Jeener–Broekaert sequence. Since RF phases and flip angles for DQF-4 and Jeener-Broekaert sequences are identical, these different types of signals can be generated simultaneously. A phase-cycling scheme is developed to differentiate the signals corresponding to residual quadrupolar coupling and biexponential relaxation after the signals are acquired by use of the same RF sequences. This technique can maximize the attainable information from Na⁺in biological tissues in a given acquisition time.     

Dynamics of Spin I=3/2 under Spin-Locking Conditions in an Ordered Environment

We have derived approximate analytic solutions to the master equation describing the evolution of the spin I=3/2 density operator in the presence of a radio-frequency (RF) field and both static and fluctuating quadrupolar interactions. Spectra resulting from Fourier transformation of the evolutions of the on-resonance spin-locked magnetization into the various coherences display two satellite pairs and, in some cases, a central line. The central line is generally trimodal, consisting of a narrow component related to a slowly relaxing mode and two broad components pertaining to two faster relaxing modes. The rates of the fast modes are sensitive to slow molecular motion. Neither the amplitude nor the width of the narrow component is affected by the magnitude of the static coupling, whereas the corresponding features of the broad components depend in a rather complicated manner on the spin-lock field strength and static quadrupolar interaction. Under certain experimental conditions, the dependencies of the amplitudes on the dynamics are seen to vanish and the relaxation rates reduce to relatively simple expressions. One of the promising emerging features is the fact that the evolutions into the selectively detected quadrupolar spin polarization order and the rank-two double-quantum coherence do not exhibit a slowly relaxing mode and are particularly sensitive to slow molecular motion. Furthermore, these coherences can only be excited in the presence of a static coupling and this makes it possible to discern nuclei in anisotropic from those in isotropic environment. The feasibility of the spin-lock pulse sequences with limited RF power and a nonvanishing average electric field gradient has been demonstrated through experiments on sodium in a dense lyotropic DNA liquid crystal.     

Internuclear distance determination of S = 1, I = 1/2 spin pairs using REAPDOR NMR

A universal function is proposed to describe REAPDOR dephasing curves of an observed spin-1/2 nucleus dipole-recoupled to a spin-1 quadrupolar nucleus ((2)H or (14)N). Previous work had shown that, in contrast to REDOR, the shape of the dephasing curve depends on a large number of parameters including the quadrupolar coupling constant and asymmetry parameter, the sample rotation speed, the RF amplitude, and the relative orientations of the quadrupole tensor and the internuclear vector. Here we demonstrate by numerical simulations that the actual dispersion of REAPDOR dephasing curves is quite small, provided the rotation speed and the RF amplitude applied to the quadrupolar nucleus satisfy an adiabaticity condition. The condition is easily met for (2)H and is also practically achievable for virtually any (14)N-containing compound. This allows the REAPDOR curves to be approximated by a simple universal gaussian-type function, comparison of which with experimental data yields internuclear distances with less than 4% error. The spin dynamics of the recoupling mechanism is discussed. The critical importance of a stable spinning speed for optimizing the signal-to-noise ratio of the (13)C echoes is demonstrated and practical suggestions for achieving high stability are presented. Examples of applications of the universal curve are given for (2)H/(13)C and (14)N/(13)C REAPDOR in alanine.     

Dynamics of spin I=3/2 under spin-locking conditions in an ordered environment

We have derived approximate analytic solutions to the master equation describing the evolution of the spin I=3/2 density operator in the presence of a radio-frequency (RF) field and both static and fluctuating quadrupolar interactions. Spectra resulting from Fourier transformation of the evolutions of the on-resonance spin-locked magnetization into the various coherences display two satellite pairs and, in some cases, a central line. The central line is generally trimodal, consisting of a narrow component related to a slowly relaxing mode and two broad components pertaining to two faster relaxing modes. The rates of the fast modes are sensitive to slow molecular motion. Neither the amplitude nor the width of the narrow component is affected by the magnitude of the static coupling, whereas the corresponding features of the broad components depend in a rather complicated manner on the spin-lock field strength and static quadrupolar interaction. Under certain experimental conditions, the dependencies of the amplitudes on the dynamics are seen to vanish and the relaxation rates reduce to relatively simple expressions. One of the promising emerging features is the fact that the evolutions into the selectively detected quadrupolar spin polarization order and the rank-two double-quantum coherence do not exhibit a slowly relaxing mode and are particularly sensitive to slow molecular motion. Furthermore, these coherences can only be excited in the presence of a static coupling and this makes it possible to discern nuclei in anisotropic from those in isotropic environment. The feasibility of the spin-lock pulse sequences with limited RF power and a nonvanishing average electric field gradient has been demonstrated through experiments on sodium in a dense lyotropic DNA liquid crystal.     

Carr-Purcell sequences with composite pulses

We present novel Carr-Purcell-like sequences using composite pulses that exhibit improved performance in strongly inhomogeneous fields. The sequences are designed to retain the intrinsic error correction of the standard Carr-Purcell-Meiboom-Gill (CPMG) sequence. This is achieved by matching the excitation pulse with the refocusing cycle such that the initial transverse magnetization lies along the axis n(Beta) characterizing the overall rotation of the refocusing cycle. Such sequences are suitable for relaxation measurements. It is shown that in sufficiently inhomogeneous fields, the echo amplitudes have an initial transient modulation that is limited to the first few echoes and then decay with the intrinsic relaxation time of the sample. We show different examples of such sequences that are constructed from simple composite pulses. Sequences of the form 90 degrees (0)-(90 degrees (90-theta/2)-theta(180-theta/2)-90 degrees (90-theta/2))(n) with theta approximately 90 degrees and 270 degrees generate signal over a bandwidth larger than that of the conventional CPMG sequence, resulting in an improved signal-to-noise ratio in inhomogeneous fields. The new sequence 127 degrees (x,y)-(127 degrees (x)-127 degrees (-x))(n) only excites signal off-resonance with a spectrum that is bimodal, peaking at Delta omega(0)=+/-omega(1). Depending on the phase and exact timing of the first pulse, symmetric or antisymmetric excitation is obtained. We also demonstrate several new sequences with improved dependence on the RF field strength. The sequence (22.5 degrees (67.5)-90 degrees (-22.5))-(90 degrees (67.5)-45 degrees (157.5)-90 degrees (67.5))(n) has the property that the phase of the signal depends on B(1), allowing coarse B(1) imaging in a one-dimensional experiment.     

Algebraic description of spin 3/2 dynamics in NMR experiments

The dynamics of spin 3/2 systems is analyzed using the density matrix theory of relaxation. By using the superoperator formalism, an algebraic formulation of the density matrix's evolution is obtained, in which the contributions from free relaxation and RF application are easily factored out. As an intermediate step, an exact form for the propagator of the density matrix for a spin 3/2 system, in the presence of static quadrupolar coupling, inhomogeneous static magnetic field, and relaxation is demonstrated. Using this algebraic formulation, exact expressions for the behavior of the density matrix in the classical one-, two-, and three-pulse experiments are derived. These theoretical formulas are then used to illustrate the bias introduced on the measured relaxation parameters by the presence of large spatial variations in the B0 and B1 fields. The theoretical predictions are easily evaluated through simple matrix algebra and the results agree very well with the experimental observations. This approach could prove useful for the characterization of the spatial variations of the signal intensity in multiple quantum-filtered sodium MRI experiments.     

Enhanced suppression of residual water in a "270" WET sequence

In certain water suppression experiments, the residual water, which comes from a region away from the center of the RF coil and experiences a much smaller flip angle than the designed one, may appear. The residual water in the WET sequence can be reduced significantly by using a composite 90(x)( degrees )90(y)( degrees )90(-x)( degrees )90(-y)( degrees ) pulse, which de-excites molecules experiencing a small flip angle. The composite pulse, however, has two null excitation points near on resonance, causing a severe loss of spectrum intensity and baseline distortion toward the null points. Since the residual water experiences a very small flip angle, it can be treated as a linear spin system; i.e., the intensity of the residual water is proportional to the pulse strength and width. Based on this principle, the residual water can be reduced dramatically by replacing the 90 degrees pulse in the "270" WET sequence with a 270 degrees pulse for one out of every four scans, without noticeable loss of intensity and baseline distortion.     

Cross-polarization schemes for peptide samples oriented in hydrated phospholipid bilayers

Continuous-wave, ramped amplitude, and frequency modulated cross-polarization schemes (abbreviated as CWCP, RACP, and FMCP, respectively) are evaluated for static samples in anisotropic phases, such as peptides oriented in lipid environments. It is shown experimentally that both RACP and FMCP give rise to 20% higher polarized signal intensity in comparison to CWCP. The CP matching bandwidths for CWCP and RACP are about the same. Because of its adiabaticity, FMCP has a much broader CP matching bandwidth than CWCP and RACP. In addition, the (15)N RF amplitude used at the center of the FMCP matching profile is much lower than that of the CWCP and RACP matching profiles. A sample of [(15)N]Leu(4) labeled gramicidin A oriented in lipid bilayers was used to demonstrate these experiments.     

Magnetization-recovery experiments for static and MAS-NMR of I=3/2 nuclei

Multifrequency pulsed NMR experiments on quadrupole-perturbed I=3/2 spins in single crystals are shown to be useful for measuring spin-lattice relaxation parameters even for a mixture of quadrupolar plus magnetic relaxation mechanisms. Such measurements can then be related to other MAS-NMR experiments on powders. This strategy is demonstrated by studies of (71)Ga and (69)Ga (both I=3/2) spin-lattice relaxation behavior in a single-crystal (film) sample of gallium nitride, GaN, at various orientations of the axially symmetric nuclear quadrupole coupling tensor. Observation of apparent single-exponential relaxation behavior in I=3/2 saturation-recovery experiments can be misleading when individual contributing rate processes are neglected in the interpretation. The quadrupolar mechanism (dominant in this study) has both a single-quantum process (T(1Q1)) and a double-quantum process (T(1Q2)), whose time constants are not necessarily equal. Magnetic relaxation (in this study most likely arising from hyperfine couplings to unpaired delocalized electron spins in the conduction band) also contributes to a single-quantum process (T(1M)). A strategy of multifrequency irradiation with observation of satellite and/or central transitions, incorporating different initial conditions for the level populations, provides a means of obtaining these three relaxation time constants from single-crystal (71)Ga data alone. The (69)Ga results provide a further check of internal consistency, since magnetic and quadrupolar contributions to its relaxation scale in opposite directions compared to (71)Ga. For both perpendicular and parallel quadrupole coupling tensor symmetry axis orientations small but significant differences between T(1Q1) and T(1Q2) were measured, whereas for a tensor symmetry axis oriented at the magic-angle (54.74 degrees ) the values were essentially equal. Magic-angle spinning introduces a number of complications into the measurement and interpretation of the spin-lattice relaxation. Comparison of (71)Ga and (69)Ga MAS-NMR saturation-recovery curves with both central and satellite transitions completely saturated by a train of 90 degrees pulses incommensurate with the rotor period provides the simplest means of assessing the contribution from magnetic relaxation, and yields results for the quadrupolar mechanism contribution that are consistent with those obtained from the film sample.     

Complete description of the interactions of a quadrupolar nucleus with a radiofrequency field. Implications for data fitting

We present a theory, with experimental tests, that treats exactly the effect of radiofrequency (RF) fields on quadrupolar nuclei, yet retains the symbolic expressions as much as possible. This provides a mathematical model of these interactions that can be easily connected to state-of-the-art optimization methods, so that chemically-important parameters can be extracted from fits to experimental data. Nuclei with spins >1/2 typically experience a Zeeman interaction with the (possibly anisotropic) local static field, a quadrupole interaction and are manipulated with RF fields. Since RF fields are limited by hardware, they seldom dominate the other interactions of these nuclei and so the spectra show unusual dependence on the pulse width used. The theory is tested with ²³Na NMR nutation spectra of a single crystal of sodium nitrate, in which the RF is comparable with the quadrupole coupling and is not necessarily on resonance with any of the transitions. Both the intensity and phase of all three transitions are followed as a function of flip angle. This provides a more rigorous trial than a powder sample where many of the details are averaged out. The formalism is based on a symbolic approach which encompasses all the published results, yet is easily implemented numerically, since no explicit spin operators or their commutators are needed. The classic perturbation results are also easily derived. There are no restrictions or assumptions on the spin of the nucleus or the relative sizes of the interactions, so the results are completely general, going beyond the standard first-order treatments in the literature.     

Diffusion in porous building materials with high internal magnetic field gradients

An algorithm to calculate NMR signals of a multi-echo pulse sequence with arbitrary position dependent B0 and B1 fields taking into account relaxation and spin-diffusion is presented. The multi-echo pulse sequence consists of an initial RF pulse ("90 degrees " RF pulse) and a series of L refocusing RF pulses with arbitrary phases and flip-angles. The calculation is exact and takes into account all the magnetization pathways that contribute to the signal on a predefined spatial grid. The theoretical prediction is verified experimentally using a high field NMR microscopy system. The algorithm was implemented in a simulation program in order to optimize the design of an inside-out MR intra-vascular catheter that is used for characterization of vessel wall tissue. Measured data obtained with the catheter are in good agreement with the theoretical prediction of the simulation.     

NMR of residual protons in partly deuterated anisotropic materials with phase-alternated decoupling of deuterium spins

A new method is presented for decoupling spins with S = 1 like deuterium in anisotropic media while observing other spins such as residual protons in partly deuterated samples. The carrier frequency of a weak radiofrequency (RF) field is applied near the center of the doublet arising from the quadrupolar interaction of the S = 1 spins. The phase of the RF field is periodically reversed with intervals matching the reciprocal of the magnitude of the quadrupolar splitting. It is shown by theory and experiment that, even when the irradiating field is quite weak, the efficiency of this phase-alternated decoupling scheme is much better than for simple continuous-wave irradiation at the center of the doublet, an established technique which is usually referred to as double quantum decoupling. The phase-alternated experiment makes it possible to decouple large quadrupolar interactions with a weak RF field. A theoretical analysis and numerical simulations are presented to demonstrate the decoupling performance. Proton spectra of partly deuterated dibromobutane in a liquid crystalline solvent have been recorded to illustrate the efficiency of phase-alternated deuterium decoupling.     

Single-slice mapping of ultrashort T(2)

In this communication we present a method for single-slice mapping of ultrashort transverse relaxation times T(2). The RF pulse sequence consists of a spin echo preparation of the magnetization followed by slice-selective ultrashort echo time (UTE) imaging with radial k-space sampling. In order to keep the minimum echo time as small as possible, avoid out-of-slice contamination and signal contamination due to unwanted echoes, the implemented pulse sequence employs a slice-selective 180° RF refocusing pulse and a 4-step phase cycle. The slice overlap of the two slice-selective RF pulses was investigated. An acceptable Gaussian slice profile could be achieved by adjusting the strength of the two slice-selection gradients. The method was tested on a short T(2) phantom consisting of an arrangement of a roll of adhesive tape, an eraser, a piece of modeling dough made of Plasticine?, and a 10% w/w agar gel. The T(2) measurements on the phantom revealed exponential signal decays for all samples with T(2)(adhesive tape)=(0.5 ± 0.1)ms, T(2)(eraser)=(2.33 ± 0.07)ms, T(2)(Plasticine?)=(2.8 ± 0.06)ms, and T(2)(10%agar)=(9.5 ± 0.83)ms. The T(2) values obtained by the mapping method show good agreement with the T(2) values obtained by a non-selective T(2) measurement. For all samples, except the adhesive tape, the effective transverse relaxation time T(2)(?) was significantly shorter than T(2). Depending on the scanner hardware the presented method allows mapping of T(2) down to a few hundreds of microseconds. Besides investigating material samples, the presented method can be used to study the rapidly decaying MR-signal from biological tissue (e.g.: bone, cartilage, and tendon) and quadrupolar nuclei (e.g.: (23)Na, (35)Cl, and (17)O).