Intermolecular Multiple-quantum Coherences Research Articles

Intermolecular multiple-quantum coherences between spin 1/2 and quadrupolar nuclei in liquid nuclear magnetic resonance

An NMR pulse sequence was used to study the signal features from intermolecular multiple-quantum coherences between spin 1/2 and quadrupolar nuclei in solution NMR for the first time. General theoretical expressions were derived from the raising and lowering operator formalism. Theoretical predictions for the relative signal intensities and the optimal pulse flip angles are in excellent agreement with experimental results. Both the magic angle gradient and 2D experiments validate that the signals are indeed from intermolecular heteronuclear multiple-quantum coherences.

Application of the forward linear prediction on high-resolution NMR spectra in inhomogeneous fields

In homogeneous fields, the advantages of forward linear prediction (LP) for processing 2D NMR data sets have long been recognized. In this paper, the forward LP method was employed to obtain high-resolution NMR spectra in inhomogeneous fields. Intermolecular multiple-quantum coherence (iMQC) signals are caused by intermolecular dipolar interactions and can be used to obtain 1D high-resolution NMR spectra from the 2D iMQC spectra acquired in inhomogeneous fields. However, when the 2D spectra are acquired with insufficient increments to save experimental time, wiggles around strong peaks and bad resolution will occur. Extending the data set by forward LP in the indirect dimension is a good way to improve spectral resolution. Compared to normal discrete Fourier transform, the forward LP method can shorten experimental time by a factor of four or more at the same level of sensitivity and resolution.

Accurate measurements of small J coupling constants under inhomogeneous fields via intermolecular multiple-quantum coherences

Two new NMR pulse sequences, based on intermolecular multiple-quantum coherences (iMQCs), were developed to obtain apparent J coupling constants with a scaling factor from one to infinity relative to the conventional J coupling constants. Here the apparent J coupling constants were defined as apparent peak separations in unit of Hz in a reconstructed spectrum for a coupled spin system. Except for the adjustable scaling factor for apparent J coupling constants, the sequences hold the advantage of high acquisition efficiency, and retain the spectral information such as chemical shifts, multiplet patterns, and relative peak areas under inhomogeneous fields. For spin systems with small scalar coupling constants, well-resolved J-spectra can be achieved by selecting a proper scaling factor. Theoretical predictions are in good agreement with simulation results and experimental observations.

High-resolution NMR spectra under inhomogeneous fields via intermolecular double-quantum coherences

High-resolution NMR spectroscopy is a powerful tool for analyzing molecular structures and compositions. Line-widths of conventional liquid NMR signals are directly proportional to the overall magnetic field inhomogeneity the sample experiences. In many circumstances, spatial and temporal homogeneity of the magnetic field is degraded. In this paper, a modified pulse sequence based on intermolecular double-quantum coherences (iDQCs) was proposed to obtain 1D high-resolution NMR spectra under inhomogeneous fields using 2D acquisition. Analytical expressions were derived from the intermolecular multiple-quantum coherence (iMQC) treatments. Both experimental and simulated spectra provide high-resolution 1D projection spectra similar to conventional 1D high-resolution spectra. Moreover, the apparent J coupling constants are threefold magnified, which allows a more accurate measurement of small J coupling constants.

Enhancement of magnetization transfer effects by inter-molecular multiple quantum filtered NMR

There are a number of methods that give MRI contrasts based on changes of the water M z magnetization as a result of magnetization transfer to macromolecules. In the present work we report that a combination of these methods with inter-molecular multiple quantum coherences (iMQC) gives enhanced effects. For the magnetization transfer contrast (MTC) method an effect of ( M z / M 0) becomes ( M z / M 0) l where l is the rank of the tensors constituting the iMQC. A similar trend was found upon combining iMQC with the Goldman–Shen experiment. It is pointed out that the method is general for all magnetization transfer methods, including the nuclear Overhauser effect.

A New Method for High‐Resolution NMR Spectra in Inhomogeneous Fields with Efficient Solvent Suppression

AbstractHigh‐resolution nuclear magnetic resonance (NMR) is one of the most powerful tools for analyzing molecular structures and dynamics. Magnetic field homogeneity is required for conventional high‐resolution spectra. However, there are many chemical and/or biological circumstances where the spatial homogeneities of the magnetic fields are degraded. Intense solvent signal is another obstacle for obtaining high‐resolution spectra, especially in in vivo and in situ NMR spectroscopy. In this paper, a new pulse sequence based on intermolecular multiple quantum coherence (iMQC) was reported. This sequence can effectively remove the effect of magnetic field inhomogeneity and suppress the solvent signal. It can recover the spectral information such as chemical shifts, coupling constants, multiplet patterns, and relative peak areas in inhomogeneous fields. Theoretical analyses and experimental verifications are presented to demonstrate the feasibility of this method.

Signal enhancement in CRAZED experiments

Many of the promising applications of the CRAZED (COSY Revamped with Asymmetric Z-gradient Echo Detection) experiments are in biomedical and clinical technologies. In tissue, however, signal from the typical CRAZED experiment is largely limited by transverse relaxation. When relaxation is included, the maximum achievable signal from a prototypical CRAZED sequence, in the linear regime, is proportional to T 2/ τ d. This means that for samples with a short T 2, as encountered in vivo, signals from intermolecular multiple-quantum coherences (iMQCs) reach very diminished signal intensities. While relaxation is generally regarded as a fundamental constraint, we show here that when T 2 is short but T 1 is long, as in tissue, there are simple sequence modifications that can increase signal beyond the T 2 limit. To better utilize the available signal intensity from iMQCs we propose a method to substitute part of the transverse magnetization with the longitudinally modulated magnetization. In this paper we show, with both simulations and experimental results, that in the presence of strong transverse relaxation the standard CRAZED scheme is not the optimal method for observing iMQCs, and can be improved upon with simple modifications.

Magnetic resonance microscopic imaging based on high-order intermolecular multiple-quantum coherences

Most imaging studies using intermolecular multiple-quantum coherences (iMQCs) have focused on the two-spin dipolar interactions--zero and double quantum coherences. Here, we report the results of various experimental studies to assess the feasibility of magnetic resonance microscopy with high-order iMQCs in model systems at 7 and 14 T. Experimental results demonstrated that the iMQC microscopic images with high coherence orders are readily observable at high field and have unique contrast depending on the sample microstructure and coherence order.

Simultaneous acquisition and effective separation of intermolecular multiple-quantum signals of different orders

A three-pulse sequence was designed to simultaneously acquire intermolecular multiple-quantum coherence (iMQC) signals of coherence order n = 2, 1, 0, −1, −2. Analytical expressions were derived from modified Bloch equations. Signal of a specific order was obtained by optimal combinations of data from different acquisition steps. This allows a time saving of 5/7 compared to the phase cycling designs targeted for individual coherence orders. The method also results in pure iMQC signal of all the above five orders which are insensitive to radio-frequency flip angle errors, in contrast to some previous methods. Theoretical predictions are supported by the experimental observations and numerically simulated results.

Diffraction-like phenomena in a periodic magnetization distribution at 1.5 T using the distant dipolar field (DDF)

In the CRAZED experiment (COSY revamped by asymmetric Z-gradient echo detection, Warren et al.), a spatially anisotropic magnetization distribution is created by application of a magnetic field gradient (strength G, duration τ) which in turn generates a response called the distant dipolar field (DDF). The DDF is a source of intermolecular multiple-quantum coherences (iMQC) which contain information on the distance d = π/( γGτ) between pairs of dipolar-coupled spins. Diffraction-like phenomena may result for periodically structured samples. In this study, we report the observation of diffraction owing to the DDF at 1.5 T using a clinical whole-body tomograph. Based on the semi-classical treatment of the problem by Robyr and Bowtell, diffraction conditions were obtained for a CRAZED-type pulse sequence that selects iMQC of order N. The predicted distinct difference in N = 2 and N ≠ 2 coherences, i.e., a dominant continuous course as a function of τ ( N = 2) and prominent diffraction peaks otherwise, could be verified in CRAZED experiments in a periodically structured sample selecting coherence orders N = 2 and N = 3. The diffractive signal component contains information on the geometric structure of the sample. Applications of this technique may permit the detection of changes in composition and geometry of periodic structures.

Gewebekontrast in MR-Bildern infolge intermolekularer Mehrquantenkohärenzen (iMQC)

Dipole-dipole interactions in 1H NMR of liquids permit a new tissue contrast in MR imaging (MRI). For this purpose, the CRAZED (COSY Revamped by Asymmetric Z-gradient Echo Detection) sequence which simply consists of two radiofrequency pulses of delay τ and a magnetic field gradient pulse of strength G, is applied to create intermolecular multiple-quantum coherences of dipolar-coupled ensembles of water protons with spatial distance d = π/(γGτ). As a consequence, the measured signal originates from “sources” that have a tunable dimension. CRAZED was first applied to MR imaging at 1.5 T by Zhong et al. To study the contrast properties and influence of sequence parameters of this technique, we implemented different sequences of this type on a clinical 1.5-T whole-body tomograph. The sequences were optimized in experiments with agar gel phantoms. We obtained images with dipolar contrast from the brain of healthy volunteers. The gradient system enabled correlation distances d in the range of 0.05 mm to 1 mm.

Intermolecular multiple quantum coherences at high magnetic field: The nonlinear regime

Experiments have been carried at magnetic-field strengths of 9.4, 14.1, and 17.6 T to explore the evolution of intermolecular multiple quantum coherences in the nonlinear regime where the system evolves for times that are much greater than the characteristic time of action of the long-range dipolar field, tau(d). The results show the expected Bessel function form of the recorded signal as a function of time of evolution, with evident zeros and sign changes. As expected, the rate of signal evolution increases at higher-field strengths as a result of the increased equilibrium magnetization. A numerical method for calculating the evolution of magnetization under the action of the distant dipolar field, relaxation, and diffusion that is based on Fourier analysis of the magnetization distribution has been applied to the correlated two-dimensional spectroscopy revamped by asymmetric z-gradient echo detection sequence in the nonlinear regime and shown to produce results that are in good agreement with experimental data acquired at different magnetic fields and rates of spatial modulation. Experiments and simulations have also been used to explore the evolution of magnetization in a mixture of two interacting spin species in the nonlinear regime.

Theoretical formalism and experimental verification of line shapes of NMR intermolecular multiple-quantum coherence spectra

Although the theories and potential applications of intermolecular multiple-quantum coherences (iMQCs) have been under active investigations for over a decade, discussion of iMQC NMR signal formation was mainly confined in the time domain. In this paper, a full line-shape theory was developed to describe iMQC signals in the frequency domain. Relevant features of the line shape, such as peak height, linewidth, and phase, were investigated in detail. Predictions based on the theory agree well with experimental and simulated results. Since radiation-damping effects always couple with iMQCs in highly polarized liquid-state NMR systems, and strongly radiation-damped signals have many spectral characteristics similar to those of iMQCs, a detailed comparison was also made between them from different spectral aspects. With detailed comparison of peak height, linewidth, and phase, this work demonstrates that the iMQC and radiation-damping phenomena result from two completely different physical mechanisms despite that both present similar signal features and coexist in highly polarized liquid-state NMR systems.

Multiple-quantum vector field imaging by magnetic resonance

We introduce a method for non-invasively mapping fiber orientation in materials and biological tissues using intermolecular multiple-quantum coherences. The nuclear magnetic dipole field of water molecules is configured by a CRAZED sequence to encode spatial distributions of material heterogeneities. At any given point r in space, we obtain the spherical coordinates of fiber orientation ( θ, ϕ) with respect to the external field by comparing three signals ∥ G X ∥, ∥ G Y ∥, and ∥ G Z ∥ (modulus), acquired with linear gradients applied along the X, Y, and Z axes, respectively. For homogeneous isotropic materials, a subtraction ∥ G Z ∥ − ∥ G X ∥ − ∥ G Y ∥ gives zero. With anisotropic materials, we find an empirical relationship relating ∥ G Z ∥ − ∥ G X ∥ − ∥ G Y ∥/(∥ G X ∥ + ∥ G Y ∥ + ∥ G Z ∥) to the polar angle θ, while ∥ G X ∥ − ∥ G Y ∥/(∥ G X ∥ + ∥ G Y ∥ + ∥ G Z ∥) is related to the azimuthal angle ϕ. Experiments in structured media confirm the structural sensitivity. This technique can probe length scales not accessible by conventional MRI and diffusion tensor imaging.

Propagator formalism and computer simulation of restricted diffusion behaviors of inter-molecular multiple-quantum coherences

In this paper, behaviors of single-quantum coherences and inter-molecular multiple-quantum coherences under restricted diffusion in nuclear magnetic resonance experiments were investigated. The propagator formalism based on the loss of spin phase memory during random motion was applied to describe the diffusion-induced signal attenuation. The exact expression of the signal attenuation under the short gradient pulse approximation for restricted diffusion between two parallel plates was obtained using this propagator method. For long gradient pulses, a modified formalism was proposed. The simulated signal attenuation under the effects of gradient pulses of different width based on the Monte Carlo method agrees with the theoretical predictions. The propagator formalism and computer simulation can provide convenient, intuitive and precise methods for the study of the diffusion behaviors.

Structural anisotropy and internal magnetic fields in trabecular bone: Coupling solution and solid dipolar interactions

We investigate the use of intermolecular multiple-quantum coherence to probe structural anisotropy in trabecular bone. Despite the low volume fraction of bone, the bone–water interface produces internal magnetic field gradients which modulate the dipolar field, depending on sample orientation, choice of dipolar correlation length, correlation gradient direction, and evolution time. For this system, the probing of internal magnetic field gradients in the liquid phase permits indirect measurements of the solid phase dipolar field. Our results suggest that measurements of volume-averaged signal intensity as a function of gradient strength and three orthogonal directions could be used to non-invasively measure the orientation of structures inside a sample or their degree of anisotropy. The system is modeled as having two phases, solid and liquid (bone and water), which differ in their magnetization density and magnetic susceptibility. A simple calculation using a priori knowledge of the material geometry and distribution of internal magnetic fields verifies the experimental measurements as a function of gradient strength, direction, and sample orientation.

Selection of intra- or inter-molecular multiple-quantum coherences in NMR of highly polarized solution

In highly polarized scalar-coupled liquid systems, nuclear magnetic resonance signals from multiple-quantum coherences (MQCs) may be formed by inter-molecular dipolar and/or intra-molecular scalar couplings. Selection of specific signals can simplify the spectra, which may help us understand the underlying physical mechanisms in complex coupled spin systems. In this paper, a pulse sequence with three selective radio-frequency (RF) pulses and phase cycling was designed for this purpose. For an I pS q ( p, q = 1 , 2 , 3 , … ) spin system, there are three kinds of MQC signals, which originate from intra-molecular I– S, inter-molecular I– S, and inter-molecular S– S (or I– I) coherences. These three kinds of signals can be detected separately by proper phase cycling of RF pulses, which is independent of coupling constants. The intra- and inter-molecular MQC signals can also be detected separately with specific preparation periods, but this method is sensitive to coupling constants. Our theoretical predictions are in good agreement with experimental observations. The method proposed herein can be extended to heteronuclear cases.

Dipolar field effects described by boson operators techniques: The case of intermolecular multiple-quantum coherences in liquids

Dipolar couplings between macroscopically distant spins in solution nuclear magnetic resonance (NMR) are treated. We propose a novel technique to calculate the intermolecular multiple-quantum coherences (iMQCs) based on a boson operators approach. The choice of an annihilation and creation operator basis set allows us to produce a general expression of the NMR signal depending on local inhomogeneities of magnetic field. The general expression we derive fits into the well known background of iMQCs signal descriptions [J. Jeener, J. Chem. Phys. 112 (2000) 5091] and turns into the conventional quantum-mechanical Warren formulation [S. Lee, W. Richter, S. Vathyam, W.S. Warren, J. Chem. Phys. 105 (1996) 874] by means of appropriate approximations.

Rotating‐frame intermolecular double‐quantum spin‐lattice relaxation T1ρ, DQC‐weighted magnetic resonance imaging

In this study, spin-locking techniques were added as a part of intermolecular multiple-quantum experiments, thereby introducing the concept of rotating-frame intermolecular double-quantum spin-lattice relaxation, T(1rho, DQC). A novel magnetic resonance imaging methodology based on intermolecular multiple-quantum coherences is demonstrated on a 7.05-T microimaging scanner. The results clearly reveal that the intermolecular double-quantum coherence T(1rho, DQC)-weighted imaging technique provides an alternative contrast mechanism to conventional imaging.

Multiplet patterns due to co-existing intermolecular dipolar and intramolecular scalar couplings in liquid nuclear magnetic resonance

When both intermolecular dipolar couplings (D couplings) and intramolecular scalar couplings (J couplings) exist in a highly polarized multiple-spin liquid, some forbidden nuclear magnetic resonance signals originating from intermolecular multiple-quantum coherences may become observable. Moreover, their multiplet patterns are quite different from what are observed in a multiple-spin system with J couplings only. In this paper, these forbidden resonance peaks and unique multiplet patterns are studied theoretically and experimentally. For comparison and verification, an I2S3+X spin system is chosen as an example to present five types of signal patterns from the interactions of D and J couplings with either selective or non-selective radio-frequency pulse sequences for double-quantum coherences. The multiplet pattern rules for a more general IpSq+Xk (p,q,k = 1,2,3,...) spin system are derived as well. It is demonstrated that some unusual multiplet amplitude patterns such as (1:0:–1) may ``magnify'' J splittings, allowing more accurate measurement of J coupling in the case of small J coupling constants and/or in inhomogeneous fields. It is shown that the theoretical predictions, computer simulations and experimental observations are all in agreement with one another very well.