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

Flat pancake distant dipolar fields for enhancement of intermolecular multiple-quantum coherence signals

Intermolecular multiple-quantum coherences (iMQCs) originated from distant dipolar field (DDF) possess some appealing unique properties for magnetic resonance imaging (MRI). DDF is usually induced with continuous wave (i.e., sine- or square-wave) magnetization modulation in the whole sample. In this article, a spatially localized and enhanced DDF was optimally tailored in a thin slice with an adiabatic inversion pulse. Evidence was provided to show that careful tailoring of the spatially localized DDF can generate highly efficient iMQC signals, with more than two-fold enhancement compared to the conventional sine-wave magnetization modulation method, and 1.5 times of that with the square-wave modulation under the similar condition. Theoretical predictions, simulation results, and experimental verifications agree well with each other. Practical implementation of this approach for efficient iMQC MRI was explored.

Nuclear magnetic resonance signal dynamics of liquids in the presence of distant dipolar fields, revisited

The description of the nuclear magnetic resonance magnetization dynamics in the presence of long-range dipolar interactions, which is based upon approximate solutions of Bloch-Torrey equations including the effect of a distant dipolar field, has been revisited. New experiments show that approximate analytic solutions have a broader regime of validity as well as dependencies on pulse-sequence parameters that seem to have been overlooked. In order to explain these experimental results, we developed a new method consisting of calculating the magnetization via an iterative formalism where both diffusion and distant dipolar field contributions are treated as integral operators incorporated into the Bloch-Torrey equations. The solution can be organized as a perturbative series, whereby access to higher order terms allows one to set better boundaries on validity regimes for analytic first-order approximations. Finally, the method legitimizes the use of simple analytic first-order approximations under less demanding experimental conditions, it predicts new pulse-sequence parameter dependencies for the range of validity, and clarifies weak points in previous calculations.

Quasiequilibrium states in thermotropic liquid crystals studied by multiple-quantum NMR

Previous work showed that by means of the Jeener-Broekaert (JB) experiment, two quasiequilibrium states can be selectively prepared in the proton spin system of thermotropic nematic liquid crystals (LCs) in a strong magnetic field. The similarity of the experimental results obtained in a variety of LC in a broad Larmor frequency range, with crystal hydrates, supports the assumption that also in LC the two spin reservoirs, into which the Zeeman order is transferred, originate in the dipolar energy and that they are associated with a separation in energy scales: A constant of motion related to the stronger dipolar interactions (S), and a second one (W) corresponding to the secular part of the weaker dipolar interactions with regard to the Zeeman and the strong dipolar part. We study the nature of these quasi-invariants in nematic 5CB (4(')-pentyl-4-biphenyl-carbonitrile) and measure their relaxation times by encoding the multiple-quantum coherences of the states following the JB pulse pair on two orthogonal bases, Z and X. The experiments were also performed in powder adamantane at 301 K which is used as a reference compound having only one dipolar quasi-invariant. We show that the evolution of the quantum states during the buildup of the quasiequilibrium state in 5CB prepared under the S condition is similar to the case of powder adamantane and that their quasiequilibrium density operators have the same tensor structure. In contrast, the second constant of motion, whose explicit operator form is not known, involves a richer composition of multiple-quantum coherences of even order on the X basis, in consistency with the truncation inherent in its definition. We exploited the exclusive presence of coherences of +/-4,+/-6,+/-8, besides 0 and +/-2 under the W condition to measure the spin-lattice relaxation time T(W) accurately, so avoiding experimental difficulties that usually impair dipolar order relaxation measurement such as Zeeman contamination at high fields and also superposition of the different quasi-invariants. This procedure opens the possibility of measuring the spin-lattice relaxation of a quasi-invariant independent of the Zeeman and S reservoirs, so incorporating a new relaxation parameter useful for studying the complex molecular dynamics in mesophases. In fact, we report the first measurement of T(W) in a LC at high magnetic fields. Comparison of the obtained value with the one corresponding to a lower field (16 MHz) points out that the relaxation of the W-order strongly depends on the intensity of the external magnetic field, similarly to the case of the S reservoir, indicating that the relaxation of the W-quasi-invariant is also governed by the cooperative molecular motions.

Quantitative time- and frequency-domain analysis of the two-pulse COSY revamped by asymmetric Z-gradient echo detection NMR experiment: Theoretical and experimental aspects, time-zero data truncation artifacts, and radiation damping

The two-pulse COSY revamped by asymmetric Z-gradient echo detection (CRAZED) NMR experiment has the basic form 90 degrees -Gdelta-t(rec)-beta-nGdelta-t(rec)-FID, with a phase-encoding gradient pulse G of length delta applied during the evolution time tau for transverse magnetization, readout pulse beta, rephasing gradient nGdelta, and recovery time t(rec) prior to acquisition of the free-induction decay. Based on the classical treatment of the spatially modulated dipolar demagnetizing field and without invoking intermolecular multiple-quantum coherence, a new formulation of the first-order approximation for the theoretical solution of the nonlinear Bloch equations has been developed. The nth-order CRAZED signal can be expressed as a simple product of a scaling function C(n)(beta,tau) and a signal amplitude function A(n)(t), where the domain t begins immediately after the beta pulse. Using a single-quantum coherence model, a generalized rf phase shift function has also been developed, which explains all known phase behavior, including nth-order echo selection by phase cycling. Details of the derivations are provided in two appendices as supplementary material. For n>1, A(n)(t) increases from zero to a maximum value at t=t(max) before decaying and can be expressed as a series of n exponential decays with antisymmetric binomial coefficients. Fourier transform gives an antisymmetric binomial series of Lorentzians, where the composite lineshape exhibits negative wings, zero integral, and a linewidth that decreases with n. Analytical functions are presented for t(max) and A(n)(t(max)) and for estimating the maximal percent error incurred for A(n)(t(max)) when using the first-order model. The preacquisition delay Delta=delta+t(rec) results in the loss of the data points for t=0 to Delta. Conventional Fourier transformation produces time-zero truncation artifacts (reduced negative wing amplitude, nonzero integral, and reduced effective T(2) ( *)), which can be avoided by time-domain fitting after right shifting the data by Delta. A doped water sample (9.93 mM NiSO(4), 10 mm sample tube) was used to study the behavior of the CRAZED signal for n=1-4 with beta=90 degrees at 7 T (300 MHz (1)H frequency) as a function of Delta, with and without radiation damping. Pulse-acquire experiments were used to determine the relaxation times (T(1)=61.8 ms and T(2) ( *)=29.7 ms), and the radiation damping time constant T(rd)=18.5 ms. When experimental CRAZED data sets were right shifted by Delta, excellent least-squares fits to the first-order model function were obtained for all n using a minimal set of free variables. Without radiation damping the fitted T(2) ( *)values (29.7-30.2 ms) agreed with the reference value. With radiation damping the fitted effective T(2) ( *) values were 16.2 ms for a 90 degrees pulse-acquire experiment and 18.8-20.2 ms for the CRAZED experiment with n=1-4 and signal amplitudes spanning a range of 10(5).

Intermolecular zero-quantum coherence NMR spectroscopy in the presence of local dipole fields

NMR experiments detecting intermolecular zero-quantum coherences (iZQCs) allow for observation of homogeneous line shapes under inhomogeneous magnetic fields. Local dipole fields impair the refocusing capacity of such experiments and render the available theoretical description of signal evolution invalid. In this article, the impact of local dipole fields on two-dimensional iZQC spectroscopy experiments was assessed by performing extensive numerical simulations, which solved the nonlinear Bloch equations for a binary solution in a magnetization array of 64(3) spatial points. Local dipole fields were simulated using spherical volumes with different magnetic susceptibility values corresponding to either a glass sphere or an air inclusion with a diameter of 100 microm. The local field resulted in a broadened distribution of difference frequencies between locally interacting spins and led to the dominating effect of decreasing the amplitude of the solute peak, before line broadening was observed in the spectra. From simulations using a magnetic field strength of 17.6 T, the smallest ratio of sample to inclusion volume that still allowed for observation of the solute peak was determined to be eta(limit)=215 and eta(limit)=392 for glass and air inclusions, respectively. Experimental data acquired with a 100 microm diameter glass sphere embedded in agar gel yielded a value of eta(limit)=252 and confirmed the order of magnitude obtained from the simulations. From these data, it was concluded that iZQC spectroscopy is possible as long as the relative volume occupied by air inclusions does not exceed the order of 0.1% of the sample volume. This limit, in contrast to the previous speculations, strongly excludes materials or tissues with high density of strong inhomogeneities from the investigation by iZQC spectroscopy.

Distant dipolar fields in laser-polarized gases on macroscopic scales

Distant dipolar fields among nuclear spins on macroscopic scales in the gas phase are reported for the first time. Their observation via interatomic multiple quantum coherences requires high nuclear spin polarization corresponding to spin temperatures of a few mK, which is generated in laser-polarized 3He, and proper control of the gas diffusion through a heavier buffer gas. This combination of physics at low and ambient temperatures opens up new ways of studying the relative translational diffusion of atoms and of gas diffusion in structures with a large range of length scales.

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.