Selective NMR excitation in strongly inhomogeneous magnetic fields

The NMR-MOUSE is a unilateral and mobile NMR sensor which operates with highly inhomogeneous magnetic fields. To produce a mobile NMR unit, RF excitation is sought, which can be produced with the most simple equipment, in particular nonlinear, low-power amplifiers, and to observe a free induction decay in strongly inhomogeneous fields, the excitation needs to be selective. The possibility to produce selective excitation by sequences of hard low-power radiofrequency pulses in the strongly inhomogeneous magnetic fields of the NMR-MOUSE is explored. The use of the DANTE sequence for selection of magnetization from parts of the sensitive volume was investigated for longitudinal and transverse magnetization by computer simulations and experiments. The spectra of the recorded FIDs and echo signals are in good agreement with those simulated for the excitation, which verifies the concept of the DANTE excitation. The results obtained are an important step towards a low-power operation of the NMR-MOUSE to improve its mobility.     

NMR of multipolar spin states excitated in strongly inhomogeneous magnetic fields

The possibility of exciting and filtering various multipolar spin states in proton NMR like dipolar encoded longitudinal magnetization (LM), double-quantum (DQ) coherences, and dipolar order (DO) in strongly inhomogeneous static and radio-frequency magnetic fields is investigated. For this purpose pulse sequences which label and manipulate the multipolar spin states in a specific way were implemented on the NMR-MOUSE (mobile universal surface explorer). The performance of the pulse sequences was also tested in homogeneous fields on a solid-state high-field NMR spectrometer. The theoretical justification of these procedures was shown for a rigid two-spin 1/2 system coupled by dipolar interactions. Dipolar encoded longitudinal magnetization decay curves, double-quantum and dipolar-order buildup curves, as well as double-quantum decay curves were recorded with the NMR-MOUSE for natural rubber samples with different crosslink density. The possibility of using these multipolar spin states for investigations of strained elastomers by NMR-MOUSE is also shown. These curves give access to quantitative values of the ratio of the total residual dipolar couplings of the protons in the series of samples which are in good agreement with those measured in homogeneous fields.     

Selective saturation in strongly inhomogeneous magnetic fields

The possibility to produce selective saturation by nuclear magnetic resonance (NMR) sequences of low-power radio-frequency pulses in strongly inhomogeneous magnetic fields is explored. The saturation of parts of the sensitive volume is produced by a particular pulse sequence with reduced amplitude distribution and the spectrum of the recorded signal is compared with the simulated spectrum. The spectra of the recorded free induction decays and echo signals are in good agreement with the simulated spectra of the pulse sequence, which demonstrates the effect of the selective saturation. The results obtained are an important step towards the development of new mobile and lowpower NMR equipments operating with inhomogeneous magnetic fields.     

Double-quantum-filtered NMR signals in inhomogeneous magnetic fields

The possibility of exciting and detecting proton NMR double-quantum coherences in inhomogeneous static and radiofrequency magnetic fields was investigated. For this purpose specialized pulse sequences which partially refocus the strongly inhomogeneous evolution of the spin system and generate double-quantum buildup and decay curves were implemented on the NMR MOUSE (mobile universal surface explorer). The theoretical justification of the method was developed for the simple two-spin-1/2 system. The performances of the same pulse sequences were also tested on a solid-state high-field NMR spectrometer. It was shown that DQ decay curves have a better signal-to-noise ratio in the initial time regime than DQ buildup curves. The double-quantum buildup and decay curves were recorded for a series of cross-linked natural rubber samples. These curves give access to quantitative values of the ratio of proton total residual dipolar couplings which are in good agreement with those measured in homogeneous fields. A linear dependence of these ratios on the sulfur-accelerator content was found.     

Diffusion exchange NMR spectroscopy in inhomogeneous magnetic fields

Two-dimensional diffusion exchange experiments in the presence of a strong, static magnetic field gradient are presented. The experiments are performed in the stray field of a single sided NMR sensor with a proton Larmor frequency of 11.7 MHz. As a consequence of the strong and static magnetic field gradient the magnetization has contributions from different coherence pathways. In order to select the desired coherence pathways, a suitable phase cycling scheme is introduced. The pulse sequence is applied to study diffusion as well as the molecular exchange properties of organic solvents embedded in a mesoporous matrix consisting of a sieve of zeolites with a pore size of 0.8 nm and grain size of 2 μm. This pulse sequence extends the possibilities of the study of transport properties in porous media, with satisfying sensitivity in measurement times of a few hours, in a new generation of relatively inexpensive low-field NMR mobile devices.     

Self-diffusion measurements by a constant-relaxation method in strongly inhomogeneous magnetic fields

The simple pulse sequence thetax-tau1-2thetay-tau1+tau2-2thetay-tau2-Hahn echo used to measure the self-diffusion coefficient D under constant-relaxation condition, i.e., for tau1+tau2=const. was investigated in the presence of strongly inhomogeneous static as well as radiofrequency magnetic fields. The encoding of the Hahn-echo amplitude by the pulse flip angle and diffusion was evaluated by taking into account the spatial distribution of the off-resonance field, the strength and orientation of the local field gradients, and the pulse flip angles by a computer simulation program. As input files, this program uses maps of static and radiofrequency fields, and the D coefficient can be evaluated from the time dependence of the Hahn-echo amplitude. The method was applied to a mobile one-sided NMR sensor, NMR-MOUSE with a bar magnet by measuring D for a series of liquids with different viscosities. The method was shown to be particularly useful for measuring D of solvents in elastomers without the need for measurements of the transverse relaxation rates. The self-diffusion coefficient of toluene in a series of crosslinked natural rubber samples was measured and correlated with the crosslink density. Finally, the method was applied to measure the diffusion anisotropy of free water in bovine Achilles tendon.     

Distributions of transverse relaxation times for soft-solids measured in strongly inhomogeneous magnetic fields

The single-sided NMR-MOUSE sensor that operates in highly inhomogeneous magnetic fields is used to record a CPMG ¹H transverse relaxation decay by CPMG echo trains for a series of cross-linked natural rubber samples. Effective transverse relaxation rates 1/T_2,short and 1/T_2,long were determined by a bi-exponential fit. A linear dependence of transverse relaxation rates on cross-link density is observed for medium to large values of cross-link density. As an alternative to multi-exponential fits the possibility to analyze the dynamics of soft polymer network in terms of multi-exponential decays via the inverse Laplace transformation was studied. The transient regime and the effect of the T₁/T₂ ratio in inhomogeneous static and radiofrequency magnetic fields on the CPMG decays were studied numerically using a dedicated C++ program to simulate the temporal and spatial dependence of the CPMG response. A correction factor T₂/T_2,eff is derived as a function of the T₁/T₂ ratio from numerical simulations and compared with earlier results from two different well logging devices. High-resolution T₁–T₂ correlations maps are obtained by two-dimensional Laplace inversion of CPMG detected saturation recovery curves. The T₁–T₂ experimental correlations maps were corrected for the T₁/T₂ effect using the derived T₂/T_2,eff correction factor.     

High-resolution absorptive intermolecular multiple-quantum coherence NMR spectroscopy under inhomogeneous fields

Intermolecular multiple-quantum coherence (iMQC) is capable of improving NMR spectral resolution using a 2D shearing manipulation method. A pulse sequence termed CT-iDH, which combines intermolecular double-quantum filter (iDQF) with a modified constant-time (CT) scheme, is designed to achieve fast acquisition of high-resolution intermolecular zero-quantum coherences (iZQCs) and intermolecular double-quantum coherences (iDQCs) spectra without strong coupling artifacts. Furthermore, double-absorption lineshapes are first realized in 2D intermolecular multi-quantum coherences (iMQCs) spectra under inhomogeneous fields through a combination of iZQC and iDQC signals to double the resolution without loss of sensitivity. Theoretically the spectral linewidth can be further reduced by half compared to original iMQC high-resolution spectra. Several experiments were performed to test the feasibility of the new method and the improvements are evaluated quantitatively. The study suggests potential applications for in vivo spectroscopy.     

High-resolution NMR spectra in inhomogeneous and unstable fields via the three-pulse method

In modern solution nuclear magnetic resonance (NMR), the spectral resolution is mainly dependent on the spatial homogeneity and temporal stability of the magnetic field. The spectral linewidths are usually proportional to the overall field homogeneity and the stability experienced by the sample. Many high-resolution NMR methods have been developed, but few are applicable in inhomogeneous and unstable fields. In this paper, a high-resolution three-pulse method based on intermolecular zero-quantum coherences (iZQCs) is proposed. Since this method is insensitive to field inhomogeneity and instability, spectral information such as the chemical shift can be retained in the resulting spectra. In comparison with the CPMG-HOMOGENIZED method, the new method provides almost pure solvent–solute iZQC signals.     

Phase transition in strongly inhomogeneous ferromagnets

A field theoretical model is proposed to describe the critical behaviour of a strongly inhomogeneous spin system with a position dependent concentration of magnetic atoms C(R) and magnetisation M(R). Assuming a finite number of $\text{n}$ Fouriermodes $\text{C}{}_{\mathrm{<mtext>Q</mtext>}}{}_{\mathrm{<mtext>v</mtext>}}\text{v}\text{= 1}$,..., $\text{n}$, to express C(R), the quenched randomness requires to interpret {$\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}{}^2$} on a set of invariant or marginal lengths. As consequence, M(R) can be described by n Fourier-modes M_Qv, where $\text{n ?}\text{n}$. For short range spin-spin interaction, we find for strong inhomogeneity, i.e. large n, the critical exponent between those of the related homogeneous system and those of the spherical model.     

NMR spectroscopy in inhomogeneous B0 and B1 fields with non-linear correlation

Resolved NMR spectra from samples in inhomogeneous B0 and B1 fields can be obtained with the so-called "ex situ" methodology, employing a train of composite or adiabatic z-rotation RF pulses to periodically refocus the inhomogeneous broadening during the detection of the time-domain signal. Earlier schemes relied on a linear correlation between the inhomogeneous B0 and B1 fields. Here the pulse length, bandwidth, and amplitude of the adiabatic pulses of the hyperbolic secant type are adjusted to improve the refocusing for a setup with non-linear correlation. The field correlation is measured using a two-dimensional nutation experiment augmented with a third dimension with varying RF carrier frequency accounting for off-resonance effects. The pulse optimization is performed with a computer algorithm using the experimentally determined field correlation and a standard adiabatic z-rotation pulse as a starting point for the iterative optimization procedure. The shape of the z-rotation RF pulse is manipulated to provide refocusing for the conditions given by the sample-, magnet-, and RF-coil geometry.     

High-resolution NMR spectra in inhomogeneous fields utilizing the CRAZED sequence without coherence selection gradients

Coherence selection gradients have been considered as indispensable for high-resolution NMR spectroscopy in inhomogeneous fields utilizing the CRAZED-type sequences. However, our experimental results demonstrate that these gradients can be omitted if an appropriate phase cycling is applied. The measured linewidth of reconstructing 1D high-resolution spectral peaks does not depend on the dipolar correlation distance determined by the coherence selection gradients, but is only affected by diffusion and T(2) relaxation. This finding suggests the need to reconsider the mechanism for the iMQC-based high-resolution spectroscopy.     

Imaged deconvolution: a method for extracting high-resolution NMR spectra from inhomogeneous fields

We present a novel method for obtaining high resolution NMR spectra in the presence of grossly inhomogeneous magnetic fields, such as those encountered in one-sided access NMR. Our method combines the well-known principle of reference deconvolution with NMR imaging in order to resolve spectral features with frequency resolution orders of magnitude smaller than the prevailing line-broadening due to field inhomogeneity. We demonstrate that, in cases of inhomogeneous field line-broadening more than an order of magnitude larger than the spectral features to be resolved, rather than performing reference deconvolution on the sample as a whole, it is more favourable in terms of SNR to divide the target region of a sample into smaller sub-regions, by means of chemical shift imaging, and then to perform reference deconvolution on the individual sub-region spectra, finally summing the results In this way, significant resolution enhancements can be obtained in the presence of severe magnetic field inhomogeneity without an unacceptable loss in SNR.     

Singularity spectra of strongly inhomogeneous multifractals

Generalized multifractal formalism is used to study singularity spectra of strongly inhomogeneous multifractals characterized by coarse-grained probability measures with zero minimal and/or infinite maximal H?lder exponents. Due to involving two additional types of scaling indices, the generalized formalism is shown to be able to describe complex multifractal objects by families of bivariate spectra rather than familiar single spectra of singularity strengths of one type, providing a more complete and adequate characteristics of such objects. It is proved that the families of extended singularity spectra can reveal unusual forms with many maxima, reflecting complex scaling structures of strongly inhomogeneous multifractals. Received 25 April 2001 and Received in final form 26 February 2002     

Spatially encoded pulse sequences for the acquisition of high resolution NMR spectra in inhomogeneous fields

We have recently proposed a protocol for retrieving nuclear magnetic resonance (NMR) spectra based on a spatially-dependent encoding of the MR interactions. It has also been shown that the spatial selectivity with which spins are manipulated during such encoding opens up new avenues towards the removal of magnetic field inhomogeneities; not by demanding extreme Bo field uniformities, but rather by compensating for the dephasing effects introduced by the field distribution at a radiofrequency excitation and/or refocusing level. The present study discusses in further detail a number of strategies deriving from this principle, geared at acquiring both uni- as well as multi-dimensional spectroscopic data at high resolution conditions. Different variants are presented, tailored according to the relative sensitivity and chemical nature of the spin system being explored. In particular a simple multi-scan experiment is discussed capable of affording substantial improvements in the spectral resolution, at nearly no sensitivity or scaling penalties. This new compensation scheme is therefore well-suited for the collection of high-resolution data in low-field systems possessing limited signal-to-noise ratios, where magnetic field heterogeneities might present a serious obstacle. Potential areas of applications of these techniques include high-field in vivo NMR studies in regions near tissue/air interfaces, clinical low field MR spectroscopy on relatively large off-center volumes difficult to shim, and ex situ NMR. The principles of the different compensation methods are reviewed and experimentally demonstrated for one-dimensional inhomogeneities; further improvements and extensions are briefly discussed.     

Focused antenna array in a strongly inhomogeneous medium

A focused acoustic antenna array is considered in a strongly inhomogeneous stationary medium. An opportunity is indicated to determine the coordinates of a number of objects by active location. It is assumed that, in insonifying the objects by a wave with an arbitrary wave front, they scatter spherical waves and are sufficiently separated in distance and angle to be resolved by the same array in a homogeneous medium. The procedure of determining the coordinates of the objects involves a wave front inversion for distinguishing between the signals from different objects. The coordinates are determined by estimating the parameters for each individual object. The parameter estimation procedure is shown to provide a high efficiency of extracting the argument of a complex signal. The results of the numerical modeling and solution of the problem are presented.     

Restricted diffusion in grossly inhomogeneous fields

We analyze the effects of geometrical restriction on the nuclear magnetization of spins diffusing in grossly inhomogeneous fields where radio-frequency (RF) pulses are weak relative to the total field inhomogeneity, making the rotation angle space-dependent and thus exciting multiple coherence pathways. We show how to separate the effects of restricted diffusion from the effects of the pulses in the case when the change in the field experienced by a diffusing spin in the course of the experiment is small compared to the RF magnitude. We then derive explicit formulas for the contribution of individual coherence pathways to the total magnetization in arbitrary pulse sequences. We find that, for long diffusion times, restriction can dramatically alter the spectrum and the shape of a particular echo, while for short times, the correction will be proportional to the pore space surface-to-volume ratio. We demonstrate these results on the example of the early echoes of the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence.