Two-dimensional high-resolution NMR spectra in matched B(0) and B(1) field gradients

Spatially resolved spectroscopy using tapered stripline NMR

Magnetic field B0 gradients are essential in modern Nuclear Magnetic Resonance spectroscopy and imaging. Although RF/B1 gradients can be used to fulfill a similar role, this is not used in common practice because of practical limitations in the design of B1 gradient coils. Here we present a new method to create B1 gradients using stripline RF coils. The conductor-width of a stripline NMR chip and the strength of its radiofrequency field are correlated, so a stripline chip can be tapered to produce any arbitrary shaped B1 field gradient. Here we show the characterization of this tapered stripline configuration and demonstrate three applications: magnetic resonance imaging on samples with nL-μL volumes, reaction monitoring of fast chemical reactions (10(-2)-10(1)s) and the compensation of B0 field gradients to obtain high-resolution spectra in inhomogeneous magnetic fields.

High-resolution NMR spectroscopy in inhomogeneous fields

High-resolution NMR spectroscopy, providing information on chemical shifts, J coupling constants, multiplet patterns, and relative peak areas, is a mainstream tool for analysis of molecular structures, conformations, compositions, and dynamics. Generally, a homogeneous magnetic field is a prerequisite for obtaining high-resolution NMR information. Magnetic field inhomogeneity, whether from non-ideal experimental conditions or from intrinsic magnetic susceptibility discontinuities in samples, represents a hurdle for applications of high-resolution NMR. Numerous techniques have been proposed for measuring high-resolution NMR spectra free from the influence of inhomogeneous magnetic fields. Besides developments and improvements in NMR instrumentation, various types of experimental approaches have been established for recovering NMR information in inhomogeneous magnetic fields. Three main types are systematically described in this review. In addition, other high-resolution NMR approaches or data processing methods are also briefly described. All high-resolution NMR approaches covered in this review have individual advantages and disadvantages in practical applications, and no one technique is applicable to all practical circumstances. Hence, they are complementary for high-resolution NMR applications in inhomogeneous fields. The underlying mechanisms of these approaches are presented, together with analyses of their applicability and efficiency.

Imaging of the B1 distribution and background signal in a MAS NMR probehead using inhomogeneous B0 and B1 fields

Several widely used methods for suppressing the "background" signal in (1)H magic angle spinning (MAS) NMR spectroscopy are based on the assumption of a significant difference between the B1 radiofrequency field experienced by the sample (within the MAS rotor) and that felt by static components of the probehead (where the background signal is believed to originate). In this work, a two-dimensional correlation experiment employing inhomogeneous B0 and B1 fields is used to image the B1 distribution in a MAS NMR probehead. The experiment, which can be performed on any spectrometer, allows the distribution of the B1 field to be measured and also correlated with the spatial location of the NMR signal within the probehead. The method can also readily be combined with various "depth pulse" techniques for background suppression, allowing their performances to be more rigorously evaluated.

High-resolution MR spectroscopy via intermolecular double-quantum coherences in inhomogeneous B0 and B1 fields

Inhomogeneity in static field B0 and/or RF field B1 is inevitable under some circumstances. In this work, a method based on intermolecular double-quantum coherences is employed for high-resolution 1D MR spectroscopy via 2D acquisition under such a condition. High-resolution information on chemical shifts, multiplet patterns, J coupling constants and relative peak areas can be retained in the resulting 1D projected spectra, as shown with results from a narrow-bore NMR spectrometer and a whole-body clinical scanner.

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 (1)H 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 T(1)/T(2) 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 T(2)/T(2,eff) is derived as a function of the T(1)/T(2) ratio from numerical simulations and compared with earlier results from two different well logging devices. High-resolution T(1)-T(2) correlations maps are obtained by two-dimensional Laplace inversion of CPMG detected saturation recovery curves. The T(1)-T(2) experimental correlations maps were corrected for the T(1)/T(2) effect using the derived T(2)/T(2,eff) correction factor.

Study of order and dynamic processes in tendon by NMR and MRI

Tendons are composed of a parallel arrangement of densely packed collagen fibrils that results in unique biomechanical properties of strength and flexibility. In the present review we discuss several advanced magnetic resonance spectroscopy (MRS) and imaging (MRI) techniques that have allowed us to better understand the biophysical properties of tendons and ligaments. The methods include multiple quantum and T(2) filtering combined with NMR and MRI techniques. It is shown in detail how these techniques can be used to extract a number of useful parameters: 1) the (1)H-(1)H and (1)H-(2)H dipolar interactions; 2) the proton exchange rates between water and collagen, and between water molecules; 3) the distribution of fibril orientations; and 4) the anisotropy of diffusion. It is shown that relaxation data as a function of angular dependence can be obtained in vivo using mobile NMR sensors. Finally, this article describes how double quantum filtered (DQF) MRI can be used to image and monitor the healing process in injured tendons.

Self-diffusion measurements by a mobile single-sided NMR sensor with improved magnetic field gradient

A simple and fast method of measuring self-diffusion coefficients of protonated systems with a mobile single-sided NMR sensor is discussed. The NMR sensor uses a magnet geometry that generates a highly flat sensitive volume where a strong and highly uniform static magnetic field gradient is defined. Self-diffusion coefficients were measured by Hahn- and stimulated echoes detected in the presence of the uniform magnetic field gradient of the static field. To improve the sensitivity of these experiments, a Carr-Purcell-Meiboom-Gill pulse sequence was applied after the main diffusion-encoding period. By adding the echo train the experimental time was strongly shortened, allowing the measurement of complete diffusion curves in less than 1min. This method has been tested by measuring the self-diffusion coefficients D of various organic solvents and poly(dimethylsiloxane) samples with different molar masses. Diffusion coefficients were also measured for n-hexane absorbed at saturation in natural rubber with different cross-link densities. The results show a dependence on the concentration that is in good agreement with the theoretical prediction. Moreover, the stimulated-echo sequence was successfully used to measure the diffusion coefficient as a function of the evolution time in systems with restricted diffusion. This type of experiment proves the pore geometry and gives access to the surface-to-volume ratio. It was applied to measure the diffusion of water in sandstones and sheep Achilles tendon. Thanks to the strong static gradient G(0), all diffusion coefficients could be measured without having to account for relaxation during the pulse sequence.

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.

"Shim pulses" for NMR spectroscopy and imaging

A way to use adiabatic radiofrequency pulses and modulated magnetic-field gradient pulses, together constituting a "shim pulse," for NMR spectroscopy and imaging is demonstrated. These pulses capitalize on phase shifts derived from probe gradient coils to compensate for nonlinear intrinsic main magnetic field homogeneity for spectroscopy, as well as for deviations from linear gradients for imaging. This approach opens up the possibility of exploiting cheaper, less-than-perfect magnets and gradient coils for NMR applications.

Self-diffusion measurements with chemical shift resolution in inhomogeneous magnetic fields

A methodology for chemical shift resolved molecular self-diffusion measurements in time-independent static and radiofrequency field gradients is demonstrated. Diffusion encoding is provided by a stimulated echo sequence with additional z-storage that allows for a change of diffusion time without affecting the relaxation weighting. The signal is acquired stroboscopically between the pulses of a train of adiabatic double passages that induces a z-rotation counteracting the phase spread resulting from precession in the inhomogeneous static field, as demonstrated in recent approaches to the goal of high-resolution "ex situ" NMR. Simulations of the pulse sequence show that the acquired signal results from the desired coherence pathway. Successful demonstrations of the experiment were performed on a mixture of water and isopropanol.

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.

Hole-burning diffusion measurements in high magnetic field gradients

We describe methods for the measurement of translational diffusion in very large static magnetic field gradients by NMR. The techniques use a "hole-burning" sequence that, with the use of fringe field gradients of 42 T/m, can image diffusion along one dimension on a submicron scale. Two varieties of this method are demonstrated, including a particularly efficient mode called the "hole-comb," in which multiple diffusion times comprising an entire diffusive evolution can be measured within the span of a single detected slice. The advantages and disadvantages of these methods are discussed, as well as their potential for addressing non-Fickian diffusion, diffusion in restricted media, and spatially inhomogeneous diffusion.

BlochLib: a fast NMR C++ tool kit

Computational power, speed, and algorithmic complexity are increasing at a continuing rate. As a result, scientific simulations continue to investigate more and more complex systems. Nuclear magnetic resonance (NMR) is no exception. NMR theory and language is extremely well developed, that simulations have become a standard by which experiments are measured. Nowadays, complex computations can be performed on normal workstations and workstation clusters. Basic numerical operations have also become extremely optimized and new computer language paradigms have become implemented. Currently there exists no complete NMR tool kit which uses these newer techniques. This paper describes such a tool kit, BlochLib. BlochLib is designed to be the next generation of NMR simulation packages; however, the basic techniques implemented are applicable to almost any problem. BlochLib enables the user to simulate almost any NMR idea both experimental or theoretical in nature. Both classical and quantum mechanical techniques are included and demonstrated, as well as several powerful user interface tools. The total tool kit and documentation can be found at http://waugh.cchem.berkeley.edu/blochlib/.