Achievement of a 920-MHz high resolution NMR

We have developed a 920-MHz NMR system and performed the proton NMR measurement of H(2)O and ethylbenzene using the superconducting magnet operating at 21.6 T (920 MHz for proton), which is the highest field produced by a superconducting NMR magnet in the persistent mode. From the NMR measurements, it is verified that both homogeneity and stability of the magnet have a specification sufficient for a high resolution NMR.     

An Extension of Alias Sampling Method for Parametrized Probability Distributions

An extension of the alias sampling technique for distribution functions depending on a number of parameters was developed. It takes advantage of modern computer architectures with large amounts of cheap memory, by using discrete representations of probability distribution functions. The sampling is done by fast interpolation techniques involving only elementary logical and arithmetical operations, allowing one to keep a higher degree of accuracy as the grids spacing is controlled by the user. By this method it is possible to obtain the value of interest by direct interpolation between the sampled values obtained with the same set of random numbers for the grid values of the parameters adjacent to the values of interest. Sampling tests carried for the case of Molière electron multi-scatter angle distribution show that this method can be successfully used in Monte Carlo codes for sampling complex probability distributions.     

NMR Relaxation and Diffusion Measurements on Iron(III)-Doped Kaolin Clay

Kaolin clay samples were mixed with various amounts of Fe₂O₃ powder. The influence of this magnetic impurity on NMR relaxation and diffusion measurements on the water in this porous material was investigated. The NMR relaxation measurements showed a nearly mono-exponential decay, leading to the conclusion that the pore size distribution of the clay samples is either narrow and/or that the pores are interconnected very well. Both the longitudinal and the transverse relaxation rate depend linearly on the concentration of the Fe₂O₃ impurity. The NMR diffusion measurements revealed that the Fe₂O₃ causes internal magnetic field gradients that largely exceed the maximum external gradient that could be applied by our NMR apparatus (0.3 T/m). Additional SQUID measurements yielded the magnetization and magnetic susceptibility of the samples at the magnetic field strength used in the NMR measurements (0.8 T). A theoretical estimate of the internal magnetic field gradients leads to the conclusion that the water in the porous clay samples cannot be described by the commonly observed motional averaging regime. Probably an intermediate or a localization regime is induced by the large internal gradients, which are estimated to be on the order of 1 to 10 T/m in the pore volume and may exceed 1000 T/m at the pore surface.     

An Incompressible Three-Dimensional Multiphase Particle-in-Cell Model for Dense Particle Flows

A three-dimensional, incompressible, multiphase particle-in-cell method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to an Eulerian grid and then mapping back computed stress tensors to particle positions. A subgrid particle, normal stress model for discrete particles which is robust and eliminates the need for an implicit calculation of the particle normal stress on the grid is presented. Interpolation operators and their properties are defined which provide compact support, are conservative, and provide fast solution for a large particle population. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. Particles are implicitly coupled to the fluid phase, and the fluid momentum and pressure equations are implicitly solved, which gives a robust solution.     

Changes in Porcine Muscle Water Characteristics during Growth—An in Vitro Low-Field NMR Relaxation Study

This study investigates the effects of developmental stage and muscle type on the mobility and distribution of water within skeletal muscles, using low-field ¹H-NMR transverse relaxation measurements in vitro on four different porcine muscles (M. longissimus dorsi, M. semitendinosus, M. biceps femoris, M. vastus intermedius) from a total of 48 pigs slaughtered at various weight classes between 25 kg and 150 kg. Principal component analysis (PCA) revealed effects of both slaughter weight and muscle type on the transverse relaxation decay. Independent of developmental stage and muscle type, distributed exponential analysis of the NMR T₂ relaxation data imparted the existence of three distinct water populations, T_2b, T₂₁, and T₂₂, with relaxation times of approximately 1–10, 45–120, and 200–500 ms, respectively. The most profound change during muscle growth was a shift toward faster relaxation in the intermediate time constant, T₂₁. It decreased by approx. 24% in all four muscle types during the period from 25 to 150 kg live weight. Determination of dry matter, fat, and protein content in the muscles showed that the changes in relaxation time of the intermediate time constant, T₂₁, during growth should be ascribed mainly to a change in protein content, as the protein content explained 77% of the variation in the T₂₁ time constant. Partial least squares (PLS) regression revealed validated correlations in the region of 0.58 to 0.77 between NMR transverse relaxation data and muscle development for all the four muscle types, which indicates that NMR relaxation measurements may be used in the prediction of muscle developmental stage.     

An Error Indicator Monitor Function for an r-Adaptive Finite-Element Method

An r-adaptive finite-element method based on moving-mesh partial differential equations (PDEs) and an error indicator is presented. The error indicator is obtained by applying a technique developed by Bank and Weiser to elliptic equations which result in this case from temporal discretization of the underlying physical PDEs on moving meshes. The construction of the monitor function based on the error indicator is discussed. Numerical results obtained with the current method and the commonly used method based on solution gradients are presented and analyzed for several examples.     

An Efficient NMR Experiment for Analyzing Sugar-Puckering in Unlabeled DNA: Application to the 26-kDa Dead Ringer–DNA Complex

We present a new NMR experiment for estimating the type and degree of sugar-puckering in high-molecular-weight unlabeled DNA molecules. The experiment consists of a NOESY sequence preceded by a constant-time scalar coupling period. Two subexperiments are compared, each differing in the amount of time the (3)J(H3'H2') and (3)J(H3'H2") couplings are active on the H3' magnetization. The resultant data are easy to analyze, since a comparison of the signal intensities of any resolved NOE cross peak originating from H3' atoms of the duplex can be used to estimate the sum of the (3)J(H3'H2') and (3)J(H3'H2") couplings and thus the puckering type of the deoxyribose ring. Isotope filters to eliminate signals of the (13)C-labeled component in the F1-dimension are implemented, facilitating analyses of high-molecular-weight protein-DNA complexes containing (13)C-labeled protein and unlabeled DNA. The utility of the experiment is demonstrated on the 26-kDa Dead Ringer protein-DNA complex and reveals that the DNA uniformly adopts the S-type configuration when bound to protein.     

H NMR Characterization of the Product from Single Solid-Phase Resin Beads Using Capillary NMR Flow Probes

A capillary NMR flow probe was designed to generate high-resolution ¹H NMR spectra at 600 MHz from the cleaved product of individual 160-μm Tentagel combinatorial chemistry beads. By injecting a dissolved sample sandwiched between an immiscible, perfluorinated organic liquid directly into the probe, NMR spectra of the product cleaved from single beads were acquired in just 1 h of spectrometer time without diffusional dilution. Sample handling efficiency on the single bead scale was comparable to that obtained with a bulk sample. Using the relative intensity of the DMSO-d₅H versus the analyte signals in a fully relaxed CPMG spectrum, the amount of product cleaved from a single bead was determined to be 540±170 pmol in one of the samples. Following the NMR data collection, the samples were examined with electrospray ionization mass spectrometry to provide additional structural information. By coupling with microliter-volume fluidic capabilities, the capillary flow probe described here will enable multidimensional characterization of single solid-phase resin products in an online manner.     

One micrometer resolution NMR microscopy

We obtained a magnetic resonance image of 1 microm resolution and 75 microm(3) voxel volume for a phantom filled with hydrocarbon oil within an hour at 14.1 T. For this work, a specially designed probe with a high sensitivity RF coil and gradient coils generating over 1000 G/cm was built. The optimal pulse sequence was analyzed in consideration of the bandwidth, diffusion coefficients, and T(1) and T(2) relaxations of the medium. The system was applied to the in vivo imaging of a geranium leaf stem to get the images of 2 microm resolution and 200 microm(3) voxel volume.     

Longitudinally detected ESR magnetometer for wide-range measurements of low fields

A new magnetometer utilizing a longitudinally detected ESR (LODESR) method was developed. The probe head of the LODESR magnetometer is equipped with a single-turn coil (8 mm in diameter) which has a very wide bandwidth because the reactance of the coil is always smaller than the resistance of the transmission line (50 ohm) at frequencies less than 700 MHz. Thus, an absolute magnetic field could be measured over a wide range (2 to 9 mT) using this magnetometer without changing the probe head.     

A rotational approach to localized SPAMM 1-1 tagging

Magnetic resonance tagging usually relies on controlling the phase dispersion of the transverse magnetization component. Phase dispersion is, however, affected by the inherent phase of selective excitation pulses, thus limiting their combination with tagging sequences to the application of refocusable pulses, as in the localized spatial modulation of magnetization (L-SPAMM) technique. In this study, we examine the effect of selective excitation pulses on a L-SPAMM 1-1 sequence, showing that in the case of two identical pulses the phase component is canceled out, and thus preemphasis and refocus gradients are not needed, allowing us to take advantage of a constant gradient throughout the tagging sequence, and also that one might choose nonrefocusable maximum and minimum phase pulses.     

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.     

Probe--sample coupling in the magnetic resonance force microscope

The magnetic resonance force microscope (MRFM) provides a route to achieving scanned probe magnetic resonance imaging with extremely high spatial resolution. Achieving this capability will require understanding the force exerted on a microscopic magnetic probe by a spatially extended sample over which the probe is scanned. Here we present a detailed analysis of this interaction between probe and sample. We focus on understanding the situation where the micromagnet mounted on the mechanical resonator generates a very inhomogeneous magnetic field and is scanned over a sample with at least one spatial dimension much larger than that of the micromagnet. This situation differs quite significantly from the conditions under which most MRFM experiments have been carried out where the sample is mounted on the mechanical resonator and placed in a rather weak magnetic field gradient. In addition to the concept of a sensitive slice (the spatial region where the magnetic resonance condition is met) it is valuable to map the forces exerted on the probe by spins at various locations; this leads to the concept of the force slice (the region in which spins exert force on the resonator). Results of this analysis, obtained both analytically and numerically, will be qualitatively compared with an initial experimental finding from an EPR-MRFM experiment carried out on DPPH at 4 K.     

Design and implementation of a protection system for NMR spectrometers

We have implemented a scheme, SPECMON, for monitoring various parameters of a spectrometer, such as nitrogen pressure and sample temperature, and taking corrective action. The scheme is based on considerations of protection management which are of general application. Evaluation of the spectrometer state is incorporated in macros of the application software (VNMR) and is therefore very flexible. In contrast, corrective action is limited to the single one which is deemed fully safe: complete shutdown of the spectrometer and logging. Shutdown is implemented by a minor hardware modification of the spectrometer: the introduction of a second input to a relay already present for protection of the spectrometer power supply. Monitoring is handled by the host computer, and the shutdown command is transmitted via control lines of its series port, independent of the standard connection between the host computer and the NMR system console. The monitoring system (software and hardware) is unobtrusive in normal conditions, and it can be tested without affecting the operation of the spectrometer.     

Improved Lanczos algorithms for blackbox MRS data quantitation

Magnetic resonance spectroscopy (MRS) has been shown to be a potentially important medical diagnostic tool. The success of MRS depends on the quantitative data analysis, i.e., the interpretation of the signal in terms of relevant physical parameters, such as frequencies, decay constants, and amplitudes. A variety of time-domain algorithms to extract parameters have been developed. On the one hand, there are so-called blackbox methods. Minimal user interaction and limited incorporation of prior knowledge are inherent to this type of method. On the other hand, interactive methods exist that are iterative, require user involvement, and allow inclusion of prior knowledge. We focus on blackbox methods. The computationally most intensive part of these blackbox methods is the computation of the singular value decomposition (SVD) of a Hankel matrix. Our goal is to reduce the needed computational time without affecting the accuracy of the parameters of interest. To this end, algorithms based on the Lanczos method are suitable because the main computation at each step, a matrix-vector product, can be efficiently performed by means of the fast Fourier transform exploiting the structure of the involved matrix. We compare the performance in terms of accuracy and efficiency of four algorithms: the classical SVD algorithm based on the QR decomposition, the Lanczos algorithm, the Lanczos algorithm with partial reorthogonalization, and the implicitly restarted Lanczos algorithm. Extensive simulation studies show that the latter two algorithms perform best.     

An Efficient Finite Element Method for Computing Spectra of Photonic and Acoustic Band-Gap Materials: I. Scalar Case

The paper describes an efficient finite element method for computing spectra of photonic and acoustic band-gap materials. In the photonic case only the scalar models are treated. The full vector model will be considered in the next publication.     

GAMMA simulations of stray field responses: slice thickness and pulse calibration

A stray field (STRAFI) module has been added to the GAMMA magnetic resonance simulation platform in order to facilitate computational investigations of NMR experiments in large static field gradients that are on the order of 50 T/m. The package has been used to examine system response during echo trains generated by the application of shaped pulses. The associated echo amplitude maxima and effective slice thickness are presented. A new accurate method for STRAFI pulse calibration based on relative echo amplitudes is proposed.     

Separation of intra- and extramyocellular lipid signals in proton MR spectra by determination of their magnetic field distribution

In skeletal musculature intramyocellular (IMCL) and extramyocellular lipids (EMCL) are stored in compartments of different geometry and experience different magnetic field strengths due to geometrical susceptibility effects. The effect is strong enough to---at least partly---separate IMCL and EMCL contributions in (1)H MR spectroscopy, despite IMCL and EMCL consisting of the same substances. The assessment of intramyocellular lipid stores in skeletal musculature by (1)H MR spectroscopy plays an important role for studying physiological and pathological aspects of lipid metabolism. Therefore, a method using mathematical tools of Fourier analysis is developed to obtain the magnetic field distribution (MFD) from the measured spectra by deconvolution. A reference lipid spectrum is required which was recorded in tibial yellow bone marrow. It is shown that the separation of IMCL contributions can be performed more precisely---compared to other methods---based on the MFD. Examples of deconvolution in model systems elucidate the principle. Applications of the proposed approach on in vivo examinations in m. soleus and m. tibialis anterior are presented. Fitting the IMCL part of the MFD by a Gaussian lineshape with a linewidth kept fixed with respect to the linewidth of creatine and with the assumption of a smooth but not necessarily symmetrical shape for the EMCL part, the only free fit parameter, the amplitude of the IMCL part, is definite and subtraction leads to the EMCL part in the MFD. This procedure is especially justified for the soleus muscle showing a severely asymmetrical distribution which might lead to a marked overestimation of IMCL using common line fitting procedures.     

Coherent Raman and Infrared Studies of Sulfur Trioxide

High-resolution (0.001 cm⁻¹) coherent anti-Stokes Raman scattering (CARS) was used to observe the Q-branch structure of the IR-inactive ν₁ symmetric stretching mode of ³²S¹⁶O₃ and its various ¹⁸O isotopomers. The ν₁ spectrum of ³²S¹⁶O₃ reveals two intense Q-branches in the region 1065–1067 cm⁻¹, with surprisingly complex vibrational–rotational structure not resolved in earlier studies. Efforts to simulate this with a simple Fermi-resonance model involving ν₁ and 2ν₄ states do not reproduce the spectral detail, nor do they yield reasonable spectroscopic parameters. A more subtle combination of Fermi resonance and indirect Coriolis interactions with nearby states, 2ν₄(1=0, ±2), ν₂+ν₄(1=±1), 2ν₂(1=0), is suspected and a determination of the location of these coupled states by high-resolution infrared measurements is under way. At medium resolution (0.125 cm⁻¹), the infrared spectra reveal Q-branch features from which approximate band origins are estimated for the ν₂, ν₃, and ν₄ fundamental modes of ³²S¹⁸O₃, ³²S¹⁸O₂¹⁶O, and ³²S¹⁸O¹⁶O₂. These and literature data for ³²S¹⁶O₃ are used to calculate force constants for SO₃ and a comparison is made with similar values for SO₂ and SO. The frequencies and force constants are in excellent agreement with those obtained by Martin in a recent ab initio calculation.