Optimized angle selection for radial sampled NMR experiments

Sparse sampling offers tremendous potential for overcoming the time limitations imposed by traditional Cartesian sampling of indirectly detected dimensions of multidimensional NMR data. Unfortunately, several otherwise appealing implementations are accompanied by spectral artifacts that have the potential to contaminate the spectrum with false peak intensity. In radial sampling of linked time evolution periods, the artifacts are easily identified and removed from the spectrum if a sufficient set of radial sampling angles is employed. Robust implementation of the radial sampling approach therefore requires optimization of the set of radial sampling angles collected. Here we describe several methods for such optimization. The approaches described take advantage of various aspects of the general simultaneous multidimensional Fourier transform in the analysis of multidimensional NMR data. Radially sampled data are primarily contaminated by ridges extending from authentic peaks. Numerical methods are described that definitively identify artifactual intensity and the optimal set of sampling angles necessary to eliminate it under a variety of scenarios. The algorithms are tested with both simulated and experimentally obtained triple resonance data.     

SEnD NMR: Sensitivity Enhanced n-Dimensional NMR

Sparse sampling offers tremendous potential for overcoming the time limitations imposed by traditional Cartesian sampling of indirectly detected dimensions of multidimensional NMR data. However, in many instances sensitivity rather than time remains of foremost importance when collecting data on protein samples. Here we explore how to optimize the collection of radial sampled multidimensional NMR data to achieve maximal signal-to-noise. A method is presented that exploits a rigorous definition of the minimal set of radial sampling angles required to resolve all peaks of interest in combination with a fundamental statistical property of radial sampled data. The approach appears general and can achieve a substantial sensitivity advantage over Cartesian sampling for the same total data acquisition time. Termed Sensitivity Enhanced n-Dimensional or SEnD NMR, the method involves three basic steps. First, data collection is optimized using routines to determine a minimal set of radial sampling angles required to resolve frequencies in the radially sampled chemical shift evolution dimensions. Second, appropriate combinations of experimental parameters (transients and increments) are defined by simple statistical considerations in order to optimize signal-to-noise in single angle frequency domain spectra. Finally, the data is processed with a direct multidimensional Fourier transform and a statistical artifact and noise removal step is employed.     

Reduced aliasing artifacts using shaking projection k-space sampling trajectory

Radial imaging techniques, such as projection-reconstruction （PR）, are used in magnetic resonance imaging （MRI） for dynamic imaging, angiography, and short-T2 imaging. They are less sensitive to flow and motion artifacts, and support fast imaging with short echo times. However, aliasing and streaking artifacts are two main sources which degrade radial imaging quality. For a given fixed number of k-space projections, data distributions along radial and angular directions will influence the level of aliasing and streaking artifacts. Conventional radial k-space sampling trajectory introduces an aliasing artifact at the first principal ring of point spread function （PSF）. In this paper, a shaking projection （SP） k-space sampling trajectory was proposed to reduce aliasing artifacts in MR images. SP sampling trajectory shifts the projection alternately along the k-space center, which separates k-space data in the azimuthal direction. Simulations based on conventional and SP sampling trajectories were compared with the same number projections. A significant reduction of aliasing artifacts was observed using the SP sampling trajectory. These two trajectories were also compared with different sampling frequencies. ASP trajectory has the same aliasing character when using half sampling frequency （or half data） for reconstruction. SNR comparisons with different white noise levels show that these two trajectories have the same SNR character. In conclusion, the SP trajectory can reduce the aliasing artifact without decreasing SNR and also provide a way for undersampling recon- struction. Furthermore, this method can be applied to three-dimensional （3D） hybrid or spherical radial k-space sampling for a more efficient reduction of aliasing artifacts.     

Phasing arbitrarily sampled multidimensional NMR data

The recent re-introduction of the two-dimensional Fourier transformation (2D-FT) has allows for the transformation of arbitrarily sampled time domain signals. In this respect, radial sampling, where two incremented time dimensions (t(1) and t(2)) are sampled such that t(1)=taucosalpha and t(2)=tausinalpha, is especially appealing because of the relatively small leakage artifacts that occur upon Fourier transformation. Unfortunately radially sampled time domain data results in a fundamental artifact in the frequency domain manifested as a ridge of intensity extending through the peak positions perpendicular to +/- the radial sampling angle. Successful removal of the ridge artifacts using existing algorithms requires absorptive line shapes. Here we present two procedures for retrospective phase correction of arbitrarily sampled data.     

O-space with high resolution readouts outperforms radial imaging

PurposeWhile O-Space imaging is well known to accelerate image acquisition beyond traditional Cartesian sampling, its advantages compared to undersampled radial imaging, the linear trajectory most akin to O-Space imaging, have not been detailed. In addition, previous studies have focused on ultrafast imaging with very high acceleration factors and relatively low resolution. The purpose of this work is to directly compare O-Space and radial imaging in their potential to deliver highly undersampled images of high resolution and minimal artifacts, as needed for diagnostic applications. We report that the greatest advantages to O-Space imaging are observed with extended data acquisition readouts.Theory and methodsA sampling strategy that uses high resolution readouts is presented and applied to compare the potential of radial and O-Space sequences to generate high resolution images at high undersampling factors. Simulations and phantom studies were performed to investigate whether use of extended readout windows in O-Space imaging would increase k-space sampling and improve image quality, compared to radial imaging.ResultsExperimental O-Space images acquired with high resolution readouts show fewer artifacts and greater sharpness than radial imaging with equivalent scan parameters. Radial images taken with longer readouts show stronger undersampling artifacts, which can cause small or subtle image features to disappear. These features are preserved in a comparable O-Space image.ConclusionsHigh resolution O-Space imaging yields highly undersampled images of high resolution and minimal artifacts. The additional nonlinear gradient field improves image quality beyond conventional radial imaging.     

Two-dimensional Fourier transform of arbitrarily sampled NMR data sets

A new procedure for Fourier transform with respect to more than one time variable simultaneously is proposed for NMR data processing. In the case of two-dimensional transform the spectrum is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Therefore, it enables one to Fourier transform arbitrarily sampled time domain and thus allows for analysis of high dimensionality spectra acquired in a short time. The proposed method is not limited to radial sampling, it requires only to fulfill the Nyquist theorem considering two or more time domains at the same time. We show the application of new approach to the 3D HNCO spectrum acquired for protein sample with radial and spiral time domain sampling.     

Narrow peaks and high dimensionalities: Exploiting the advantages of random sampling

Level of artifacts in spectra obtained by Multidimensional Fourier Transform has been studied, considering randomly sampled signals of high dimensionality and long evolution times. It has been shown theoretically and experimentally, that this level is dependent on the number of time domain samples, but not on its relation to the number of points required in appropriate conventional experiment. Independence of the evolution time domain size (in the terms of both: dimensionality and evolution time reached), suggests that random sampling should be used rather to design new techniques with large time domain than to accelerate standard experiments. 5D HC(CC-TOCSY)CONH has been presented as the example of such approach. The feature of Multidimensional Fourier Transform, namely the possibility of calculating spectral values at arbitrary chosen frequency points, allowed easy examination of resulting spectrum. We present the example of such approach, referred to as Sparse Multidimensional Fourier Transform.     

Optical circular sampling system for translation and rotation invariant pattern recognition

A simple but effective rotation invariant pattern recognition method based on optical circular sampling of the input pattern is described. The object is decomposed by a set of concentric rings. The distribution of energy between those rings is independent of the orientation of the object and characterizes it sufficiently to allow its classification. A computer generated hologram formed of concentric diffraction grating rings of suitable spatial frequencies may perform the sampling in parallel. In combination with a lens, each ring is then focused to a given position on a CCD detector where the intensity distribution may be found. Translation invariance is added to the system by sampling the intensity of the Fourier transform of the input object in combination with a liquid crystal light valve. A phototypesetter is used to write the hologram whose quality is demonstrated by optical experiments.     

Rotating surface solitons

We introduce a novel type of surface waves that form at the edge of guiding structures consisting of several concentric rings. Such surface waves rotate steadily upon propagation and, in contrast with nonrotating waves, for high rotation frequencies they do not exhibit power thresholds for their existence. There exists an upper limit for the surface wave rotation frequency, which depends on the radius of the outer guiding ring and on its depth.     

Magnetoexciton in semiconductor concentric double rings

We investigate theoretically the magnetoexciton states in semiconductor concentric quantum double rings using the multi-band effective mass theory. We find that a perpendicular magnetic field can lead to oscillations in the exciton energy which appear as kinks in the magneto-photoluminescence (PL) spectra as the magnetic field increases. The spatial distribution of the exciton over the rings depends sensitively on the thicknesses of the inner and outer rings. The tunneling coupling between the inner and outer rings and the heavy-hole and light-hole mixing results in different anticrossing behaviors. Exciton can be converted into a spatially separated type-II exciton by tuning the thickness, the inner and/or outer ring radius and the magnetic field. We show that this type I–type II transition is reflected in the oscillator strength of the PL spectrum which will be the experimental signature that will provide us with information about the spatial distribution of the exciton.     

Magnetoexciton in semiconductor concentric double rings

We investigate theoretically the magnetoexciton states in semiconductor concentric quantum double rings using the multi-band effective mass theory. We find that a perpendicular magnetic field can lead to oscillations in the exciton energy which appear as kinks in the magneto-photoluminescence (PL) spectra as the magnetic field increases. The spatial distribution of the exciton over the rings depends sensitively on the thicknesses of the inner and outer rings. The tunneling coupling between the inner and outer rings and the heavy-hole and light-hole mixing results in different anticrossing behaviors. Exciton can be converted into a spatially separated type-II exciton by tuning the thickness, the inner and/or outer ring radius and the magnetic field. We show that this type I–type II transition is reflected in the oscillator strength of the PL spectrum which will be the experimental signature that will provide us with information about the spatial distribution of the exciton.     

Optimized 3D-NMR sampling for resonance assignment of partially unfolded proteins

Resonance assignment of NMR spectra of unstructured proteins is made difficult by severe overlap due to the lack of secondary structure. Fortunately, this drawback is partially counterbalanced by the narrow line-widths due to the internal flexibility. Alternate sampling schemes can be used to achieve better resolution in less experimental time. Deterministic schemes (such as radial sampling) suffer however from the presence of systematic artifacts. Random acquisition patterns can alleviate this problem by randomizing the artifacts. We show in this communication that quantitative well-resolved spectra can be obtained, provided that the data points are properly weighted before FT. These weights can be evaluated using the concept of Voronoi cells associated with the data points. The introduced artifacts do not affect the direct surrounding of the peaks and thus do not alter the amplitude and frequency of the signals. This procedure is illustrated on 60-residue viral protein, which lacks any persistent secondary structure and thus exhibits major signal overlap.     

Study on the radial vibration and acoustic field of an isotropic circular ring radiator

Based on the exact analytical theory, the radial vibration of an isotropic circular ring is studied and its electro-mechanical equivalent circuit is obtained. By means of the equivalent circuit model, the resonance frequency equation is derived; the relationship between the radial resonance frequency, the radial displacement amplitude magnification and the geometrical dimensions, the material property is analyzed. For comparison, numerical method is used to simulate the radial vibration of isotropic circular rings. The resonance frequency and the radial vibrational displacement distribution are obtained, and the radial radiation acoustic field of the circular ring in radial vibration is simulated. It is illustrated that the radial resonance frequencies from the analytical method and the numerical method are in good agreement when the height is much less than the radius. When the height becomes large relative to the radius, the frequency deviation from the two methods becomes large. The reason is that the exact analytical theory is limited to thin circular ring whose height must be much less than its radius.     

Cardiac magnetic resonance imaging using radial k-space sampling and self-calibrated partial parallel reconstruction

Radial sampling has been demonstrated to be potentially useful in cardiac magnetic resonance imaging because it is less susceptible to motion than Cartesian sampling. Nevertheless, its capability of imaging acceleration remains limited by undersampling-induced streaking artifacts. In this study, a self-calibrated reconstruction method was developed to suppress streaking artifacts for highly accelerated parallel radial acquisitions in cardiac magnetic resonance imaging. Two- (2D) and three-dimensional (3D) radial k-space data were collected from a phantom and healthy volunteers. Images reconstructed using the proposed method and the conventional regridding method were compared based on statistical analysis on a four-point scale imaging scoring. It was demonstrated that the proposed method can effectively remove undersampling streaking artifacts and significantly improve image quality (P<.05). With the use of the proposed method, image score (1–4, 1=poor, 2=good, 3=very good, 4=excellent) was improved from 2.14 to 3.34 with the use of an undersampling factor of 4 and from 1.09 to 2.5 with the use of an undersampling factor of 8. Our study demonstrates that the proposed reconstruction method is effective for highly accelerated cardiac imaging applications using parallel radial acquisitions without calibration data.     

Fracture of metallic rings during magnetic-pulse shock loading

Metallic rings made of aluminum and copper foils are studied after the action of a distributed radial magnetic-pulse load. Two loading approach modifications allowed us to substantially decrease the period of an applied sinusoidal load and to determine the time from load application to sample failure. A method is proposed to estimate the radial force on a metallic ring from coil turns. The profiles of radial pressure on the inner ring surface are measured, and the circumferential tensile stresses in ring fracture are determined. Microstructural studies of failed ring samples show that they underwent dynamic recrystallization. It is found that, as the operating load period shortens, the fraction of the ductile component in a fracture surface decreases and the samples undergo more brittle fracture.     

The effects of normal current density and the plasma spatial structuring in argon DBDs

This paper presents the results of theoretical studies of high-pressure dielectric barrier discharges (DBD) in argon. Two different DBDs at the megahertz and the kilohertz power frequency range were simulated. The effect of normal current density was obtained in the numerical model for both types of the discharge. The discharge of megahertz range was uniform over the radius. The increase in the discharge current is accompanied by increase in the discharge area. The discharge of kilohertz range is not uniform over the radius. The concentric ring formation was observed during calculations. The increase in the discharge current occurs due to increase in the number of rings and as a result in the discharge area. The developed 2D model is able to describe only the first stage of the filament formation – the formation of concentric plasma rings. The filament formation starts at the edge of the current channel and spreads to its centre. Both the effect of normal current density and the filaments formation are caused by the nonstationarity at the current channel boundary.     

Aharonov–Bohm effect in non-uniform crater-like quantum dot with double rim

We study electron energies in a double concentric quantum ring with anisotropy in the rims heights in the presence of the external magnetic field applied along the symmetry axis. To this end, we consider a model in which the thickness grows linearly from the axis up to the inner rim with a slope different from one between the inner and the outer rims. The anisotropy in the rims heights originated by the presence in the structure of various valleys we simulate by periodic dependence of the slope on the radial direction. We show that the wave functions of the electron confined in such structure can be found analytically if the slopes in all radial directions are the same, and by using a simple exact diagonalization procedure otherwise. The behavior of the electron energies as functions of the magnetic field, rings radii and rims heights, as well as the number of the valleys and their depths is consistently described with our formalism. The entanglement of the states with different radial and orbital quantum numbers, the period and the amplitude of the Aharonov–Bohm oscillations are very sensible to any variations of the rims heights.     

Influence of lateral electric field on intraband optical absorption in concentric double quantum rings

The influence of lateral electric field on one-electron states and intraband absorption in two-dimensional concentric double quantum rings is investigated. The confining potential of the rings is modeled as a double harmonic central potential. Using the exact diagonalization technique, we calculate the dependence of the electron energy spectrum as a function of the electric field strength as well as the inner ring radius. Also, different values of confinement strength are considered. Selection rule is obtained for intraband transitions, caused by the direction of incident light polarization. The intraband absorption coefficient is calculated for different values of electric field strength, inner ring radius, confinement strength and incident light polarization direction. The combined influence of electric field strength and change of confining strength show that while the increment of the first one leads only to blueshift of absorption spectrum, the augment of the second one makes the redshift. In addition, both blueshift and redshift of the spectrum have been obtained with the enlargement of inner ring radius. Finally, we show that the absorption spectrum undergoes redshift by changing the polarization of incident light from x- to y-axis.     

Semiconductor concentric double rings in a magnetic field

We report a theoretical study on the magnetooptical properties of recently synthesized concentric quantum double rings, as a function of the inner-outer ring coupling. The transition from a single to a double ring, as it is reflected in the the changes of the Aharonov-Bohm oscillation periods of the energy levels, is shown. It is found that, even when the system can be described as a single quantum ring with a small cleft, the electron energy levels show two different Aharonov-Bohm oscillation periods, which indicate that the carriers are localized in either the inner or the outer ring. For most distances between the rings, the electron and hole energy levels show almost identical Aharonov-Bohm oscillation periods. However, there is a short distances range in which they do not localize in the same ring, showing very different periods. In this region, the exciton ground state becomes dark.     

Effects of Applied DC Radial Electric Fields on Particle Transport in a Bumpy Torus Plasma

The toroidal ring of plasma contained in the NASA Lewis Bumpy Torus may be biased to positive or negative potentials approaching 50 kilovolts by applying DC voltage to twelve or fewer midplane electrode rings. The electric fields, which are responsible for raising the ions to high energies by ExB/B2 drift, then point radially outward or inward. The profiles of plasma number density are observed to be flat or triangular across the plasma diameter. The absence of a second derivative in the density profile, combined with the flat electron temperature profiles which are observed, implies that the radial transport processes are not diffusional in nature and are dominated by the strong radial electric fields which are applied to the plasma. Evidence from a paired comparison test shows that the plasma number density and confinement time can increase more than an order of magnitude if the electric field acting along the minor radius of the toroidal plasma points inward, relative to the values observed when the electric field points radially outward. Some characteristic data taken under nonoptimized conditions yielded the highest plasma number density (2.7 × 1011/cc on axis) and the longest particle containment times (1.9 milliseconds) observed so far in this experiment.