Radial 3D Research Articles

Scattering for the radial 3D cubic focusing inhomogeneous nonlinear Schrödinger equation

The purpose of this work is to study the 3D focusing inhomogeneous nonlinear Schrödinger equationiut+Δu+|x|−b|u|2u=0, where 0<b<1/2. Let Q be the ground state solution of −Q+ΔQ+|x|−b|Q|2Q=0 and sc=(1+b)/2. We show that if the radial initial data u0 belongs to H1(R3) and satisfies E(u0)scM(u0)1−sc<E(Q)scM(Q)1−sc and ‖∇u0‖L2sc‖u0‖L21−sc<‖∇Q‖L2sc‖Q‖L21−sc, then the corresponding solution is global and scatters in H1(R3). Our proof is based in the ideas introduced by Kenig–Merle [1] in their study of the energy-critical NLS and Holmer–Roudenko [2] for the radial 3D cubic NLS.

WSR-88D Radar Data Processing at NCEP

Abstract Real-time access to level II radar data became available in May 2005 at the National Centers for Environmental Prediction (NCEP) Central Operations (NCO). Using these real-time data in operational data assimilation requires the data be processed reliably and efficiently through rigorous data quality controls. To this end, advanced radar data quality control techniques developed at the National Severe Storms Laboratory (NSSL) are combined into a comprehensive radar data processing system at NCEP. Techniques designed to create a high-resolution reflectivity mosaic developed at the NSSL are also adopted and installed within the NCEP radar data processing system to generate hourly 3D reflectivity mosaics and 2D-derived products. The processed radar radial velocity and 3D reflectivity mosaics are ingested into NCEP’s data assimilation systems to improve operational numerical weather predictions. The 3D reflectivity mosaics and 2D-derived products are also used for verification of high-resolution numerical weather prediction. The NCEP radar data processing system is described.

THE STELLAR DENSITY PROFILE OF THE DISTANT GALACTIC HALO

ABSTRACT We use extensive gravity-sensitive DDO 51 photometry over 5100 square degrees, combined with Sloan Digital Sky Survey broadband photometry, to select a catalog of ∼4000 giant stars covering a large fraction of the high Galactic latitude sky and reaching out to ∼80 kpc in the Galactic halo. This sample of bright and unbiased tracers enables us to measure the radial profile and 3D structure of the stellar halo to large distances, which had previously only been measured with sparse tracers or small samples. Using population synthesis models to reproduce the observed giant star luminosity function, we find that the halo maintains a r − 3.5 profile from 30 to 80 kpc with no signs of a truncation or sharp break over this range. The radial profile measurement is largely insensitive to individual halo substructure components, but we find that attempting to measure the shape of the halo is overwhelmed by the Sagittarius stream such that no elliposidal shape is a satisfactory description in this region. These measurements allow us to begin placing the Milky Way in context with the growing sample of external galaxies where similar halo profile measurements are available, with the goal of further linking the properties of stellar halos to the accretion histories that formed them.

TESTING THE EFFECTS OF EXPANSION ON SOLAR WIND TURBULENCE

ABSTRACT We present a multi-spacecraft approach to test the predictions of recent studies on the effect of solar wind expansion on the radial spectral, variance, and local 3D anisotropies of the turbulence. We found that on small scales (5000–10,000 km) the power levels of the B-trace structure functions do not depend on the sampling direction with respect to the radial suggesting that on this scale the effect of expansion is small possibly due to fast turbulent timescales. On larger scales (110–135 R E ), the fluctuations of the radial magnetic field component are reduced by ∼20% compared to the transverse (perpendicular to radial) ones, which could be due to expansion confining the fluctuations into the plane perpendicular to radial. For the local 3D spectral anisotropy, the B-trace structure functions showed dependence on the sampling direction with respect to radial. The anisotropy in the perpendicular plane is reduced when the increments are taken perpendicular with respect to radial, which could be an effect of expansion.

Free-breathing dynamic liver examination using a radial 3D T1-weighted gradient echo sequence with moderate undersampling for patients with limited breath-holding capacity

PurposeTo compare free-breathing radial VIBE with moderate undersampling (us-radial-VIBE) with a standard breathhold T1-weighted volumetric interpolated sequence (3D GRE VIBE) in patients unable to suspend respiration during dynamic liver examination. Material and methods23 consecutive patients underwent dynamic liver MR examination using the free-breathing us-radial-VIBE sequence as part of their oncologic follow-up. All patients were eligible for the free-breathing protocol due to severe respiratory artifacts at the planning or precontrast sequences. The us-radial-VIBE acquisitions were compared to the patientś last staging liver MRI including a standard breathhold 3D GRE VIBE.For an objective image evaluation, signal intensity (SI), image noise (IN), signal-to-noise ratio (SNR) and contrast-enhancement ratio (CER) were compared. Representative image quality parameters, including typical artifacts were independently, retrospectively and blindly scored by four readers. ResultsUs-radial-VIBE had significant lower SNR (p<0.0001) and higher IN (p<0.0001), whereas SI did not differ (p=0.62). Temporal resolution assessed with CER in the arterial phase showed higher values for us-radial-VIBE (p=0.028). Subjective image quality parameters received generally slightly higher scores for 3D GRE VIBE. In a smaller subgroup comprising patients with severe respiratory artifacts also at reference breathhold 3D GRE VIBE examination, us-radial-VIBE showed significantly higher image quality scores. Furthermore, there were generally more severe respiratory artifacts in 3D GRE VIBE, whereas streaking was characteristic in almost all us-radial-VIBE acquisitions but did not affect diagnostic validity. ConclusionFree-breathing dynamic liver imaging using us-radial-VIBE delivers accurate temporal resolution, low motion artifact susceptibility and good image quality and represents a promising alternative in patients unable to suspend respiration.

Time Efficient 3D Radial UTE Sampling with Fully Automatic Delay Compensation on a Clinical 3T MR Scanner

This work’s aim was to minimize the acquisition time of a radial 3D ultra-short echo-time (UTE) sequence and to provide fully automated, gradient delay compensated, and therefore artifact free, reconstruction. The radial 3D UTE sequence (echo time 60 μs) was implemented as single echo acquisition with center-out readouts and improved time efficient spoiling on a clinical 3T scanner without hardware modifications. To assess the sequence parameter dependent gradient delays each acquisition contained a quick calibration scan and utilized the phase of the readouts to detect the actual k-space center. This calibration scan does not require any user interaction. To evaluate the robustness of this automatic delay estimation phantom experiments were performed and 19 in vivo imaging data of the head, tibial cortical bone, feet and lung were acquired from 6 volunteers. As clinical application of this fast 3D UTE acquisition single breath-hold lung imaging is demonstrated. The proposed sequence allowed very short repetition times (TR~1ms), thus reducing total acquisition time. The proposed, fully automated k-phase based gradient delay calibration resulted in accurate delay estimations (difference to manually determined optimal delay −0.13 ± 0.45 μs) and allowed unsupervised reconstruction of high quality images for both phantom and in vivo data. The employed fast spoiling scheme efficiently suppressed artifacts caused by incorrectly refocused echoes. The sequence proved to be quite insensitive to motion, flow and susceptibility artifacts and provides oversampling protection against aliasing foldovers in all directions. Due to the short TR, acquisition times are attractive for a wide range of clinical applications. For short T2* mapping this sequence provides free choice of the second TE, usually within less scan time as a comparable dual echo UTE sequence.

Numerical Simulation and Optimization of Enhanced Oil Recovery by the In Situ Generated CO2Huff-n-Puff Process with Compound Surfactant

This paper presents the numerical investigation and optimization of the operating parameters of the in situ generated CO2Huff-n-Puff method with compound surfactant on the performance of enhanced oil recovery. First, we conducted experiments of in situ generated CO2and surfactant flooding. Next, we constructed a single-well radial 3D numerical model using a thermal recovery chemical flooding simulator to simulate the process of CO2Huff-n-Puff. The activation energy and reaction enthalpy were calculated based on the reaction kinetics and thermodynamic models. The interpolation parameters were determined through history matching a series of surfactant core flooding results with the simulation model. The effect of compound surfactant on the Huff-n-Puff CO2process was demonstrated via a series of sensitivity studies to quantify the effects of a number of operation parameters including the injection volume and mole concentration of the reagent, the injection rate, the well shut-in time, and the oil withdrawal rate. Based on the daily production rate during the period of Huff-n-Puff, a desirable agreement was shown between the field applications and simulated results.

Scattering for the radial 3D cubic wave equation

Consider the Cauchy problem for the radial cubic wave equation in 1+3 dimensions with either the focusing or defocusing sign. This problem is critical in $\dot{H}^{\frac{1}{2}} \times \dot{H}^{-\frac{1}{2}}$ and subcritical with respect to the conserved energy. Here we prove that if the critical norm of a solution remains bounded on the maximal time-interval of existence, then the solution must in fact be global-in-time and scatter to free waves as $t \to \pm \infty$.

MR-PET evaluation of 1-month post-ablation therapy for hepatocellular carcinoma: preliminary observations.

The purpose of the study was to evaluate the feasibility and protocol optimization of whole-body hybrid MR-PET system performed 1-month after post-locoregional thermoablative procedures for hepatocellular carcinomas (HCCs). Eight patients (6 men and 2 women; mean age, 56.6 ± 5.5 years) with 9 ablated HCCs constituted our study population. Three readers interpreted the studies to determine the presence or absence of residual malignancy. Two readers independently assessed the fused MR-PET images to compare registration accuracy of two types of T2-weighted (triggered T2 half-Fourier acquisition single-shot turbo spin-echo and turbo spin-echo) and T1-weighted [Cartesian and radial 3D gradient echo (GRE)]. Image quality evaluation of both 3D-GRE T1-weighted sequences was evaluated. Kappa statistics were used to measure inter-observer agreement. Non-parametric Kruskal-Wallis and Wilcoxon signed-rank tests were used for qualitative data analysis. Definite residual tumor was observed in 3/9 ablations; two were PET positive. All residual tumors were isovascular on MRI. Radial 3D-GRE demonstrated significantly superior MR-PET subjective co-registration in comparison with the remaining sequences and showed a non-significant trend toward higher image quality scores than Cartesian GRE. Whole-body hybrid MR-PET is feasible as a part of 1-month follow-up post-locoregional thermoablative treatment for HCC. Radial 3D-GRE offers improved co-registration with PET data, with overall good image quality.

Simple proposal for radial 3D needlets

We present here a simple construction of a wavelet system for the three-dimensional ball, which we label \emph{Radial 3D Needlets}. The construction envisages a data collection environment where an observer located at the centre of the ball is surrounded by concentric spheres with the same pixelization at different radial distances, for any given resolution. The system is then obtained by weighting the projector operator built on the corresponding set of eigenfunctions, and performing a discretization step which turns out to be computationally very convenient. The resulting wavelets can be shown to have very good localization properties in the real and harmonic domain; their implementation is computationally very convenient, and they allow for exact reconstruction as they form a tight frame systems. Our theoretical results are supported by an extensive numerical analysis.

An approximate analytical model for temperature and power distribution in high-power Yb-doped double-clad fiber lasers

An analytical power model based on the rate equations of a high-power Yb-doped double-clad fiber laser is presented. Although it considers combiner and splices losses for the first time, the maximum and mean relative errors are less than 2.2% and 3.04% when compared with numerical and experimental results, respectively. Furthermore, an analytical temperature model based on thermal conduction equation has been reported. For the first time, the radial-dependent distribution of the heat density generated inside the fiber core is considered. Radial and longitudinal 3D distributions for temperature are presented. The results show a big difference (can reach 25%) when compared with conventional models, which consider a uniform radial distribution for heat density. In contrast, the mean relative error related to our model is less than 4.7% when compared with experimental results, whereas it reaches 9.3% in the conventional one.

Radial 3D-Needlets on the Unit Ball

AbstractWe present a simple construction of spherical wavelets for the unit ball, which we label Radial 3D Needlets. We envisage an experimental framework where data are collected on concentric spheres with the same pixelization at different radial distances from the origin. The unit ball is hence viewed as a tensor product of the unit interval with the unit sphere: a set of eigenfunctions is therefore defined on the corresponding Laplacian operator. Wavelets are then constructed by a smooth convolution of the projectors defined by these eigenfunctions. Localization properties may be rigorously shown to hold in the real and harmonic domain, and an exact reconstruction formula holds; the system allows a very convenient computational implementation.

Associations between tumor vascularization assessed by in vivo DCE‐MRI and the presence of disseminated tumor cells in bone marrow in breast cancer patients at the time of diagnosis

To explore possible associations between in vivo pharmacokinetic dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) parameters and the presence of disseminated tumor cells (DTCs) in bone marrow in breast cancer patients at the time of diagnosis. Thirty-seven women with breast cancer (stage T2-4N0-1M0) were included. Patients were classified as DTC+ if one or more DTCs were detected by immunocytochemistry. DCE-MRI was acquired with a radial 3D T1 -weighted spoiled gradient echo sequence with k-space weighted image contrast. K(trans), kep, and ve were calculated using the extended Tofts model and a population-derived arterial input function. The nonparametric Mann-Whitney U-test was used to compare the histogram distributions of the pharmacokinetic parameters for the DTC+ and the DTC- patients. DTCs were detected in 7 of the 37 patients (19%). In DTC+ patients, the distribution of tumor K(trans) and kep were significantly (P < 0.01) more shifted towards lower values than in DTC- patients. An association between vascular dependent pharmacokinetic DCE-MRI parameters and the presence of DTCs were found. Compared to DTC- patients, DTC+ patients had poorer perfusion and permeability, indicative of hypoxia. Thus, pharmacokinetic parameters might be surrogate biomarkers of metastatic potential and future relapse.

Left Ventricular Strain Reduction Is Not Confined to the Noncompacted Segments in Noncompaction Cardiomyopathy–Insights from the Three‐Dimensional Speckle Tracking Echocardiographic MAGYAR‐Path Study

Noncompaction cardiomyopathy (NCCM) is a new clinical entity characterized by prominent trabecular meshwork and deep intertrabecular recesses communicating with the left ventricular (LV) cavity due to arrest of the normal embryogenesis of the endomyocardium. The aim of the present study was to evaluate different contributions of noncompacted and compacted LV segments to the global LV dysfunction by three-dimensional (3D) speckle tracking echocardiography (3DSTE)-derived strain parameters in NCCM. The present study comprised 9 patients with typical features of NCCM. Due to the limited image quality, one patient was excluded from the evaluations. Finally, 128 segments of 8 NCCM patients were assessed. Their results were compared to 176 segments of 11 healthy volunteers. Complete two-dimensional Doppler echocardiography extended with 3DSTE has been performed in all cases. Fifty-five of 128 LV segments (43%) proved to be noncompacted in NCCM patients. All strain parameters of segments of NCCM patients were significantly lower as compared to segments of controls. Only radial strain (6.99±7.36% vs. 12.58±12.78% vs. 25.24±11.76%, P<0.001 and P<0.05, respectively) and 3D strain (7.79±7.59% vs. 14.67±14.04% vs. 27.78±12.57%, P<0.001 and P<0.05, respectively) showed further reduction in noncompacted segments as compared to compacted segments. Left ventricular strain reduction is not confined to the nocompacted segments in NCCM. Radial and 3D strain parameters show further reduction in noncompacted segments compared to compacted segments.

Accuracy of 3D Virtual Planning of Corrective Osteotomies of the Distal Radius

Corrective osteotomies of the distal radius for symptomatic malunion are time-tested procedures that rely on accurate corrections. Patients with combined intra- and extra-articular malunions present a challenging deformity. Virtual planning and patient-specific instruments (PSIs) to transfer the planning into the operating room have been used both to simplify the surgery and to make it more accurate. This report focuses on the clinically achieved accuracy in four patients treated between 2008 and 2012 with virtual planning and PSIs for a combined intra- and extraarticular malunion of the distal radius. The accuracy of the correction is quantified by comparing the virtual three-dimensional (3D) planning model with the postoperative 3D bone model. For the extraarticular malunion the 3D volar tilt, 3D radial inclination and 3D ulnar variance are measured. The volar tilt is undercorrected in all cases with an average of -6 ± 6°. The average difference between the postoperative and planned 3D radial inclination was -1 ± 5°. The average difference between the postoperative and planned 3D ulnar variances is 0 ± 1 mm. For the evaluation of the intraarticular malunion, both the arc method of measurement and distance map measurement are used. The average postoperative maximum gap is 2.1 ± 0.9 mm. The average maximum postoperative step-off is 1.3 ± 0.4 mm. The average distance between the postoperative and planned articular surfaces is 1.1 ± 0.6 mm as determined in the distance map measurement. There is a tendency to achieve higher accuracy as experience builds up, both on the surgeon's side and on the design engineering side. We believe this technology holds the potential to achieve consistent accuracy of very complex corrections.

Numerical simulation of heavy-oil/bitumen recovery by solvent injection at elevated temperatures

Abstract Hydrocarbon solvent injection into preheated reservoirs has been suggested as an alternative to sole injection of steam or solvent for heavy-oil recovery. But, this is a highly pressure and temperature sensitive process. This paper investigates this process through a numerical modeling exercise and formulates the optimal pressure and temperature conditions for maximized recovery and minimized asphaltene precipitation. We first report the results of numerical simulation of laboratory experiments, in which heavy-oil was exposed to solvent vapor at high temperatures. To achieve these results, a radial 3D numerical model of 15×1×48 cells was constructed using a commercial numeric simulator. The injection of either propane or butane into sand packs or consolidated sandstones at elevated temperatures was simulated. A pressure–temperature sensitivity analysis was carried out for different core sizes to understand the dynamics of the gravity drainage process associated with asphaltene precipitation. Asphaltene pore plugging behavior was modeled and diffusion of solvent into the heavy-oil was analyzed to determine both ideal solvent type and optimal operating conditions for propane or butane injection in a temperature range of 52–112 °C. Our results and observations showed that the solvent should be in the gas phase and its sensitivity to temperature and sample height (for effective gravity drainage) is more critical than the pressure. There also exists a critical temperature that yields a maximum recovery and this value was determined for the rock/reservoir types and solvents considered in this study. Solvents considered, i.e., propane and butane, behaved differently in terms of asphaltene precipitation and its effects on ultimate recovery.

RAZER: A pulse sequence for whole‐brain bolus tracking at high frame rates

To introduce a pulse sequence that obtains whole-brain perfusion measurements at 1.7 mm isotropic voxel resolution by dynamic susceptibility contrast MRI bolus tracking despite using a temporal resolution of 10.3 s: RAdial kZ-blipped 3D GRE-echo-planar imaging (GRE-EPI) for whole-brain pERfusion (RAZER). In RAZER, in-plane radial and through-plane 3D GRE-EPI Cartesian sampling was used to produce a 3D stack-of-stars k-space. In vivo scans on one healthy volunteer and one patient with Moyamoya disease were performed using RAZER and a typical 2D GRE-EPI pulse sequence as a reference standard. Agreement in perfusion metrics was reported using linear regression analysis and Bland-Altman plots. Sliding window reconstruction recovered dynamic information lost in the large temporal acquisition window of RAZER. Inline phase correction scans corrected N/2 ghosting artifacts and view-dependent phase variations. Whole-brain images of cerebral blood volume, cerebral blood flow, and mean transit time were calculated with RAZER at 1.7 mm isotropic voxel resolution and good reference standard agreement in both subjects when sliding window reconstruction was used (r(2) > 0.7, mean bias in mean transit time measurements < 0.5 s). Despite using a temporal resolution of 10.3 s, in vivo data indicates that RAZER is able to obtain whole-brain perfusion measurements at 1.7 mm isotropic voxel resolution and good reference standard agreement.

B1 mapping of short T 2 * spins using a 3D radial gradient echo sequence

To develop a method to acquire a radiofrequency (B1 ) field map when the signal has a short T2 *. The method is based on the actual flip angle imaging (AFI) technique and a radial 3D gradient-echo sequence known as COncurrent Dephasing and Excitation (CODE), which preserves short T2 (*) signals. CODE was implemented with Gradient-modulated Offset-Independent Adiabaticity (GOIA) pulses to obtain high estimation sensitivity with AFI. The correlation method, which removes the quadratic phase from the frequency-modulated pulse excitation, was modified to handle gradient-modulated pulses. Validity of the modified correlation procedure was tested by Bloch simulations. CODE experiments with sinc, hyperbolic secant, and GOIA pulses were performed in order to see effects from the frequency and gradient modulation. Finally, GOIA-CODE AFI was conducted and compared with conventional AFI with 3D gradient echo (GRE). The modified correlation method developed to accommodate frequency and gradient modulations of GOIA performed well as judged by the minimal impact on reconstructed image quality. GOIA-CODE AFI provided flip angle maps consistent with those measured by GRE AFI when the T2 * was long (>2 ms) and continued to perform well for short T2 * signals. The proposed technique provides a means to obtain a 3D B1 field map when imaging spins with short T2 (*) .

Reproducibility and repeatability of quantitative sodium magnetic resonance imaging in vivo in articular cartilage at 3 T and 7 T

Osteoarthritis is a degenerative disease of articular cartilage that may be associated with a loss of glycosaminoglycans. Quantitative sodium magnetic resonance imaging is highly specific to glycosaminoglycan content and could be used to assess the biochemical degradation of cartilage in early osteoarthritis. However, the reproducibility and repeatability of this technique are not well documented. The aim of this study is to test the reproducibility and repeatability of sodium quantification in cartilage in vivo using intraday and interday acquisitions at 3 T and 7 T, with a radial 3D sequence, with and without fluid suppression. Fluid suppression was obtained by adiabatic inversion recovery (IR WURST) and is expected to improve the sensitivity of the method to glycosaminoglycan content. The root mean square of coefficients of variation are all in the range of 7.5-13.6%. No significant intermagnet, intersequence, intraday, and interday differences in the coefficients of variation were observed. Sodium quantification using IR WURST gave values closer to those reported in the literature for healthy cartilage (220-310 mM) than radial 3D. In conclusion, IR WURST was more accurate in context of sodium measurement, with a reproducibility and repeatability comparable to other compositional magnetic resonance imaging techniques of cartilage.

Free-Breathing 3D T1-Weighted Gradient-Echo Sequence With Radial Data Sampling in Abdominal MRI: Preliminary Observations

The purposes of this study were to evaluate the feasibility of a free-breathing 3D gradient-recalled echo sequence with radial data sampling (radial 3D GRE) in abdominal MRI compared with a standard 3D GRE volumetric interpolated breath-hold examination (VIBE) sequence for imaging of cooperative patients and to perform a preliminary assessment in imaging of noncooperative patients. Fifty-five consecutively registered patients who underwent unenhanced and contrast-enhanced abdominal MRI with the free-breathing radial 3D GRE technique constituted the study population. Two readers independently and blindly evaluated the images. Overall image quality with the contrast-enhanced radial 3D GRE sequence was lower than but rated at least nearly as good as that with the 3D GRE VIBE sequence (p < 0.0001). Higher scores were recorded for 3D GRE VIBE images with respect to pixel graininess, streaking artifact, and sharpness (p = 0.0009 to p < 0.0001). Except for sharpness of vessels on unenhanced images, results for the radial 3D GRE sequence did not differ significantly in the comparison of cooperative and noncooperative patients (p = 0.004). For imaging of noncooperative patients, radial 3D GRE images of children had higher ratings for shading (unenhanced, p = 0.0004; contrast-enhanced, p < 0.0001) and streaking artifacts on contrast-enhanced images (p = 0.0017) than did those of adults. Overall image quality was higher for pediatric patients. In lesion analysis, use of the 3D GRE VIBE sequence was associated with significantly greater detectability, confidence, and conspicuity than was use of the radial 3D GRE sequence (p = 0.00026-0.011). A free-breathing radial 3D GRE sequence is feasible for abdominal MRI and may find application in imaging of patients who are unable to suspend respiration, especially children.