The isotropic nuclear magnetic shielding constants of acetone in supercritical water: A sequential Monte Carlo/quantum mechanics study including solute polarization

The nuclear isotropic shielding constants sigma((17)O) and sigma((13)C) of the carbonyl bond of acetone in water at supercritical (P=340.2 atm and T=673 K) and normal water conditions have been studied theoretically using Monte Carlo simulation and quantum mechanics calculations based on the B3LYP/6-311++G(2d,2p) method. Statistically uncorrelated configurations have been obtained from Monte Carlo simulations with unpolarized and in-solution polarized solute. The results show that solvent effects on the shielding constants have a significant contribution of the electrostatic interactions and that quantitative estimates for solvent shifts of shielding constants can be obtained modeling the water molecules by point charges (electrostatic embedding). In supercritical water, there is a decrease in the magnitude of sigma((13)C) but a sizable increase in the magnitude of sigma((17)O) when compared with the results obtained in normal water. It is found that the influence of the solute polarization is mild in the supercritical regime but it is particularly important for sigma((17)O) in normal water and its shielding effect reflects the increase in the average number of hydrogen bonds between acetone and water. Changing the solvent environment from normal to supercritical water condition, the B3LYP/6-311++G(2d,2p) calculations on the statistically uncorrelated configurations sampled from the Monte Carlo simulation give a (13)C chemical shift of 11.7 +/- 0.6 ppm for polarized acetone in good agreement with the experimentally inferred result of 9-11 ppm. (C) 2008 American Institute of Physics.

Isotropic and anisotropic spin-spin interactions and a quantum phase transition in a dinuclear Cu(II) compound

We report electron-paramagnetic resonance (EPR) studies at similar to 9.5 GHz (X band) and similar to 34 GHz (Q band) of powder and single-crystal samples of the compound Cu(2)[TzTs](4) [N-thiazol-2-yl-toluenesulfonamidatecopper(II)], C(40)H(36)Cu(2)N(8)O(8)S(8), having copper(II) ions in dinuclear units. Our data allow determining an antiferromagnetic interaction J(0)=(-113 +/- 1) cm(-1) (H(ex)=-J(0)S(1)center dot S(2)) between Cu(II) ions in the dinuclear unit and the anisotropic contributions to the spin-spin coupling matrix D (H(ani)=S(1)center dot D center dot S(2)), a traceless symmetric matrix with principal values D/4=(0.198 +/- 0.003) cm(-1) and E/4=(0.001 +/- 0.003) cm(-1) arising from magnetic dipole-dipole and anisotropic exchange couplings within the units. In addition, the single-crystal EPR measurements allow detecting and estimating very weak exchange couplings between neighbor dinuclear units, with an estimated magnitude parallel to J(')parallel to=(0.060 +/- 0.015) cm(-1). The interactions between a dinuclear unit and the ""environment"" of similar units in the structure of the compound produce a spin dynamics that averages out the intradinuclear dipolar interactions. This coupling with the environment leads to decoherence, a quantum phase transition that collapses the dipolar interaction when the isotropic exchange coupling with neighbor dinuclear units equals the magnitude of the intradinuclear dipolar coupling. Our EPR experiments provide a new procedure to follow the classical exchange-narrowing process as a shift and collapse of the line structure (not only as a change of the resonance width), which is described with general (but otherwise simple) theories of magnetic resonance. Using complementary procedures, our EPR measurements in powder and single-crystal samples allow measuring simultaneously three types of interactions differing by more than three orders of magnitude (between 113 cm(-1) and 0.060 cm(-1)).

Isotropic singularities in shear-free perfect fluid cosmologies

We investigate barotropic perfect fluid cosmologies which admit an isotropic singularity. From the General Vorticity Result of Scott, it is known that these cosmologies must be irrotational. In this paper we prove, using two different methods, that if we make the additional assumption that the perfect fluid is shear-free, then the fluid flow must be geodesic. This then implies that the only shear-free, barotropic, perfect fluid cosmologies which admit an isotropic singularity are the FRW models.

General properties of cosmological models with an isotropic singularity

Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a gamma-law equation of state. There are, however, some general properties of cosmological models which admit an Isotropic Singularity, irrespective of the matter source. In particular, we show that the Isotropic Singularity is a point-like singularity and that vacuum space-times cannot admit an Isotropic Singularity. The relationships between the Isotropic Singularity, and the energy conditions, and the Hubble parameter is explored. A review of work by the authors, regarding the Isotropic Singularity, is presented.

Effective isotropic potential for dipolar hard spheres

A new effective isotropic potential is proposed for the dipolar hard-sphere fluid, on the basis of recent results by others for its angle-averaged radial distribution function. The new effective potential is shown to exhibit oscillations even for moderately high densities and moderately strong dipole moments, which are absent from earlier effective isotropic potentials. The validity and significance of this result are briefly discussed.

Use of 2D Sensitivity Encoding for Slow-Infusion Contrast-Enhanced Isotropic 3-T Whole-Heart Coronary MR Angiography.

OBJECTIVE. The purpose of this study was to improve the blood-pool signal-to-noise ratio (SNR) and blood-myocardium contrast-to-noise ratio (CNR) of slow-infusion 3-T whole-heart coronary MR angiography (MRA).SUBJECTS AND METHODS. In 2D sensitivity encoding (SENSE), the number of acquired k-space lines is reduced, allowing less radiofrequency excitation per cardiac cycle and a longer TR. The former can be exploited for signal enhancement with a higher radiofrequency excitation angle, and the latter leads to noise reduction due to lower data-sampling bandwidth. Both effects contribute to SNR gain in coronary MRA when spatial and temporal resolution and acquisition time remain identical. Numeric simulation was performed to select the optimal 2D SENSE pulse sequence parameters and predict the SNR gain. Eleven patients underwent conventional unenhanced and the proposed 2D SENSE contrast-enhanced coronary MRA acquisition. Blood-pool SNR, blood-myocardium CNR, visible vessel length, vessel sharpness, and number of side branches were evaluated.RESULTS. Consistent with the numeric simulation, using 2D SENSE in contrast-enhanced coronary MRA resulted in significant improvement in aortic blood-pool SNR (unenhanced vs contrast-enhanced, 37.5 +/- 14.7 vs 121.3 +/- 44.0; p < 0.05) and CNR (14.4 +/- 6.9 vs 101.5 +/- 40.8; p < 0.05) in the patient sample. A longer length of left anterior descending coronary artery was visualized, but vessel sharpness, coronary artery coverage, and image quality score were not improved with the proposed approach.CONCLUSION. In combination with contrast administration, 2D SENSE was found effective in improving SNR and CNR in 3-T whole-heart coronary MRA. Further investigation of cardiac motion compensation is necessary to exploit the SNR and CNR advantages and to achieve submillimeter spatial resolution.

Accelerated tumor invasion under non-isotropic cell dispersal in glioblastomas

Glioblastomas are highly diffuse, malignant tumors that have so far evaded clinical treatment. The strongly invasive behavior of cells in these tumors makes them very resistant to treatment, and for this reason both experimental and theoretical efforts have been directed toward understanding the spatiotemporal pattern of tumor spreading. Although usual models assume a standard diffusion behavior, recent experiments with cell cultures indicate that cells tend to move in directions close to that of glioblastoma invasion, thus indicating that a biasedrandom walk model may be much more appropriate. Here we show analytically that, for realistic parameter values, the speeds predicted by biased dispersal are consistent with experimentally measured data. We also find that models beyond reaction–diffusion–advection equations are necessary to capture this substantial effect of biased dispersal on glioblastoma spread

Stochastic generation of homogeneous isotropic turbulence with well-defined-spectra

A precise and simple computational model to generate well-behaved two-dimensional turbulent flows is presented. The whole approach rests on the use of stochastic differential equations and is general enough to reproduce a variety of energy spectra and spatiotemporal correlation functions. Analytical expressions for both the continuous and the discrete versions, together with simulation algorithms, are derived. Results for two relevant spectra, covering distinct ranges of wave numbers, are given.

Stability of de Sitter spacetime under isotropic perturbations in semiclassical gravity

A spatially flat Robertson-Walker spacetime driven by a cosmological constant is nonconformally coupled to a massless scalar field. The equations of semiclassical gravity are explicitly solved for this case, and a self-consistent de Sitter solution associated with the Bunch-Davies vacuum state is found (the effect of the quantum field is to shift slightly the effective cosmological constant). Furthermore, it is shown that the corrected de Sitter spacetime is stable under spatially isotropic perturbations of the metric and the quantum state. These results are independent of the free renormalization parameters.

Radiative isotropic cosmologies with extra dimensions

We solve Einsteins equations in an n-dimensional vacuum with the simplest ansatz leading to a Friedmann-Robertson-Walker (FRW) four-dimensional space time. We show that the FRW model must be of radiation. For the open models the extra dimensions contract as a result of cosmological evolution. For flat and closed models they contract only when there is one extra dimension.

Stochastic generation of homogeneous isotropic turbulence with well-defined-spectra

A precise and simple computational model to generate well-behaved two-dimensional turbulent flows is presented. The whole approach rests on the use of stochastic differential equations and is general enough to reproduce a variety of energy spectra and spatiotemporal correlation functions. Analytical expressions for both the continuous and the discrete versions, together with simulation algorithms, are derived. Results for two relevant spectra, covering distinct ranges of wave numbers, are given.

Free-breathing 3D coronary MRA: the impact of "isotropic" image resolution.

During conventional x-ray coronary angiography, multiple projections of the coronary arteries are acquired to define coronary anatomy precisely. Due to time constraints, coronary magnetic resonance angiography (MRA) usually provides only one or two views of the major coronary vessels. A coronary MRA approach that allowed for reconstruction of arbitrary isotropic orientations might therefore be desirable. The purpose of the study was to develop a three-dimensional (3D) coronary MRA technique with isotropic image resolution in a relatively short scanning time that allows for reconstruction of arbitrary views of the coronary arteries without constraints given by anisotropic voxel size. Eight healthy adult subjects were examined using a real-time navigator-gated and corrected free-breathing interleaved echoplanar (TFE-EPI) 3D-MRA sequence. Two 3D datasets were acquired for the left and right coronary systems in each subject, one with anisotropic (1.0 x 1.5 x 3.0 mm, 10 slices) and one with "near" isotropic (1.0 x 1.5 x 1.0 mm, 30 slices) image resolution. All other imaging parameters were maintained. In all cases, the entire left main (LM) and extensive portions of the left anterior descending (LAD) and the right coronary artery (RCA) were visualized. Objective assessment of coronary vessel sharpness was similar (41% +/- 5% vs. 42% +/- 5%; P = NS) between in-plane and through-plane views with "isotropic" voxel size but differed (32% +/- 7% vs. 23% +/- 4%; P < 0.001) with nonisotropic voxel size. In reconstructed views oriented in the through-plane direction, the vessel border was 86% more defined (P < 0.01) for isotropic compared with anisotropic images. A smaller (30%; P < 0.001) improvement was seen for in-plane reconstructions. Vessel diameter measurements were view independent (2.81 +/- 0.45 mm vs. 2.66 +/- 0.52 mm; P = NS) for isotropic, but differed (2.71 +/- 0.51 mm vs. 3.30 +/- 0.38 mm; P < 0.001) between anisotropic views. Average scanning time was 2:31 +/- 0:57 minutes for anisotropic and 7:11 +/- 3:02 minutes for isotropic image resolution (P < 0.001). We present a new approach for "near" isotropic 3D coronary artery imaging, which allows for reconstruction of arbitrary views of the coronary arteries. The good delineation of the coronary arteries in all views suggests that isotropic 3D coronary MRA might be a preferred technique for the assessment of coronary disease, although at the expense of prolonged scan times. Comparative studies with conventional x-ray angiography are needed to investigate the clinical utility of the isotropic strategy.

Self-navigated isotropic three-dimensional cardiac T2 mapping.

PURPOSE: To implement and characterize an isotropic three-dimensional cardiac T2 mapping technique. METHODS: A self-navigated three-dimensional radial segmented balanced steady-state free precession pulse sequence with an isotropic 1.7-mm spatial resolution was implemented at 3T with a variable T2 preparation module. Bloch equation and Monte Carlo simulations were performed to determine the influence of the heart rate, B1 inhomogeneity and noise on the T2 fitting accuracy. In a phantom study, the accuracy of the pulse sequence was studied through comparison with a gold-standard spin-echo T2 mapping method. The robustness and homogeneity of the technique were ascertained in a study of 10 healthy adult human volunteers, while first results obtained in patients are reported. RESULTS: The numerical simulations demonstrated that the heart rate and B1 inhomogeneity cause only minor deviations in the T2 fitting, whereas the phantom study showed good agreement of the technique with the gold standard. The volunteer study demonstrated an average myocardial T2 of 40.5 ± 3.3 ms and a <15% T2 gradient in the base-apex and anterior-inferior direction. In three patients, elevated T2 values were measured in regions with expected edema. CONCLUSION: This respiratory self-navigated isotropic three-dimensional technique allows for accurate and robust in vitro and in vivo T2 quantification. Magn Reson Med 73:1549-1554, 2015. © 2014 Wiley Periodicals, Inc.