High b-value q-space diffusion MRI in myelin-deficient rat spinal cords

In this study, we explore the effect of the lack of myelin on the diffusion characteristics and diffusion anisotropy obtained from high b-value q-space diffusion-weighted MRI (q-space DWI) in excised rat spinal cords. Twenty-one-day-old myelin-deficient (md) mutant (N=6) and control rats (N=6) were used in this study. The MRI protocol included multi-slice T(1), T(2), proton density (PD) MR images and high b-value q-space diffusion MRI measured perpendicular and parallel to the fibers of the spine. q-Space displacement and probability maps, in both directions, as well as displacement anisotropy maps, were computed from the diffusion data. At the end of the MRI protocol, representative spinal cords from both groups were subjected to electron microscopy (EM). The md spinal cords show different gray/white matter contrast in the T(1), T(2) and PD MR images as compared with controls. In addition, the mean displacement extracted from the high b-value q-space diffusion data was found to be dramatically higher in the white matter (WM) of the md spinal cords than the controls when diffusion was measured perpendicular and parallel to the fibers of the spine. However, interestingly, at the diffusion time used in the present study, the difference in the WM displacement anisotropies of the two groups was not found to be statistically significant. Myelin was found to have a pronounced effect on the diffusion characteristics of water in WM but less so on the diffusion anisotropy observed at the diffusion time used in the present study.     

The Nevai Condition

We study Nevai’s condition that for orthogonal polynomials on the real line, $K_{n}(x,x_{0})^{2}K_{n}(x_{0},x_{0})^{-1}\,d\rho(x)\to\delta_{x_{0}}We study Nevai’s condition that for orthogonal polynomials on the real line, K_n(x,x₀)²K_n(x₀,x₀)^-1 dr(x)?d_x0K_{n}(x,x_{0})^{2}K_{n}(x_{0},x_{0})^{-1}\,d\rho(x)\to\delta_{x_{0}} , where K _n is the Christoffel–Darboux kernel. We prove that it holds for the Nevai class of a finite gap set uniformly on the spectrum, and we provide an example of a regular measure on [−2,2] where it fails on an interval.     

Products of random variables and the first digit phenomenon

We provide conditions on dependent and on non-stationary random variables $X_n$ ensuring that the mantissa of the sequence of products $\left({\prod }_1^n{X}_k\right)$ is almost surely distributed following Benford’s law or converges in distribution to Benford’s law. This is achieved through proving new generalizations of Lévy’s and Robbins’s results on distribution modulo 1 of sums of independent random variables.     

The role of water molecules in a resorcinarene capsule as probed by NMR diffusion measurements

[structure: see text] NMR diffusion measurements were used to probe the role of water molecules in a resorcinarene capsule in a CDCl(3) solution. It was found that the water/resorcinarene ratio affects both the chemical shift and the diffusion coefficient of the water molecules. From the NMR diffusion measurements we could conclude that the major species in the chloroform solution is the hexamer having eight water molecules that are in fast exchange, on the NMR time scale, with the bulk water.     

Thermal polymerization of levoglucosan

The uncatalyzed polymerization of neat levoglucosan (1,6-anhydro-β-D -glucopyranose) was studied at 190–210°C under argon, and the course of the reaction was followed by analyzing samples at various reaction times; the residual levoglucosan was determined by GLC, and the optical rotation of the mixture was also measured. The plots of percentage reaction versus time were sigmoid, indicating the occurrence of an autocatalytic reaction. A. kinetic equation of the form, dA/dt = k₂[A₁]² + k₁[A_t] ([A₀] ? [A_t]), where [A₀] and [A_t] denote the concentrations of levoglucosan at zero time and time t, was found to fit the results. A reaction scheme is proposed, consisting of a slower dimerization (k₂) followed by a faster reaction between levoglucosan and the dimers and other oligomers formed (k₁). This scheme results from the mechanistic assumption that axial hydroxyl groups in the unchanged levoglucosan are less reactive than equatorial hydroxyl groups present only in the oligomers, while the highest reactivity is ascribed to the primary hydroxyl at C₆, again only present in the oligomers. The relation between the mechanisms of the reactions occurring and the structure of the product are discussed.     

WST11, a novel water-soluble bacteriochlorophyll derivative; cellular uptake, pharmacokinetics, biodistribution and vascular-targeted photodynamic activity using melanoma tumors as a model

WST11 is a novel negatively charged water-soluble palladium-bacteriochlorophyll derivative that was developed for vascular-targeted photodynamic therapy (VTP) in our laboratory. The in vitro results suggest that WST11 cellular uptake, clearance and phototoxicity are mediated by serum albumin trafficking. In vivo, WST11 was found to clear rapidly from the circulation (t1/2=1.65 min) after intravenous bolus injection in the mouse, whereas a longer clearance time (t1/2=7.5 min) was noted in rats after 20 min of infusion. The biodistribution of WST11 in mouse tissues indicates hepatic clearance (t1/2=20 min), with minor (kidney, lung and spleen) or no intermediary accumulation in other tissues. As soon as 1 h after injection, WST11 had nearly cleared from the body of the mouse, except for a temporal accumulation in the lungs from which it cleared within 40 min. On the basis of these results, we set the VTP protocol for a short illumination period (5 min), delivered immediately after WST11 injection. On subjecting M2R melanoma xenografts to WST11-VTP, we achieved 100% tumor flattening at all doses and a 70% cure with 9 mg/kg and a light exposure dose of 100 mW/cm2. These results provide direct evidence that WST11 is an effective agent for VTP and provide guidelines for further development of new candidates.     

Studies on anabolic steroids. I. Integrated methodological approach to the gas chromatographic-mass spectrometric analysis of anabolic steroid metabolites in urine

The analytical and methodological imperatives for large-scale and routine gas chromatographic-mass spectrometric screening of anabolic steroid urinary metabolites are described. Several aspects of their isolation, enzymatic hydrolysis, derivatization and metabolism in humans are discussed. Gas chromatographic-mass spectrometric data illustrating artifacts arising from enzymatic hydrolysis of 3 beta-ol-5-en steroids, and describing new metabolites of boldenone, methanedienone and stanozolol, as well as the conversion of norethisterone into 19-nortestosterone metabolites through de-ethylation at C-17, are presented. The analytical approach developed for gas chromatographic-mass spectrometric screening of anabolic steroids is based on the sequential selection-ion monitoring of specific and discrete ion groups characteristic to the steroids of interest under high-resolution chromatographic conditions. The major analytical and methodological requirements necessary to provide irrefutable evidence, in the case where the presence of a synthetic anabolic steroid or a testosterone to epitestosterone ratio higher than 6:1 is suspected in a given urine specimen, are also discussed.     

Numerical model of non-isothermal pervaporation in a rectangular channel

A numerical model of non-isothermal pervaporation was developed to investigate the development of the velocity, concentration and temperature fields in rectangular membrane module geometry. The model consists of the coupled Navier–Stokes equations to describe the flow field, the energy equation for the temperature field, and the species convection-diffusion equations for the concentration fields of the solution species. The coupled nonlinear transport equations were solved simultaneously for the velocity, temperature and concentration fields via a finite element approach. Simulation test cases for trichloroethylene/water, ethanol/water and iso-propanol/water pervaporation, under laminar flow conditions, revealed temperature drop axially along the module and orthogonal to the membrane surface. The nonlinear character of the concentration and temperature boundary-layers are most significant near the membrane surface. Estimation of the mass transfer coefficient assuming isothermal assumption conditions can significantly deviate from the non-isothermal predictions. For laminar conditions, predictions of the feed-side mass transfer coefficient converged to predictions from the classical Lévêque solution as the feed temperature approached the permeate temperature.