Spectroscopic imaging with volume selection by unpaired adiabatic pi pulses: theory and application

In NMR spectroscopy, volume selection can be advantageously achieved using adiabatic pi pulses, which enable high bandwidth and B(1) insensitivity. In order to avoid the generation of non-linear phase profiles and the subsequent signal loss caused by incoherent averaging, adiabatic pi pulses are usually used in pairs for volume selection in each spatial dimension. Alternatively, when performing spectroscopic imaging (SI), a high enough spatial resolution results in negligible phase dispersion within each pixel. This allows using only one pulse per selected spatial dimension, resulting in a reduced echo-time and reduced power deposition. In this work, the feasibility of such an approach is explored theoretically and numerically, allowing the derivation of explicit conditions to obtain SI images without artifact. Adequate spatial and spectral post-processing procedures are described to compensate for the effect of non-linear phase profiles. These developments are applied to SI in the rat brain at 9.4 T, using a new adiabatic sequence named Pseudo-LASER.     

In vivo 13C NMR spectroscopy and metabolic modeling in the brain: a practical perspective

In vivo 13C NMR spectroscopy has the unique capability to measure metabolic fluxes noninvasively in the brain. Quantitative measurements of metabolic fluxes require analysis of the 13C labeling time courses obtained experimentally with a metabolic model. The present work reviews the ingredients necessary for a dynamic metabolic modeling study, with particular emphasis on practical issues.     

Straightforward stereoselective synthesis of spiro-epoxyoxindoles

[reaction: see text] The in situ preparation of a sulfonium ylide reagent achieved the highly diastereoselective epoxidation of isatins, so that a new and straightforward access to biologically significant spiro-epoxyoxindoles is provided. The first investigations of an asymmetric version are reported with enantiopure sulfides.     

Multipliers and Morrey Spaces

We study the pointwise multipliers from one Morrey space to another Morrey space. We give a necessary and sufficient condition to grant that the space of those multipliers is a Morrey space as well.     

Simultaneous measurement of neuronal and glial metabolism in rat brain in vivo using co-infusion of [1,6-C2]glucose and [1,2-C2]acetate

In this work the feasibility of measuring neuronal-glial metabolism in rat brain in vivo using co-infusion of [1,6-¹³C₂]glucose and [1,2-¹³C₂]acetate was investigated. Time courses of ¹³C spectra were measured in vivo while infusing both ¹³C-labeled substrates simultaneously. Individual ¹³C isotopomers (singlets and multiplets observed in ¹³C spectra) were quantified automatically using LCModel. The distinct ¹³C spectral pattern observed in glutamate and glutamine directly reflected the fact that glucose was metabolized primarily in the neuronal compartment and acetate in the glial compartment. Time courses of concentration of singly and multiply-labeled isotopomers of glutamate and glutamine were obtained with a temporal resolution of 11 min. Although dynamic metabolic modeling of these ¹³C isotopomer data will require further work and is not reported here, we expect that these new data will allow more precise determination of metabolic rates as is currently possible when using either glucose or acetate as the sole ¹³C-labeled substrate.     

Real interpolation method,Lorentz spaces and refined Sobolev inequalities

In this article we give a straightforward proof of refined inequalities between Lorentz spaces and Besov spaces and we generalize previous results of H. Bahouri and A. Cohen [2]. Our approach is based in the characterization of Lorentz spaces as real interpolation spaces. We will also study the sharpness and optimality of these inequalities.     

Euler Equations and Real Harmonic Analysis

We re-prove various existence theorems of regular solutions for the Euler equations, using classical tools of real harmonic analysis such as singular integrals, atomic decompositions and maximal functions.