A note on the moving hyperplane method

We give more precision on the regularity of the domain that is needed to have the monotonicity and symmetry results recently proved by Damascelli and Pacella, result concerning p-Laplace equations. For this purpose, we study the continuity and semicontinuity of some parameters linked with the moving hyperplane method.Comment: 4 pages, 2 figure

Magnetic and structural properties of nanocrystalline PrCo3_3

The structure and magnetic properties of nanocrystalline PrCo$_3$ obtained from high energy milling technique are investigated by X-ray diffraction, Curie temperature determination and magnetic properties measurements are reported. The as-milled samples have been annealed in a temperature range of 1023 K to 1273 K for 30 mn to optimize the extrinsic properties. The Curie temperature is 349\,K and coercive fields of 55\,kOe at 10\,K and 12\,kOe at 293\,K are obtained on the samples annealed at 1023\,K. A simulation of the magnetic properties in the framework of micromagnetism has been performed in order to investigate the influence of the nanoscale structure. A composite model with hard crystallites embedded in an amorphous matrix, corresponding to the as-milled material, leads to satisfying agreement with the experimental magnetization curve. [ K. Younsi, V. Russier and L. Bessais, J. Appl. Phys. {\bf 107}, 083916 (2010)]. The microscopic scale will also be considered from DFT based calculations of the electronic structure of $R$Co$_x$ compounds, where $R$ = (Y, Pr) and $x$ = 2,3 and 5.Comment: To be published in J. Phys.: Conference Series in the JEMS 2010 special issue. To be found once published at http://iopscience.iop.org/1742-659

Quantitative MR renography using a calibrated internal signal (ERETIC)

To measure MR renograms, cortical and medullary kidney signal intensity evolution is followed after contrast agent injection. To obtain an accurate quantitative signal measurement, the use of a reference signal is necessary to correct the potential MRI system variations in time. The ERETIC method (Electronic Reference To access In vivo Concentrations) provides an electronic reference signal. It is synthesized as an amplitude modulated RF pulse applied during the acquisition. The ERETIC method was as precise as the external tube reference method but presents major advantages like its free adjustability (shape, location and magnitude) to the characteristics of the organ studied as well as its not taking room inside the magnet. Even though ERETIC showed a very good intrinsic stability, systems’ variations still affect its signal in the same way as real NMR signals are affected. This method can be easily implemented on any imaging system with two RF channels

In vitro expansion of U87-MG human glioblastoma cells under hypoxic conditions affects glucose metabolism and subsequent in vivo growth

Hypoxia is a characteristic feature of solid tumors leading to the over expression of hypoxia-inducible factor (HIF)-1α protein and therefore to a specific cellular behavior. However, even though the oxygen tension in tumors is low (<5 %), most of the cell lines used in cancer studies are grown under 21 % oxygen tension. This work focuses on the impact of oxygen conditions during in vitro cell culture on glucose metabolism using 1-13C-glucose. Growing U87-MG glioma cells under hypoxic conditions leads to a two- to threefold reduction of labeled glutamine and an accumulation of fructose. However, under both hypoxic and normoxic conditions, glucose is used for de novo synthesis of pyrimidine since the 13C label is found both in the uracil and ribose moieties. Labeling of the ribose ring demonstrates that U87-MG glioma cells use the reversible branch of the non-oxidative pentose phosphate pathway. Interestingly, stereotactic implantation of U87-MG cells grown under normoxia or mild hypoxia within the striatum of nude mice led to differential growth; the cells grown under hypoxia retaining an imprint of the oxygen adaptation as their development is then slowed down

Susceptibility gradient quantization by MRI signal response mapping (SIRMA) to dephaser

Purpose: Susceptibility effects are a very efficient source of contrast in magnetic resonance imaging. However, detection is hampered by the fact the induced contrast is negative. In this work, the SIgnal Response MApping (SIRMA) to dephaser method is proposed to map susceptibility gradient to improve visualization. Methods: In conventional gradient echo acquisitions, the echo formation of susceptibility affected spins is shifted in k -space, the shift being proportional to the susceptibility gradient. Susceptibility gradients map can be produced by measuring this induced shifts. The SIRMA method measures these shifts from a series of dephased images collected with additional incremental dephasers. These additional dephasers correspond either to a slice refocusing gradient offset or to a reconstruction window off-centering. The signal intensity profile as a function of the additional dephaser was determined on a pixel-by-pixel basis from the ensemble of dephased images. Susceptibility affected voxels presented a signal response profile maximum shifted compared to nonaffected voxels ones. Shift magnitude and sign were measured for each pixel to determine susceptibility gradients and produce a susceptibility gradient map. Results: In vitro experiments demonstrated the ability of the method to map gradient inhomogeneities induced by a cylinder. Quantization accuracy was evaluated comparing SIRMA images and simulations performed on the well-characterized air filled cylinder model. Performances of the SIRMA method, evaluated in vitro on cylinders filled with various superparamagnetic iron oxide SPIO concentrations, showed limited influence of acquisition parameters. Robustness of the method was then assessed in vivo after an infusion of SPIO-loaded nanocapsules into the rat brain using a convection-enhanced drug delivery approach. The region of massive susceptibility gradient induced by the SPIO-loaded nanocapsules was clearly delineated on SIRMA maps and images were compared to T 2 weighted images, Susceptibility Gradient Map (SGM), and histological Perl\u27s staining slice. The potential for quantitative evaluation of SPIO distribution volume was demonstrated. Conclusions: The proposed method is a promising technique for a wide range of applications especially in molecular or cellular imaging with respect to its quantitative nature and its computational simplicity

Prenatal evaluation of kidney function in mice using dynamic contrast-enhanced magnetic resonance imaging

Glomerular differentiation starts as soon as embryonic stage 12 in mice and suggests that kidneys may be functional at this stage. Dynamic contrast-enhanced magnetic resonance microscopy, a noninvasive imaging technique, was used to assess renal function establishment in utero. Indeed, in adults (n = 3), an intravenous injection of gadolinium-DOTA induced in a first step a massive and rapid drop in kidney signal intensity followed, in a second step, by a drop in bladder signal intensity. The delay in signal changes between kidney and bladder reflected glomerular filtration. Pregnant mice underwent anatomical and dynamic contrast-enhanced magnetic resonance microscopy on postcoital days 12-13 (n = 2), 13-14 (n = 1), 14-15 (n = 3), 15-16 (n = 2), 16-17 (n = 3), 17-18 (n = 3), and 18-19 (n = 1). Kidneys and bladder were unambiguously depicted prior to contrast agent injection on stage 15-16 embryos. Contrast agent injection allowed kidney, detection as early as stage 12-13 but not bladder. Kinetics of signal changes demonstrated that glomerular filtration is established at embryonic stage 15-16 in mice. Thus, anatomical and dynamic contrast-enhanced magnetic resonance microscopy may be a powerful noninvasive method for in vivo prenatal developmental and functional studies

Generalized Forward-Backward Splitting

This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form $F + \sum_{i=1}^n G_i$, where $F$ has a Lipschitz-continuous gradient and the $G_i$'s are simple in the sense that their Moreau proximity operators are easy to compute. While the forward-backward algorithm cannot deal with more than $n = 1$ non-smooth function, our method generalizes it to the case of arbitrary $n$. Our method makes an explicit use of the regularity of $F$ in the forward step, and the proximity operators of the $G_i$'s are applied in parallel in the backward step. This allows the generalized forward backward to efficiently address an important class of convex problems. We prove its convergence in infinite dimension, and its robustness to errors on the computation of the proximity operators and of the gradient of $F$. Examples on inverse problems in imaging demonstrate the advantage of the proposed methods in comparison to other splitting algorithms.Comment: 24 pages, 4 figure

Volumetric assessment of myocardial viability in rats using 3D double contrast enhanced T1 and T2-weighted MRI

OBJECTIVE: Volumetric evaluation of the myocardial viability post-infarction in rats using 3D in vivo MR imaging at 7 T using injection of an extracellular paramagnetic contrast agent and intravascular superparamagnetic iron oxide nanoparticles in the same imaging session. MATERIALS AND METHODS: Five hours after induction of permanent myocardial infarction in rats (n=6), 3D in vivo T1- and T2-weighted MR Imaging was performed prior to and after Gd-DOTA injection (0.2 mmol/kg) and prior to and after nanoparticle injection (5 mg Fe/kg) to assess infarct size and myocardial viability. RESULTS: 3D MR Imaging using a successive contrast agent injection showed a difference of infarct size after Gd-DOTA injection on T1-weighted images compared to the one measured on T2-weighted images after Gd-DOTA and nanoparticle injection. CONCLUSION: The use of 3D T1- and T2-weighted MR Imaging using a double contrast agents protocol made possible the accurate characterization of myocardial infarction volume and allowed the detection of myocardial viability post-infarction in rats

Assessment of myocardial viability in rats: Evaluation of a new method using superparamagnetic iron oxide nanoparticles and Gd-DOTA at high magnetic field

The aim of this study was to detect salvageable peri-infarction myocardium by MRI in rats after infarction, using with a double contrast agent (CA) protocol at 7 Tesla. Intravascular superparamagnetic iron oxide (SPIO) nanoparticles and an extracellular paramagnetic CA (Gd-DOTA) were used to characterize the peri-infarction zone, which may recover function after reperfusion occurs. Infarcted areas measured from T1-weighted (T1-w) images post Gd-DOTA administration were overestimated compared to histological TTC staining (52% +/- 3% of LV surface area vs. 40% +/- 3%, P=0.03) or to T2-w images post SPIO administration (41% +/- 4%, P=0.04), whereas areas measured from T2-w images post SPIO administration were not significantly different from those measured histologically (P=0.7). Viable and nonviable myocardium portions of ischemically injured myocardium were enhanced after diffusive Gd-DOTA injection. The subsequent injection of vascular SPIO nanoparticles enables the discrimination of viable peri-infarction regions by specifically altering the signal of the still-vascularized myocardium