Delay nonlinear boundary conditions as limit of reactions concentrating in the boundary

In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction-diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter epsilon goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary. (C) 2012 Elsevier Inc. All rights reserved.

Beyond the diffraction limit of optical/IR interferometers I. Angular diameter and rotation parameters of Achernar from differential phases

Context. Spectrally resolved long-baseline optical/IR interferometry of rotating stars opens perspectives to investigate their fundamental parameters and the physical mechanisms that govern their interior, photosphere, and circumstellar envelope structures. Aims. Based on the signatures of stellar rotation on observed interferometric wavelength-differential phases, we aim to measure angular diameters, rotation velocities, and orientation of stellar rotation axes. Methods. We used the AMBER focal instrument at ESO-VLTI in its high-spectral resolution mode to record interferometric data on the fast rotator Achernar. Differential phases centered on the hydrogen Br gamma line (K band) were obtained during four almost consecutive nights with a continuous Earth-rotation synthesis during similar to 5h/night, corresponding to similar to 60 degrees position angle coverage per baseline. These observations were interpreted with our numerical code dedicated to long-baseline interferometry of rotating stars. Results. By fitting our model to Achernar's differential phases from AMBER, we could measure its equatorial radius R-eq = 11.6 +/- 0.3 R-circle dot, equatorial rotation velocity V-eq = 298 +/- 9 km s(-1), rotation axis inclination angle i = 101.5 +/- 5.2 degrees, and rotation axis position angle (from North to East) PA(rot) = 34.9 +/- 1.6 degrees. From these parameters and the stellar distance, the equatorial angular diameter circle divide(eq) of Achernar is found to be 2.45 +/- 0.09 mas, which is compatible with previous values derived from the commonly used visibility amplitude. In particular, circle divide(eq) and PA(rot) measured in this work with VLTI/AMBER are compatible with the values previously obtained with VLTI/VINCI. Conclusions. The present paper, based on real data, demonstrates the super-resolution potential of differential interferometry for measuring sizes, rotation velocities, and orientation of rotating stars in cases where visibility amplitudes are unavailable and/or when the star is partially or poorly resolved. In particular, we showed that differential phases allow the measurement of sizes up to similar to 4 times smaller than the diffraction-limited angular resolution of the interferometer.

Low sclerostin levels: a predictive marker of persistent inflammation in ankylosing spondylitis during anti-tumor necrosis factor therapy?

Abstract Introduction Sclerostin levels have been reported to be low in ankylosing spondylitis (AS), but there is no data regarding the possible role of this Wnt inhibitor during anti-tumor necrosis factor (TNF) therapy. The present study longitudinally evaluated sclerostin levels, inflammatory markers and bone mineral density (BMD) in AS patients under anti-TNF therapy. Methods Thirty active AS patients were assessed at baseline, 6 and 12 months after anti-TNF therapy regarding clinical parameters, inflammatory markers, BMD and baseline radiographic damage (mSASSS). Thirty age- and sex-matched healthy individuals comprised the control group. Patients' sclerostin levels, sclerostin binding low-density lipoprotein receptor-related protein 6 (LRP6) and BMD were evaluated at the same time points and compared to controls. Results At baseline, AS patients had lower sclerostin levels (60.5 ± 32.7 vs. 96.7 ± 52.9 pmol/L, P = 0.002) and comparable sclerostin binding to LRP6 (P = 0.387) than controls. Improvement of Bath Ankylosing Spondylitis Disease Activity Index (BASDAI), Bath Ankylosing Spondylitis Functional Index (BASFI), Bath Ankylosing Spondylitis Metrology Index (BASMI), Ankylosing Spondylitis quality of life (ASQoL) was observed at baseline vs. 6 vs. 12 months (P < 0.01). Concomitantly, a gradual increase in spine BMD (P < 0.001) and a positive correlation between baseline mSASSS and spine BMD was found (r = 0.468, P < 0.01). Inflammatory parameters reduction was observed comparing baseline vs. 6 vs. 12 months (P <0.01). Sclerostin levels progressively increased [baseline (60.5 ± 32.7) vs. 6 months (67.1 ± 31.9) vs. 12 months (72.7 ± 32.3) pmol/L, P <0.001]. At 12 months, the sclerostin levels remained significantly lower in patients compared to controls (72.7 ± 32.3 vs. 96.70 ± 52.85 pmol/L, P = 0.038). Moreover, sclerostin serum levels at 12 months were lower in the 10 patients with high C reactive protein (CRP) (≥ 5 mg/l) compared to the other 20 patients with normal CRP (P = 0.004). Of note, these 10 patients with persistent inflammation also had lower sclerostin serum levels at baseline compared to the other patients (P = 0.023). Univariate logistic regression analysis demonstrated that AS patients with lower sclerostin serum levels had an increased risk to have high CRP at 12 months (odds ratio = 7.43, 95% CI 1.23 to 45.01, P = 0.020) than those with higher sclerostin values. Conclusions Persistent low sclerostin levels may underlie continuous inflammation in AS patients under anti-TNF therapy.

A comparative study on the anti-inflammatory effects of single oral doses of naproxen and its hydrogen sulfide (H2S)-releasing derivative ATB-346 in rats with carrageenan-induced synovitis

Abstract Background Non-steroidal antiinflammatory drugs (NSAIDs) are the most commonly prescribed agents for arthritic patients, although gastric effects limit their long-term use. Considering the reported gastric safety of hydrogen sulfide (H2S)-releasing NSAIDs, in addition to the anti-inflammatory effects of H2S administration to rats with synovitis, we decided to evaluate the effects of the H2S-releasing naproxen derivative ATB-346 in this animal model. Methods Male Wistar rats were anesthetized with inhalatory halothane and pre-treated with equimolar oral doses of either naproxen (0.3, 1, 3 or 10 mg/kg) or ATB-346 (0.48, 1.6, 4.8, or 16 mg/kg) 30 min before the i.art. injection of 7.5 mg of carrageenan (CGN) into the right knee joint cavity. Joint swelling and pain score were assessed after 1, 3 and 5 h, and tactile allodynia after 2 and 4 h. After the last measurement, the joint cavity lavages were performed for counting of the recruited leukocytes. The drugs (at the highest doses) were also tested for their gastric effects by evaluating macroscopical damage score and neutrophil recruitment (measured as myeloperoxidase – MPO activity) in the stomachs 5 h after administration of the drugs. In addition, the serum naproxen pharmacokinetic profiles of both compounds, administered at the highest equimolar doses, were obtained during the first 6 h after dosing. Results At the two highest tested doses, both naproxen and ATB-346 reduced edema and pain score (measured 3 and 5 h after CGN; P < 0.001). Tactile allodynia was similarly inhibited by ~45% 4 h after CGN by both naproxen (at 1, 3 and 10 mg/kg) and ATB-346 (at 1.6 and 4.8 mg/kg; P < 0.001), as well as leukocyte infiltration. Naproxen (but not ATB-346) induced significant gastric damage and, despite the increased gastric MPO activity by ~130% in the naproxen-, but not in the ATB-346-treated rats, this effect was of no statistical significance. Conclusion The presence of a H2S-releasing moiety in the ATB-346 structure does not impair the antiinflammatory activity of the parent compound in rats with CGN-induced synovitis. In addition, released H2S may account for the absence of deleterious gastric effects, thus making of ATB-346 a potentially useful therapeutic alternative to traditional naproxen for treatment of patients with arthritis.

A comparative study on the anti-inflammatory effects of single oral doses of naproxen and its hydrogen sulfide (H2S)-releasing derivative ATB-346 in rats with carrageenan-induced synovitis

BACKGROUND: Non-steroidal antiinflammatory drugs (NSAIDs) are the most commonly prescribed agents for arthritic patients, although gastric effects limit their long-term use. Considering the reported gastric safety of hydrogen sulfide (H2S)-releasing NSAIDs, in addition to the anti-inflammatory effects of H2S administration to rats with synovitis, we decided to evaluate the effects of the H2S-releasing naproxen derivative ATB-346 in this animal model. METHODS: Male Wistar rats were anesthetized with inhalatory halothane and pre-treated with equimolar oral doses of either naproxen (0.3, 1, 3 or 10 mg/kg) or ATB-346 (0.48, 1.6, 4.8, or 16 mg/kg) 30 min before the i.art. injection of 7.5 mg of carrageenan (CGN) into the right knee joint cavity. Joint swelling and pain score were assessed after 1, 3 and 5 h, and tactile allodynia after 2 and 4 h. After the last measurement, the joint cavity lavages were performed for counting of the recruited leukocytes. The drugs (at the highest doses) were also tested for their gastric effects by evaluating macroscopical damage score and neutrophil recruitment (measured as myeloperoxidase - MPO activity) in the stomachs 5 h after administration of the drugs. In addition, the serum naproxen pharmacokinetic profiles of both compounds, administered at the highest equimolar doses, were obtained during the first 6 h after dosing. RESULTS: At the two highest tested doses, both naproxen and ATB-346 reduced edema and pain score (measured 3 and 5 h after CGN; P < 0.001). Tactile allodynia was similarly inhibited by ~45% 4 h after CGN by both naproxen (at 1, 3 and 10 mg/kg) and ATB-346 (at 1.6 and 4.8 mg/kg; P < 0.001), as well as leukocyte infiltration. Naproxen (but not ATB-346) induced significant gastric damage and, despite the increased gastric MPO activity by ~130% in the naproxen-, but not in the ATB-346-treated rats, this effect was of no statistical significance. CONCLUSION: The presence of a H2S-releasing moiety in the ATB-346 structure does not impair the antiinflammatory activity of the parent compound in rats with CGN-induced synovitis. In addition, released H2S may account for the absence of deleterious gastric effects, thus making of ATB-346 a potentially useful therapeutic alternative to traditional naproxen for treatment of patients with arthritis.