Self-similar extinction for a diffusive Hamilton-Jacobi equation with critical absorption

International audienceThe behavior near the extinction time is identified for non-negative solutions to the diffusive Hamilton-Jacobi equation with critical gradient absorption ∂_t u − ∆_p u + |∇u|^{p−1} = 0 in (0, ∞) × R^N , and fast diffusion 2N/(N + 1) < p < 2. Given a non-negative and radially symmetric initial condition with a non-increasing profile which decays sufficiently fast as |x| → ∞, it is shown that the corresponding solution u to the above equation approaches a uniquely determined separate variable solution of the form U (t, x) = (T_e − t)^{1/(2−p)} f_* (|x|), (t, x) ∈ (0, T_e) × R^N , as t → T_e , where T_e denotes the finite extinction time of u. A cornerstone of the convergence proof is an underlying variational structure of the equation. Also, the selected profile f_* is the unique non-negative solution to a second order ordinary differential equation which decays exponentially at infinity. A complete classification of solutions to this equation is provided, thereby describing all separate variable solutions of the original equation. One important difficulty in the uniqueness proof is that no monotonicity argument seems to be available and it is overcome by the construction of an appropriate Pohozaev functional

Acatalasemic mice are mildly susceptible to adriamycin nephropathy and exhibit increased albuminuria and glomerulosclerosis

Background: Catalase is an important antioxidant enzyme that regulates the level of intracellular hydrogen peroxide and hydroxyl radicals. The effects of catalase deficiency on albuminuria and progressive glomerulosclerosis have not yet been fully elucidated. The adriamycin (ADR) nephropathy model is considered to be an experimental model of focal segmental glomerulosclerosis. A functional catalase deficiency was hypothesized to exacerbate albuminuria and the progression of glomerulosclerosis in this model. Methods: ADR was intravenously administered to both homozygous acatalasemic mutant mice (C3H/AnLCs(b)Cs(b)) and control wild-type mice (C3H/AnLCs(a)Cs(a)). The functional and morphological alterations of the kidneys, including albuminuria, renal function, podocytic, glomerular and tubulointerstitial injuries, and the activities of catalase were then compared between the two groups up to 8 weeks after disease induction. Moreover, the presence of a mutation of the toll-like receptor 4 (tlr4) gene, which was previously reported in the C3H/HeJ strain, was investigated in both groups. Results: The ADR-treated mice developed significant albuminuria and glomerulosclerosis, and the degree of these conditions in the ADR-treated acatalasemic mice was higher than that in the wild-type mice. ADR induced progressive renal fibrosis, renal atrophy and lipid peroxide accumulation only in the acatalasemic mice. In addition, the level of catalase activity was significantly lower in the kidneys of the acatalasemic mice than in the wild-type mice during the experimental period. The catalase activity increased after ADR injection in wild-type mice, but the acatalasemic mice did not have the ability to increase their catalase activity under oxidative stress. The C3H/AnL strain was found to be negative for the tlr4 gene mutation. Conclusions: These data indicate that catalase deficiency plays an important role in the progression of renal injury in the ADR nephropathy model

Beta1-Adrenoceptor Polymorphism Predicts Flecainide Action in Patients with Atrial Fibrillation

BACKGROUND: Antiarrhythmic action of flecainide is based on sodium channel blockade. Beta(1)-adrenoceptor (beta(1)AR) activation induces sodium channel inhibition, too. The aim of the present study was to evaluate the impact of different beta(1)AR genotypes on antiarrhythmic action of flecainide in patients with structural heart disease and atrial fibrillation. METHODOLOGY/PRINCIPAL FINDINGS: In 145 subjects, 87 with atrial fibrillation, genotyping was performed to identify the individual beta(1)AR Arg389Gly and Ser49Gly polymorphism. Resting heart rate during atrial fibrillation and success of flecainide-induced cardioversion were correlated with beta(1)AR genotype. The overall cardioversion rate with flecainide was 39%. The Arg389Arg genotype was associated with the highest cardioversion rate (55.5%; OR 3.30; 95% CI; 1.34-8.13; p = 0.003) compared to patients with Arg389Gly (29.5%; OR 0.44; 95% CI; 0.18-1.06; p = 0.066) and Gly389Gly (14%; OR 0.24; 95% CI 0.03-2.07; p = 0.17) variants. The single Ser49Gly polymorphism did not influence the conversion rate. In combination, patients with Arg389Gly-Ser49Gly genotype displayed the lowest conversion rate with 20.8% (OR 0.31; 95% CI; 0.10-0.93; p = 0.03). In patients with Arg389Arg variants the heart rate during atrial fibrillation was significantly higher (110+/-2.7 bpm; p = 0.03 vs. other variants) compared to Arg389Gly (104.8+/-2.4 bpm) and Gly389Gly (96.9+/-5.8 bpm) carriers. The Arg389Gly-Ser49Gly genotype was more common in patients with atrial fibrillation compared to patients without atrial fibrillation (27.6% vs. 5.2%; HR 6.98; 95% CI; 1.99-24.46; p<0.001). CONCLUSIONS: The beta(1)AR Arg389Arg genotype is associated with increased flecainide potency and higher heart rate during atrial fibrillation. The Arg389Gly-Ser49Gly genotype might be of predictive value for atrial fibrillation

Effect of dynamic compressive loading and its combination with a growth factor on the chondrocytic phenotype of 3-dimensional scaffold-embedded chondrocytes

Background and purpose Three-dimensionally (3D-) embedded chondrocytes have been suggested to maintain the chondrocytic phenotype. Furthermore, mechanical stress and growth factors have been found to be capable of enhancing cell proliferation and ECM synthesis. We investigated the effect of mechanical loading and growth factors on reactivation of the 3D-embedded chondrocytes