The PML for rough surface scattering

In this paper we investigate the use of the perfectly matched layer (PML) to truncate a time harmonic rough surface scattering problem in the direction away from the scatterer. We prove existence and uniqueness of the solution of the truncated problem as well as an error estimate depending on the thickness and composition of the layer. This global error estimate predicts a linear rate of convergence (under some conditions on the relative size of the real and imaginary parts of the PML function) rather than the usual exponential rate. We then consider scattering by a half-space and show that the solution of the PML truncated problem converges globally at most quadratically (up to logarithmic factors), providing support for our general theory. However we also prove exponential convergence on compact subsets. We continue by proposing an iterative correction method for the PML truncated problem and, using our estimate for the PML approximation, prove convergence of this method. Finally we provide some numerical results in 2D.(C) 2008 IMACS. Published by Elsevier B.V. All rights reserved

Beneficial effect of prolonged heme oxygenase 1 activation in a rat model of chronic heart failure.

SUMMARY We and others have previously demonstrated that heme oxygenase 1 (HO-1) induction by acute hemin administration exerts cardioprotective effects. Here, we developed a rat model of heart failure to investigate whether a long-term induction of HO-1 by chronic hemin administration exerted protective effects. Sprague Dawley rats that underwent permanent ligation of the left coronary artery were closely monitored for survival rate analysis and sacrificed on day 28 post-operation. Administration of hemin (4 mg/kg body weight) every other day for 4 weeks induced a massive increase in HO-1 expression and activity, as shown by the increased levels of the two main metabolic products of heme degradation, bilirubin and carbon monoxide (CO). These effects were associated with significant improvement in survival and reduced the extension of myocardial damage. The ischemic hearts of the hemin-treated animals displayed reduced oxidative stress and apoptosis in comparison with the non-treated rats, as shown by the decreased levels of lipid peroxidation, free-radical-induced DNA damage, caspase-3 activity and Bax expression. Besides, chronic HO-1 activation suppressed the elevated levels of myeloperoxidase (MPO) activity, interleukin 1β (IL-1β) production and tumor necrosis factor-α (TNFα) production that were evoked by the ischemic injury, and increased the plasma level of the anti-inflammatory cytokine IL-10. Interestingly, HO-1 inhibitor zinc protoporphyrin IX (ZnPP-IX; 1 mg/kg) lowered bilirubin and CO concentrations to control values, thus abolishing all the cardioprotective effects of hemin. In conclusion, the results demonstrate that chronic HO-1 activation by prolonged administration of hemin improves survival and exerts protective effects in a rat model of myocardial ischemia by exerting a potent antioxidant activity and disrupting multiple levels of the apoptotic and inflammatory cascade