Cubature rules based on bivariate spline quasi-interpolation for weakly singular integrals

In this paper we present a new class of cubature rules with the aim of accurately integrating weakly singular double integrals. In particular we focus on those integrals coming from the discretization of Boundary Integral Equations for 3D Laplace boundary value problems, using a collocation method within the Isogeometric Analysis paradigm. In such setting the regular part of the integrand can be defined as the product of a tensor product B-spline and a general function. The rules are derived by using first the spline quasi-interpolation approach to approximate such function and then the extension of a well known algorithm for spline product to the bivariate setting. In this way efficiency is ensured, since the locality of any spline quasi-interpolation scheme is combined with the capability of an ad--hoc treatment of the B-spline factor. The numerical integration is performed on the whole support of the B-spline factor by exploiting inter-element continuity of the integrand

IgA-BEM for 3D Helmholtz problems using conforming and non-conforming multi-patch discretizations and B-spline tailored numerical integration

An Isogeometric Boundary Element Method (IgA-BEM) is considered for the numerical solution of Helmholtz problems on 3D bounded or unbounded domains, admitting a smooth multi-patch representation of their finite boundary surface. The discretization spaces are formed by C0 inter-patch continuous functional spaces whose restriction to a patch simplifies to the span of tensor product B-splines composed with the given patch NURBS parameterization. Both conforming and non-conforming spaces are allowed, so that local refinement is possible at the patch level. For regular and singular integration, the proposed model utilizes a numerical procedure defined on the support of each trial B-spline function, which makes possible a function-by-function implementation of the matrix assembly phase. Spline quasi-interpolation is the common ingredient of all the considered quadrature rules; in the singular case it is combined with a B-spline recursion over the spline degree and with a singularity extraction technique, extended to the multi-patch setting for the first time. A threshold selection strategy is proposed to automatically distinguish between nearly singular and regular integrals. The non-conforming C0 joints between spline spaces on different patches are implemented as linear constraints based on knot removal conditions, and do not require a hierarchical master-slave relation between neighbouring patches. Numerical examples on relevant benchmarks show that the expected convergence orders are achieved with uniform discretization and a small number of uniformly spaced quadrature nodes

Impact of N-myc amplification on median survival in children with neuroblastoma

Background: Neuroblastoma is the most common extracranial malignant solid tumor in children under 5 years, and it is characterized by wide clinical and biological heterogeneity. N-myc oncogene amplification is considered to be one of the most important prognostic factors used to evaluate survival in these patients. Objectives: The aim of our study was to determine amplification of the N-myc oncogene using real-time quantitative polymerase chain reaction (PCR) and to show the influence of N-myc amplified tumors on the overall survival rate. Patients and Methods: This study is an analytical historical cohort study of forty children with neuroblastoma admitted to the Shafa Hospital, Iran from 1999 to 2010. Paraffined blocks of tumoral tissue were analyzed for N-myc amplification by a PCR. The degree of N-myc amplification was derived from the ratio of the N-myc oncogene and the single copy reference gene, NAGK. In the statistical analysis, a Kaplan-Meier survival analysis was used. Results: We found a variable degree of N-myc amplification, from 3 to 2 200, in 32 of the 40 neuroblastomas (80%). NMYC amplification was seen more frequently in patients older than 2.5 years (71.9%), stage 4 (65.6%) and female (53.1%). Median survival time in the males was significantly longer than in the females (P = 0.03). The overall median survival for N-myc amplified tumor patients was 20 months, and 30 months for the non amplified tumors. Conclusions: The N-myc amplified tumors may increase the probability of more aggressive behavior and rapid tumor progression, especially in advanced stages of neuroblastoma. This study confirmed the importance of obtaining correct measurements of oncogene amplification in the early evaluation of neuroblastomas in order to target more aggressive therapies in patients with a higher risk of cancer progression

Metabolic fate of extracellular NAD in human skin fibroblasts

Extracellular NAD is degraded to pyridine and purine metabolites by different types of surface-located enzymes which are expressed differently on the plasmamembrane of various human cells and tissues. In a previous report, we demonstrated that NAD-glycohydrolase, nucleotide pyrophosphatase and 5'-nucleotidase are located on the outer surface of human skin fibroblasts. Nucleotide pyrophosphatase cleaves NAD to nicotinamide mononucleotide and AMP, and 5'-nucleotidase hydrolyses AMP to adenosine. Cells incubated with NAD, produce nicotinamide, nicotinamide mononucleotide, hypoxanthine and adenine. The absence of ADPribose and adenosine in the extracellular compartment could be due to further catabolism and/or uptake of these products. To clarify the fate of the purine moiety of exogenous NAD, we investigated uptake of the products of NAD hydrolysis using U-[(14)C]-adenine-NAD. ATP was found to be the main labeled intracellular product of exogenous NAD catabolism; ADP, AMP, inosine and adenosine were also detected but in small quantities. Addition of ADPribose or adenosine to the incubation medium decreased uptake of radioactive purine, which, on the contrary, was unaffected by addition of inosine. ADPribose strongly inhibited the activity of ecto-NAD-hydrolyzing enzymes, whereas adenosine did not. Radioactive uptake by purine drastically dropped in fibroblasts incubated with (14)C-NAD and dipyridamole, an inhibitor of adenosine transport. Partial inhibition of [(14)C]-NAD uptake observed in fibroblasts depleted of ATP showed that the transport system requires ATP to some extent. All these findings suggest that adenosine is the purine form taken up by cells, and this hypothesis was confirmed incubating cultured fibroblasts with (14)C-adenosine and analyzing nucleoside uptake and intracellular metabolism under different experimental conditions. Fibroblasts incubated with [(14)C]-adenosine yield the same radioactive products as with [(14)C]-NAD; the absence of inhibition of [(14)C]-adenosine uptake by ADPribose in the presence of alpha-beta methyleneADP, an inhibitor of 5' nucleotidase, demonstrates that ADPribose coming from NAD via NAD-glycohydrolase is finally catabolised to adenosine. These results confirm that adenosine is the NAD hydrolysis product incorporated by cells and further metabolized to ATP, and that adenosine transport is partially ATP dependent

Omalizumab treatment in Samter's triad: case series and review of the literature

OBJECTIVE: Samter’s triad is the combination of asthma, aspirin sensitization, and nasal polyposis. Few data are available on the use of omalizumab in this disease. The study aimed to describe the impact of omalizumab on clinical and functional parameters and the quality of life of a series of patients with Samter’s triad. Moreover, we aimed to provide a review of the literature on this topic. PATIENTS AND METHODS: We retrospectively described four patients with Samter’s triad undergoing omalizumab therapy. Clinical, functional, and immunological data of these patients were collected at baseline and follow-up. RESULTS: Reduction of asthma exacerbations and salbutamol rescue therapy were observed in all patients after anti-IgE treatment together with an improvement in the quality of life. A significant improvement in FEV1, FVC, and FEF25-75 was observed. No major side-effects were observed. A total of 14 studies regarding omalizumab in aspirin-exacerbated respiratory diseases were included in the review, comprising 78 patients. All studies reported a good efficacy in improving asthma control; restoration of aspirin tolerance was repeatedly reported. CONCLUSIONS: The results of our case series and review of the literature suggest that omalizumab effectively improves asthma control, lung function tests, and quality of life in patients with Samter’s triad