Lowest order Virtual Element approximation of magnetostatic problems

We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general decompositions of the computational domain (as is natural for Virtual Element Methods) and uses as unknowns the (constant) tangential component of the magnetic field $\mathbf{H}$ on each edge, and the vertex values of the Lagrange multiplier $p$ (used to enforce the solenoidality of the magnetic induction $\mathbf{B}=\mu\mathbf{H}$). In this respect the method can be seen as the natural generalization of the lowest order Edge Finite Element Method (the so-called "first kind N\'ed\'elec" elements) to polyhedra of almost arbitrary shape, and as we show on some numerical examples it exhibits very good accuracy (for being a lowest order element) and excellent robustness with respect to distortions

Regulação da produção da eritropoietina e perspectivas terapêuticas na anemia

About 30 years ago, the treatment of chronic renal disease anaemia was revolutionized by the introduction of recombinant human erythropoietin, which reduced the need for blood transfusions. In spite of this huge advance, the first recombinant human erythropoietin has a relatively short half-life and needs to be administered two to three times per week. Subsequently, other molecules were developed, such as darbepoetin alfa, continuous erythropoietin receptor activator (CERA) and peginesatide, with longer half-life, but the route of administration still remains a problem. Erythropoietin has an action that exceeds erythropoiesis and plays an important role in cell protection. Based on knowledge of the molecular mechanisms that control erythropoiesis, namely the regulation of EPO gene expression, through HIF system, GATA-2 and NF-kB, several upcoming therapeutic agents and strategies for stimulating and treating anaemia emerged. The main effort in developing these treatments is to achieve other routes of administration, more convenient for the patient, such as oral therapy, not disregarding an easier production, storage and frequency of administration. Some of them are still in laboratory phase and others already in clinical trials phase II or III. In this work, based on a literature search of studies using MEDLINE, our objective is to review the regulation of erythropoietin production and its functions, as well as treatment approach for anaemia of chronic kidney disease, with particular focus on new therapiesHá cerca de 30 anos atrás, o tratamento da anemia da doença renal crónica foi revolucionado pela introdução da eritropoietina (EPO) humana recombinante que permitiu reduzir drasticamente a necessidade de transfusões sanguíneas. Apesar deste grande avanço, a primeira EPO humana recombinante tem uma semivida relativamente curta e tem de ser administrada duas a três vezes por semana. Subsequentemente, foram desenvolvidas outras moléculas, como a darbepoetina alfa, o ativador contínuo do EPO-R (CERA) e o peginesatide, com uma semivida mais longa, mas a via de administração continua a ser exclusivamente parenteral. A eritropoietina desempenha várias funções além da eritropoiética. Tendo por base os mecanismos moleculares que controlam a eritropoiese, nomeadamente a regulação da expressão do gene da EPO, através do sistema do HIF, GATA-2 e NF-kB, surgiram vários fármacos e estratégias terapêuticas para o tratamento da anemia. O principal objetivo destes novos tratamentos passa por desenvolver outras vias de administração, mais cómodas para o doente, como a terapia oral, e facilitar a produção, armazenamento e frequência de administração dos fármacos. Alguns destes ainda se encontram em fase laboratorial, enquanto outros já estão em ensaios clínicos fase II ou III. Neste trabalho, baseado na revisão bibliográfica de artigos científicos publicados na MEDLINE, procuramos rever a regulação da produção da EPO e respetivas funções, bem como abordar o tratamento da anemia da doença renal crónica, com especial enfoque nas novas terapêutica

SUPG-stabilized Virtual Elements for diffusion-convection problems: a robustness analysis

The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced in [Benedetto et al, CMAME 2016] we are able to show an "almost uniform" error bound (in the sense that the unique term that depends in an unfavorable way on the parameters is damped by a higher order mesh-size multiplicative factor). We also introduce a novel discretization of the convection term that allows us to develop error estimates that are fully robust in the convection dominated cases. We finally present some numerical result

A family of three-dimensional virtual elements with applications to magnetostatic

We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the formulation of F. Kikuchi. In doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a general polyhedral decomposition (assuming that internal degrees of freedom could be more easily eliminated by static condensation). These new spaces are meant, more generally, for the combined approximation of $H^1$-conforming ($0$-forms), $H({\rm {\bf curl}})$-conforming ($1$-forms), and $H({\rm div})$-conforming ($2$-forms) functional spaces in three dimensions, and they would surely be useful for other problems and in more general contexts.Comment: Submitted to SINU

Spatially Resolved Spitzer-IRS Spectral Maps of the Superwind in M82

We have mapped the superwind/halo region of the nearby starburst galaxy M82 in the mid-infrared with $Spitzer-IRS$. The spectral regions covered include the H$_2 S(1)-S(3)$, [NeII], [NeIII] emission lines and PAH features. We estimate the total warm H$_2$ mass and the kinetic energy of the outflowing warm molecular gas to be between $M_{warm}\sim5-17\times10^6$ M$_{\odot}$ and $E_{K}\sim6-20\times10^{53}$ erg. Using the ratios of the 6.2, 7.7 and 11.3 micron PAH features in the IRS spectra, we are able to estimate the average size and ionization state of the small grains in the superwind. There are large variations in the PAH flux ratios throughout the outflow. The 11.3/7.7 and the 6.2/7.7 PAH ratios both vary by more than a factor of five across the wind region. The Northern part of the wind has a significant population of PAH's with smaller 6.2/7.7 ratios than either the starburst disk or the Southern wind, indicating that on average, PAH emitters are larger and more ionized. The warm molecular gas to PAH flux ratios (H$_2/PAH$) are enhanced in the outflow by factors of 10-100 as compared to the starburst disk. This enhancement in the H$_2/PAH$ ratio does not seem to follow the ionization of the atomic gas (as measured with the [NeIII]/[NeII] line flux ratio) in the outflow. This suggests that much of the warm H$_2$ in the outflow is excited by shocks. The observed H$_2$ line intensities can be reproduced with low velocity shocks ($v < 40$ km s$^{-1}$) driven into moderately dense molecular gas ($10^2 <n_H < 10^4$ cm$^{-3}$) entrained in the outflow.Comment: 19 pages and 12 figures; accepted in MNRA

Urinary Biomarkers for Kidney Disease in ATTR Amyloidosis

Aim: The detection and prognosis of nephropathy in transthyretin amyloidosis depends on albuminuria and renal function. Knowing that urinary levels of alpha-1 microglobulin and beta-2 microglobulin reflect tubular dysfunction while urinary alpha-2 macroglobulin implies glomerular damage, we decide investigate the diagnostic value of these markers in the patients with transthyretin amyloidosis. Methods: Serum and urinary samples collected from 30 patients and 11 asymptomatic carriers were tested for alpha-1 microglobulin, beta-2 microglobulin, alpha-2 macroglobulin, albumin, creatinine and cystatin C. Results: Pathological urinary alpha-1 microglobulin was detected in 17 patients, beta-2 microglobulin in 6 and alpha-2 macroglobulin in 5; 5 patients had albuminuria (mg/g creatinine) 30-300 and in 20 patients values >300 were present. Asymptomatic carriers did not present pathological excretion of these biomarkers and albuminuria was >30 in 1 individual. The excretion rates of alpha-1 microglobulin and beta-2 microglobulin were positively correlated with albuminuria (P<0.001), serum creatinine (P<0.05) and cystatin C (P<0.001). Urinary alpha-2 macroglobulin was almost exclusively found in the presence of albuminuria, although their levels do not correlate. Conclusion: Urinary biomarkers emerge as a potential approach to detect renal disease but unexpectedly, urinary alpha-2 macroglobulin was not a marker of the severity of albuminuria