Weighted Sobolev spaces of radially symmetric functions

We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best constants.Comment: 38 page

Native Hypovitaminosis D in CKD Patients : From Experimental Evidence to Clinical Practice

Native hypovitaminosis D (n-hVITD) is frequently found from the early stages of chronic kidney disease (CKD) and its prevalence increases with CKD progression. Even if the implications of n-hVITD in chronic kidney disease-mineral bone disorder (CKD-MBD) have been extensively characterized in the literature, there is a lot of debate nowadays about the so called "unconventional effects" of native vitamin D (25(OH)VitD) supplementation in CKD patients. In this review, highlights of the dimension of the problem of n-hVITD in CKD stages 2-5 ND patients will be presented. In addition, it will focus on the "unconventional effects" of 25(OH)VitD supplementation, the clinical impact of n-hVITD and the most significant interventional studies regarding 25(OH)VitD supplementation in CKD stages 2-5 ND

Gut microbiota composition and frailty in elderly patients with Chronic Kidney Disease

Background Frailty is common in older patients affected by chronic kidney disease (CKD). Since gut microbiota (gMB) may contribute to frailty, we explored possible associations between gMB and frailty in CKD. Methods We studied 64 CKD patients (stage 3b-4), categorized as frail (F, 38) and not frail (NF, 26) according to Fried criteria, and 15 controls (C), all older than 65 years. In CKD we assessed serum C-reactive protein, blood neutrophil/lymphocyte ratio, Malnutrition-inflammation Score (MIS); gMB was studied by denaturing gel gradient electrophoresis (DGGE), high-throughput sequencing (16S r-RNA gene), and quantitative real-time PCR (RT-PCR). Results No differences in alpha diversity between CKD and C and between F and NF patients emerged, but high-throughput sequencing showed significantly higher abundance of potentially noxious bacteria (Citrobacter, Coprobacillus, etc) and lower abundance of saccharolytic and butyrate-producing bacteria (Prevotella spp., Faecalibacterium prausnitzii, Roseburia spp.), in CKD respect to C. Mogibacteriaceae family and Oscillospira genus abundance was positively related to inflammatory indices in the whole CKD cohort, while that of Akkermansia, Ruminococcus and Eubacterium genera was negatively related. Compared with NF, in F there was a higher abundance of some bacteria (Mogibacteriacee, Coriobacteriacee, Eggerthella, etc), many of which have been described as more abundant in other diseases. Conclusions These results suggest that inflammation and frailty could be associated to gMB modifications in CKD

A new critical curve for the Lane-Emden system

We study stable positive radially symmetric solutions for the Lane-Emden system $-\Delta u=v^p$ in $\R^N$, $-\Delta v=u^q$ in $\R^N$, where $p,q\geq 1$. We obtain a new critical curve that optimally describes the existence of such solutions.Comment: 13 pages, 1 figur

Sarcopenia is Associated with Malnutrition but Not with Systemic Inflammation in Older Persons with Advanced CKD

Background: In patients with chronic kidney disease (CKD), sarcopenia can be determined by a wide spectrum of risk factors. We evaluated the association of sarcopenia with nutritional, behavioral and inflammatory patterns in older patients with advanced CKD. Methods: we cross-sectionally evaluated 113 patients with CKD stages 3b-5. Sarcopenia was defined according to the EWGSOP2 criteria. We assessed: anthropometry, bioelectrical impedance analysis, physical, and psychological performance. Nutritional status was assessed using the Malnutrition Inflammation Score (MIS) and by verifying the eventual presence Protein Energy Wasting syndrome (PEW). Systemic inflammation was assessed by dosing: CRP, IL6, TNF\u3b1, MCP1, IL10, IL17, fetuin, IL12. Results: 24% of patients were sarcopenic. Sarcopenic individuals had lower creatinine clearance (18 \ub1 11 vs. 23 \ub1 19 mL/min; p = 0.0087) as well as lower BMI (24.8 \ub1 3.0 vs. 28.4 \ub1 5.5 Kg/m2; p < 0.0001) and a lower FTI (11.6 \ub1 3.9 vs. 14.4 \ub1 5.1 kg/m2, p = 0.023). Sarcopenic persons had higher prevalence of PEW (52 vs. 20%, p < 0.0001) and a tendency to have higher MIS (6.6 \ub1 6.5 vs. 4.5 \ub1 4.0, p = 0.09); however, they did not show any difference in systemic inflammation compared to non-sarcopenic individuals. Conclusions: CKD sarcopenic patients were more malnourished than non-sarcopenic ones, but the two groups did not show any difference in systemic inflammation

Hybrid fibroin/polyurethane small-diameter vascular grafts: from fabrication to in vivo preliminary assessment

To address the need of alternatives to autologous vessels for small-calibre vascular applications (e.g. cardiac surgery), a bio-hybrid semi-degradable material composed of silk fibroin (SF) and polyurethane (Silkothane (R)) was herein used to fabricate very small-calibre grafts (o(in) = 1.5 mm) via electrospinning. Bio-hybrid grafts were in vitro characterized in terms of morphology and mechanical behaviour, and compared to similar grafts of pure SF. Similarly, two native vessels from a rodent model (abdominal aorta and vena cava) were harvested and characterized. Preliminary implants were performed on Lewis rats to confirm the suitability of Silkothane (R) grafts for small-calibre applications, specifically as aortic insertion and femoral shunt. The manufacturing process generated pliable grafts consisting of a randomized fibrous mesh and exhibiting similar geometrical features to rat aortas. Both Silkothane (R) and pure SF grafts showed radial compliances in the range from 1.37 +/- 0.86 to 1.88 +/- 1.01% 10(-2) mmHg(-1), lower than that of native vessels. The Silkothane (R) small-calibre devices were also implanted in rats demonstrating to be adequate for vascular applications; all the treated rats survived the surgery for three months after implantation, and 16 rats out of 17 (94%) still showed blood flow inside the graft at sacrifice. The obtained results lay the basis for a deeper investigation of the interaction between the Silkothane (R) graft and the implant site, which may deal with further analysis on the potentialities in terms of degradability and tissue formation, on longer time-points