Steklov-type eigenvalues associated with best Sobolev trace constants: domain perturbation and overdetermined systems

We consider a variant of the classic Steklov eigenvalue problem, which arises in the study of the best trace constant for functions in Sobolev space. We prove that the elementary symmetric functions of the eigenvalues depend real-analytically upon variation of the underlying domain and we compute the corresponding Hadamard-type formulas for the shape derivatives. We also consider isovolumetric and isoperimetric domain perturbations and we characterize the corresponding critical domains in terms of appropriate overdetermined systems. Finally, we prove that balls are critical domains for the elementary symmetric functions of the eigenvalues subject to volume or perimeter constraint

Improved functionalization of oleic acid-coated iron oxide nanoparticles for biomedical applications

Superparamagnetic iron oxide nanoparticles can providemultiple benefits for biomedical applications in aqueous environments such asmagnetic separation or magnetic resonance imaging. To increase the colloidal stability and allow subsequent reactions, the introduction of hydrophilic functional groups onto the particles’ surface is essential. During this process, the original coating is exchanged by preferably covalently bonded ligands such as trialkoxysilanes. The duration of the silane exchange reaction, which commonly takes more than 24 h, is an important drawback for this approach. In this paper, we present a novel method, which introduces ultrasonication as an energy source to dramatically accelerate this process, resulting in high-quality waterdispersible nanoparticles around 10 nmin size. To prove the generic character, different functional groups were introduced on the surface including polyethylene glycol chains, carboxylic acid, amine, and thiol groups. Their colloidal stability in various aqueous buffer solutions as well as human plasma and serum was investigated to allow implementation in biomedical and sensing applications.status: publishe

Canagliflozin and Renal Outcomes in Type 2 Diabetes and Nephropathy

BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodium–glucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to 300 to 5000) and were treated with renin–angiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of <15 ml per minute per 1.73 m 2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P<0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P<0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years

Cardiovascular Efficacy and Safety of Bococizumab in High-Risk Patients

Bococizumab is a humanized monoclonal antibody that inhibits proprotein convertase subtilisin- kexin type 9 (PCSK9) and reduces levels of low-density lipoprotein (LDL) cholesterol. We sought to evaluate the efficacy of bococizumab in patients at high cardiovascular risk. METHODS In two parallel, multinational trials with different entry criteria for LDL cholesterol levels, we randomly assigned the 27,438 patients in the combined trials to receive bococizumab (at a dose of 150 mg) subcutaneously every 2 weeks or placebo. The primary end point was nonfatal myocardial infarction, nonfatal stroke, hospitalization for unstable angina requiring urgent revascularization, or cardiovascular death; 93% of the patients were receiving statin therapy at baseline. The trials were stopped early after the sponsor elected to discontinue the development of bococizumab owing in part to the development of high rates of antidrug antibodies, as seen in data from other studies in the program. The median follow-up was 10 months. RESULTS At 14 weeks, patients in the combined trials had a mean change from baseline in LDL cholesterol levels of -56.0% in the bococizumab group and +2.9% in the placebo group, for a between-group difference of -59.0 percentage points (P<0.001) and a median reduction from baseline of 64.2% (P<0.001). In the lower-risk, shorter-duration trial (in which the patients had a baseline LDL cholesterol level of ≥70 mg per deciliter [1.8 mmol per liter] and the median follow-up was 7 months), major cardiovascular events occurred in 173 patients each in the bococizumab group and the placebo group (hazard ratio, 0.99; 95% confidence interval [CI], 0.80 to 1.22; P = 0.94). In the higher-risk, longer-duration trial (in which the patients had a baseline LDL cholesterol level of ≥100 mg per deciliter [2.6 mmol per liter] and the median follow-up was 12 months), major cardiovascular events occurred in 179 and 224 patients, respectively (hazard ratio, 0.79; 95% CI, 0.65 to 0.97; P = 0.02). The hazard ratio for the primary end point in the combined trials was 0.88 (95% CI, 0.76 to 1.02; P = 0.08). Injection-site reactions were more common in the bococizumab group than in the placebo group (10.4% vs. 1.3%, P<0.001). CONCLUSIONS In two randomized trials comparing the PCSK9 inhibitor bococizumab with placebo, bococizumab had no benefit with respect to major adverse cardiovascular events in the trial involving lower-risk patients but did have a significant benefit in the trial involving higher-risk patients

Ezetimibe added to statin therapy after acute coronary syndromes

BACKGROUND: Statin therapy reduces low-density lipoprotein (LDL) cholesterol levels and the risk of cardiovascular events, but whether the addition of ezetimibe, a nonstatin drug that reduces intestinal cholesterol absorption, can reduce the rate of cardiovascular events further is not known. METHODS: We conducted a double-blind, randomized trial involving 18,144 patients who had been hospitalized for an acute coronary syndrome within the preceding 10 days and had LDL cholesterol levels of 50 to 100 mg per deciliter (1.3 to 2.6 mmol per liter) if they were receiving lipid-lowering therapy or 50 to 125 mg per deciliter (1.3 to 3.2 mmol per liter) if they were not receiving lipid-lowering therapy. The combination of simvastatin (40 mg) and ezetimibe (10 mg) (simvastatin-ezetimibe) was compared with simvastatin (40 mg) and placebo (simvastatin monotherapy). The primary end point was a composite of cardiovascular death, nonfatal myocardial infarction, unstable angina requiring rehospitalization, coronary revascularization ( 6530 days after randomization), or nonfatal stroke. The median follow-up was 6 years. RESULTS: The median time-weighted average LDL cholesterol level during the study was 53.7 mg per deciliter (1.4 mmol per liter) in the simvastatin-ezetimibe group, as compared with 69.5 mg per deciliter (1.8 mmol per liter) in the simvastatin-monotherapy group (P<0.001). The Kaplan-Meier event rate for the primary end point at 7 years was 32.7% in the simvastatin-ezetimibe group, as compared with 34.7% in the simvastatin-monotherapy group (absolute risk difference, 2.0 percentage points; hazard ratio, 0.936; 95% confidence interval, 0.89 to 0.99; P = 0.016). Rates of pre-specified muscle, gallbladder, and hepatic adverse effects and cancer were similar in the two groups. CONCLUSIONS: When added to statin therapy, ezetimibe resulted in incremental lowering of LDL cholesterol levels and improved cardiovascular outcomes. Moreover, lowering LDL cholesterol to levels below previous targets provided additional benefit

The Canagliflozin and Renal Endpoints in Diabetes with Established Nephropathy Clinical Evaluation (CREDENCE) Study Rationale, Design, and Baseline Characteristics

Background: People with diabetes and kidney disease have a high risk of cardiovascular events and progression of kidney disease. Sodium glucose co-transporter 2 inhibitors lower plasma glucose by reducing the uptake of filtered glucose in the kidney tubule, leading to increased urinary glucose excretion. They have been repeatedly shown to induce modest natriuresis and reduce HbA1c, blood pressure, weight, and albuminuria in patients with type 2 diabetes. However, the effects of these agents on kidney and cardiovascular events have not been extensively studied in patients with type 2 diabetes and established kidney disease. Methods: The Canagliflozin and Renal Endpoints in Diabetes with Established Nephropathy Clinical Evaluation (CREDENCE) trial aims to compare the efficacy and safety of canagliflozin ­versus placebo at preventing clinically important kidney and cardiovascular outcomes in patients with diabetes and established kidney disease. CREDENCE is a randomized, double-blind, event-driven, placebo-controlled trial set in in 34 countries with a projected duration of â\u88¼5.5 years and enrolling 4,401 adults with type 2 diabetes, estimated glomerular filtration rate â\u89¥30 to 300 to â\u89¤5,000 mg/g). The study has 90% power to detect a 20% reduction in the risk of the primary outcome (α = 0.05), the composite of end-stage kidney disease, doubling of serum creatinine, and renal or cardiovascular death. Conclusion: CREDENCE will provide definitive evidence about the effects of canagliflozin on renal (and cardiovascular) outcomes in patients with type 2 diabetes and established kidney disease. Trial Registration: EudraCT number: 2013-004494-28; ClinicalTrials.gov identifier: NCT02065791