A remark on an overdetermined problem in Riemannian Geometry

Let $(M,g)$ be a Riemannian manifold with a distinguished point $O$ and assume that the geodesic distance $d$ from $O$ is an isoparametric function. Let $\Omega\subset M$ be a bounded domain, with $O \in \Omega$, and consider the problem $\Delta_p u = -1$ in $\Omega$ with $u=0$ on $\partial \Omega$, where $\Delta_p$ is the $p$-Laplacian of $g$. We prove that if the normal derivative $\partial_{\nu}u$ of $u$ along the boundary of $\Omega$ is a function of $d$ satisfying suitable conditions, then $\Omega$ must be a geodesic ball. In particular, our result applies to open balls of $\mathbb{R}^n$ equipped with a rotationally symmetric metric of the form $g=dt^2+\rho^2(t)\,g_S$, where $g_S$ is the standard metric of the sphere.Comment: 8 pages. This paper has been written for possible publication in a special volume dedicated to the conference "Geometric Properties for Parabolic and Elliptic PDE's. 4th Italian-Japanese Workshop", organized in Palinuro in May 201

Dynamics of extracellular matrix in ovarian follicles and corpora lutea of mice

Despite the mouse being an important laboratory species, little is known about changes in its extracellular matrix (ECM) during follicle and corpora lutea formation and regression. Follicle development was induced in mice (29 days of age/experimental day 0) by injections of pregnant mare’s serum gonadotrophin on days 0 and 1 and ovulation was induced by injection of human chorionic gonadotrophin on day 2. Ovaries were collected for immunohistochemistry (n=10 per group) on days 0, 2 and 5. Another group was mated and ovaries were examined on day 11 (n=7). Collagen type IV α1 and α2, laminin α1, β1 and γ1 chains, nidogens 1 and 2 and perlecan were present in the follicular basal lamina of all developmental stages. Collagen type XVIII was only found in basal lamina of primordial, primary and some preantral follicles, whereas laminin α2 was only detected in some preantral and antral follicles. The focimatrix, a specialised matrix of the membrana granulosa, contained collagen type IV α1 and α2, laminin α1, β1 and γ1 chains, nidogens 1 and 2, perlecan and collagen type XVIII. In the corpora lutea, staining was restricted to capillary sub-endothelial basal laminas containing collagen type IV α1 and α2, laminin α1, β1 and γ1 chains, nidogens 1 and 2, perlecan and collagen type XVIII. Laminins α4 and α5 were not immunolocalised to any structure in the mouse ovary. The ECM composition of the mouse ovary has similarities to, but also major differences from, other species with respect to nidogens 1 and 2 and perlecan

In vitro morphological studies on antibody-dependent nonimmune lymphocyte-mediated cytotoxicity in chronic active liver disease

Using an in vitro system of antibody-dependent cellular cytotoxicity (ADCC), the killing effect of chronic liver disease sera on target Chang cells, mediated by effector nonimmune lymphocytes (NLy), was studied. NLy destroyed Chang cells in monolayers pretreated with sera of patients with chronic active liver disease (CALD). Sera from these patients with CALD, after receiving steroid therapy, demonstrated a significant decrease of the cytotoxic action of NLy. The target cells treated with sera of normal subjects or patients with chronic persistent hepatitis were only minimally affected. Morphological observations of the cytotoxic action in a CALD serum-treated group showed intimate contact between NLy and the target cells in the areas of the plaques, where large numbers of the target Chang cells were injured and were closely associated with effector NLy. The Chang cells developed cytoplasmic swelling. The surface became ruffled, and intracytoplasmic organelles displayed vesicular degeneration. Thereafter, cell rupture and fragmentation occurred. The sera in patients with CALD appear to possess a membrane reactive factor, presumably antibody, against the surface membrane of Chang cells. This immunological mode of reaction between the effectors and target cells (ADCC) may be important in the perpetuation and pathogenesis of hepatocyte death in CALD.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44386/1/10620_2005_Article_BF01073183.pd

Identifying associations between diabetes and acute respiratory distress syndrome in patients with acute hypoxemic respiratory failure: an analysis of the LUNG SAFE database

Background: Diabetes mellitus is a common co-existing disease in the critically ill. Diabetes mellitus may reduce the risk of acute respiratory distress syndrome (ARDS), but data from previous studies are conflicting. The objective of this study was to evaluate associations between pre-existing diabetes mellitus and ARDS in critically ill patients with acute hypoxemic respiratory failure (AHRF). Methods: An ancillary analysis of a global, multi-centre prospective observational study (LUNG SAFE) was undertaken. LUNG SAFE evaluated all patients admitted to an intensive care unit (ICU) over a 4-week period, that required mechanical ventilation and met AHRF criteria. Patients who had their AHRF fully explained by cardiac failure were excluded. Important clinical characteristics were included in a stepwise selection approach (forward and backward selection combined with a significance level of 0.05) to identify a set of independent variables associated with having ARDS at any time, developing ARDS (defined as ARDS occurring after day 2 from meeting AHRF criteria) and with hospital mortality. Furthermore, propensity score analysis was undertaken to account for the differences in baseline characteristics between patients with and without diabetes mellitus, and the association between diabetes mellitus and outcomes of interest was assessed on matched samples. Results: Of the 4107 patients with AHRF included in this study, 3022 (73.6%) patients fulfilled ARDS criteria at admission or developed ARDS during their ICU stay. Diabetes mellitus was a pre-existing co-morbidity in 913 patients (22.2% of patients with AHRF). In multivariable analysis, there was no association between diabetes mellitus and having ARDS (OR 0.93 (0.78-1.11); p = 0.39), developing ARDS late (OR 0.79 (0.54-1.15); p = 0.22), or hospital mortality in patients with ARDS (1.15 (0.93-1.42); p = 0.19). In a matched sample of patients, there was no association between diabetes mellitus and outcomes of interest. Conclusions: In a large, global observational study of patients with AHRF, no association was found between diabetes mellitus and having ARDS, developing ARDS, or outcomes from ARDS. Trial registration: NCT02010073. Registered on 12 December 2013

Spontaneous Breathing in Early Acute Respiratory Distress Syndrome: Insights From the Large Observational Study to UNderstand the Global Impact of Severe Acute Respiratory FailurE Study

OBJECTIVES: To describe the characteristics and outcomes of patients with acute respiratory distress syndrome with or without spontaneous breathing and to investigate whether the effects of spontaneous breathing on outcome depend on acute respiratory distress syndrome severity. DESIGN: Planned secondary analysis of a prospective, observational, multicentre cohort study. SETTING: International sample of 459 ICUs from 50 countries. PATIENTS: Patients with acute respiratory distress syndrome and at least 2 days of invasive mechanical ventilation and available data for the mode of mechanical ventilation and respiratory rate for the 2 first days. INTERVENTIONS: Analysis of patients with and without spontaneous breathing, defined by the mode of mechanical ventilation and by actual respiratory rate compared with set respiratory rate during the first 48 hours of mechanical ventilation. MEASUREMENTS AND MAIN RESULTS: Spontaneous breathing was present in 67% of patients with mild acute respiratory distress syndrome, 58% of patients with moderate acute respiratory distress syndrome, and 46% of patients with severe acute respiratory distress syndrome. Patients with spontaneous breathing were older and had lower acute respiratory distress syndrome severity, Sequential Organ Failure Assessment scores, ICU and hospital mortality, and were less likely to be diagnosed with acute respiratory distress syndrome by clinicians. In adjusted analysis, spontaneous breathing during the first 2 days was not associated with an effect on ICU or hospital mortality (33% vs 37%; odds ratio, 1.18 [0.92-1.51]; p = 0.19 and 37% vs 41%; odds ratio, 1.18 [0.93-1.50]; p = 0.196, respectively ). Spontaneous breathing was associated with increased ventilator-free days (13 [0-22] vs 8 [0-20]; p = 0.014) and shorter duration of ICU stay (11 [6-20] vs 12 [7-22]; p = 0.04). CONCLUSIONS: Spontaneous breathing is common in patients with acute respiratory distress syndrome during the first 48 hours of mechanical ventilation. Spontaneous breathing is not associated with worse outcomes and may hasten liberation from the ventilator and from ICU. Although these results support the use of spontaneous breathing in patients with acute respiratory distress syndrome independent of acute respiratory distress syndrome severity, the use of controlled ventilation indicates a bias toward use in patients with higher disease severity. In addition, because the lack of reliable data on inspiratory effort in our study, prospective studies incorporating the magnitude of inspiratory effort and adjusting for all potential severity confounders are required

Epidemiology and patterns of tracheostomy practice in patients with acute respiratory distress syndrome in ICUs across 50 countries

Background: To better understand the epidemiology and patterns of tracheostomy practice for patients with acute respiratory distress syndrome (ARDS), we investigated the current usage of tracheostomy in patients with ARDS recruited into the Large Observational Study to Understand the Global Impact of Severe Acute Respiratory Failure (LUNG-SAFE) study. Methods: This is a secondary analysis of LUNG-SAFE, an international, multicenter, prospective cohort study of patients receiving invasive or noninvasive ventilation in 50 countries spanning 5 continents. The study was carried out over 4 weeks consecutively in the winter of 2014, and 459 ICUs participated. We evaluated the clinical characteristics, management and outcomes of patients that received tracheostomy, in the cohort of patients that developed ARDS on day 1-2 of acute hypoxemic respiratory failure, and in a subsequent propensity-matched cohort. Results: Of the 2377 patients with ARDS that fulfilled the inclusion criteria, 309 (13.0%) underwent tracheostomy during their ICU stay. Patients from high-income European countries (n = 198/1263) more frequently underwent tracheostomy compared to patients from non-European high-income countries (n = 63/649) or patients from middle-income countries (n = 48/465). Only 86/309 (27.8%) underwent tracheostomy on or before day 7, while the median timing of tracheostomy was 14 (Q1-Q3, 7-21) days after onset of ARDS. In the subsample matched by propensity score, ICU and hospital stay were longer in patients with tracheostomy. While patients with tracheostomy had the highest survival probability, there was no difference in 60-day or 90-day mortality in either the patient subgroup that survived for at least 5 days in ICU, or in the propensity-matched subsample. Conclusions: Most patients that receive tracheostomy do so after the first week of critical illness. Tracheostomy may prolong patient survival but does not reduce 60-day or 90-day mortality. Trial registration: ClinicalTrials.gov, NCT02010073. Registered on 12 December 2013