Vibrational modes of circular free plates under tension

The vibrational frequencies of a plate under tension are given by the eigenvalues $\omega$ of the equation $\Delta^2u-\tau\Delta u=\omega u$. This paper determines the eigenfunctions and eigenvalues of this bi-Laplace problem on the ball under natural (free) boundary conditions. In particular, the fundamental modes --- the eigenfunctions of the lowest nonzero eigenvalue --- are identified and found to have simple angular dependence.Comment: 17 pages. To be submitted for publication shortly

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Misdiagnosis of narcolepsy

BACKGROUND: Narcolepsy is a chronic primary sleep disorder, characterized by excessive daytime sleepiness and sleep dysfunction with or without cataplexy. Narcolepsy is uncommon, with a low prevalence rate which makes it difficult to diagnose definitively without a complex series of tests and a detailed history. The aim of this study was to review patients referred to a tertiary sleep centre who had been labelled with a diagnosis of narcolepsy prior to referral in order to assess if the diagnosis was accurate, and if not, to determine the cause of diagnostic misattribution. METHODS: All patients seen at a sleep centre from 2007–2013 (n = 551) who underwent detailed objective testing including an MSLT PSG, as well as wearing an actigraphy watch and completing a sleep diary for 2 weeks, were assessed for a pre-referral and final diagnosis of narcolepsy. RESULTS: Of the 41 directly referred patients with a diagnostic label of narcolepsy, 19 (46 %) were subsequently confirmed to have narcolepsy on objective testing and assessment by a sleep physician using ICSD-2 criteria. CONCLUSIONS: The diagnosis of narcolepsy was incorrectly attributed to almost 50 % of patients labelled with a diagnosis of narcolepsy who were referred for further opinion by a variety of specialists and generalists. Accurate diagnosis of narcolepsy is critical for many reasons, such as the impact it has on quality of life, driving, employment, insurance and pregnancy in women as well as medication management

Walk well:a randomised controlled trial of a walking intervention for adults with intellectual disabilities: study protocol

Background - Walking interventions have been shown to have a positive impact on physical activity (PA) levels, health and wellbeing for adult and older adult populations. There has been very little work carried out to explore the effectiveness of walking interventions for adults with intellectual disabilities. This paper will provide details of the Walk Well intervention, designed for adults with intellectual disabilities, and a randomised controlled trial (RCT) to test its effectiveness. Methods/design - This study will adopt a RCT design, with participants allocated to the walking intervention group or a waiting list control group. The intervention consists of three PA consultations (baseline, six weeks and 12 weeks) and an individualised 12 week walking programme. A range of measures will be completed by participants at baseline, post intervention (three months from baseline) and at follow up (three months post intervention and six months from baseline). All outcome measures will be collected by a researcher who will be blinded to the study groups. The primary outcome will be steps walked per day, measured using accelerometers. Secondary outcome measures will include time spent in PA per day (across various intensity levels), time spent in sedentary behaviour per day, quality of life, self-efficacy and anthropometric measures to monitor weight change. Discussion - Since there are currently no published RCTs of walking interventions for adults with intellectual disabilities, this RCT will examine if a walking intervention can successfully increase PA, health and wellbeing of adults with intellectual disabilities

Non-Invasive Molecular Imaging of Fibrosis Using a Collagen-Targeted Peptidomimetic of the Platelet Collagen Receptor Glycoprotein VI

Background: Fibrosis, which is characterized by the pathological accumulation of collagen, is recognized as an important feature of many chronic diseases, and as such, constitutes an enormous health burden. We need non-invasive specific methods for the early diagnosis and follow-up of fibrosis in various disorders. Collagen targeting molecules are therefore of interest for potential in vivo imaging of fibrosis. In this study, we developed a collagen-specific probe using a new approach that takes advantage of the inherent specificity of Glycoprotein VI (GPVI), the main platelet receptor for collagens I and III. Methodology/Principal: Findings An anti-GPVI antibody that neutralizes collagen-binding was used to screen a bacterial random peptide library. A cyclic motif was identified, and the corresponding peptide (designated collagelin) was synthesized. Solid-phase binding assays and histochemical analysis showed that collagelin specifically bound to collagen (Kd 10−7 M) in vitro, and labelled collagen fibers ex vivo on sections of rat aorta and rat tail. Collagelin is therefore a new specific probe for collagen. The suitability of collagelin as an in vivo probe was tested in a rat model of healed myocardial infarctions (MI). Injecting Tc-99m-labelled collagelin and scintigraphic imaging showed that uptake of the probe occurred in the cardiac area of rats with MI, but not in controls. Post mortem autoradiography and histological analysis of heart sections showed that the labeled areas coincided with fibrosis. Scintigraphic molecular imaging with collagelin provides high resolution, and good contrast between the fibrotic scars and healthy tissues. The capacity of collagelin to image fibrosis in vivo was confirmed in a mouse model of lung fibrosis. Conclusion/Significance: Collagelin is a new collagen-targeting agent which may be useful for non-invasive detection of fibrosis in a broad spectrum of diseases.Psycholog

Remodelling of the angular collagen fiber distribution in cardiovascular tissues

Understanding collagen fiber remodelling is desired to optimize the mechanical conditioning protocols in tissue-engineering of load-bearing cardiovascular structures. Mathematical models offer strong possibilities to gain insight into the mechanisms and mechanical stimuli involved in these remodelling processes. In this study, a framework is proposed to investigate remodelling of angular collagen fiber distribution in cardiovascular tissues. A structurally based model for collagenous cardiovascular tissues is extended with remodelling laws for the collagen architecture, and the model is subsequently applied to the arterial wall and aortic valve. For the arterial wall, the model predicts the presence of two helically arranged families of collagen fibers. A branching, diverging hammock-type fiber architecture is predicted for the aortic valve. It is expected that the proposed model may be of great potential for the design of improved tissue engineering protocols and may give further insight into the pathophysiology of cardiovascular diseases

SCN5A mutations in 442 neonates and children: genotype-phenotype correlation and identification of higher-risk subgroups.

Aims To clarify the clinical characteristics and outcomes of children with SCN5A-mediated disease and to improve their risk stratification. Methods and results A multicentre, international, retrospective cohort study was conducted in 25 tertiary hospitals in 13 countries between 1990 and 2015. All patients ≤16 years of age diagnosed with a genetically confirmed SCN5A mutation were included in the analysis. There was no restriction made based on their clinical diagnosis. A total of 442 children {55.7% boys, 40.3% probands, median age: 8.0 [interquartile range (IQR) 9.5] years} from 350 families were included; 67.9% were asymptomatic at diagnosis. Four main phenotypes were identified: isolated progressive cardiac conduction disorders (25.6%), overlap phenotype (15.6%), isolated long QT syndrome type 3 (10.6%), and isolated Brugada syndrome type 1 (1.8%); 44.3% had a negative electrocardiogram phenotype. During a median follow-up of 5.9 (IQR 5.9) years, 272 cardiac events (CEs) occurred in 139 (31.5%) patients. Patients whose mutation localized in the C-terminus had a lower risk. Compound genotype, both gain- and loss-of-function SCN5A mutation, age ≤1 year at diagnosis in probands and age ≤1 year at diagnosis in non-probands were independent predictors of CE. Conclusion In this large paediatric cohort of SCN5A mutation-positive subjects, cardiac conduction disorders were the most prevalent phenotype; CEs occurred in about one-third of genotype-positive children, and several independent risk factors were identified, including age ≤1 year at diagnosis, compound mutation, and mutation with both gain- and loss-of-function