Recursive integral method for transmission eigenvalues

Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse problems for target identification and nondestructive testing. The problem is numerically challenging because it is non-selfadjoint and nonlinear. In this paper, we propose a recursive integral method for computing transmission eigenvalues from a finite element discretization of the continuous problem. The method, which overcomes some difficulties of existing methods, is based on eigenprojectors of compact operators. It is self-correcting, can separate nearby eigenvalues, and does not require an initial approximation based on some a priori spectral information. These features make the method well suited for the transmission eigenvalue problem whose spectrum is complicated. Numerical examples show that the method is effective and robust.Comment: 18 pages, 8 figure

Twenty year predictors of peripheral arterial disease (PAD) compared with coronary heart disease (CHD) in the Scottish Heart Health Extended Cohort (SHHEC)

Background Coronary heart disease (CHD) and peripheral arterial disease (PAD) affect different vascular territories. Supplementing baseline findings with assays from stored serum, we compared their twenty-year predictors. Methods and Results Recruited randomly across Scotland 1984-1995 and followed through 2009 for death and hospital diagnoses, of 15 737 disease-free men and women aged 30-75y, 3098 developed CHD (19.7%), and 499 PAD (3.2%). Hazard ratios (HRs) for 45 variables in the Cox model were adjusted for age and sex, and for factors in the 2007 ASSIGN cardiovascular risk score. Forty four were entered into parsimonious predictive models, tested by c-statistics and NRIs (Net Reclassification Improvements). Many HRs diminished with adjustment and parsimonious modeling, leaving significant survivors. HRs were mostly higher in PAD. New parsimonious models increased the c-statistic and NRI over ASSIGN variables alone, but varied in their components and ranking. CHD and PAD shared seven of the nine factors from ASSIGN: age, sex, family history, socioeconomic status, diabetes mellitus, tobacco smoking, and systolic blood pressure (SBP), (but not total, nor HDL-cholesterol), plus four new ones: NT-pro BNP, cotinine, hsC-Reactive Protein, and cystatin-C. Highest ranked HRs for continuous factors in CHD were: age, total cholesterol, hsTroponin, NT-pro-BNP, cotinine, apolipoprotein A, waist circumference, (…plus ten more); in PAD: age, hsCRP, SBP, expired carbon monoxide, cotinine, socioeconomic status, lipoprotein (a), (…plus five more). Conclusion The mixture of shared with disparate determinants for arterial disease in the heart and the legs implies non-identical pathogenesis–cholesterol dominant in the former–inflammation (hsCRP, diabetes, smoking) in the latter

QT peak prolongation predicts cardiac death following stroke

Cardiac death has been linked in many populations to prolongation of the QT interval (QTe). However, basic science research suggested that the best estimate of the time point when repolarisation begins is near the T-wave peak. We found QT peak (QTp) was longer in hypertensive subjects with LVH. A prolonged “depolarisation” phase, rather than “repolarisation” (T peak to T end) might therefore account for the higher incidence of cardiac death linked to long QT. Hypothesis: We have tested the hypothesis that QT peak (QTp) prolongation predicts cardiac death in stroke survivors. Methods and Results: ECGs were recorded from 296 stroke survivors (152 male), mean age 67.2 (SD 11.6) approximately 1 year after the event. Their mean blood pressure was 152/88 mmHg (SD 29/15mmHg). These ECGs were digitised by one observer who was blinded to patient outcome. The patients were followed up for a median of 3.3 years. The primary endpoint was cardiac death. A prolonged heart rate corrected QT peak (QTpc) of lead I carried the highest relative risk of death from all cause as well as cardiac death, when compared with the other more conventional QT indices. In multivariate analyses, when adjusted for conventional risk factors of atherosclerosis, a prolonged QTpc of lead I was still associated with a 3-fold increased risk of cardiac death. (adjusted relative risk 3.0 [95% CI 1.1 - 8.5], p=0.037). Conclusion: QT peak prolongation in lead I predicts cardiac death after strok

Towards understanding the clinical significance of QT peak prolongation: a novel marker of myocardial ischemia independently demonstrated in two prospective studies

Background: QT peak prolongation identified patients at risk of death or non-fatal MI. We tested the hypothesis that QT peak prolongation might be associated with significant myocardial ischaemia in two separate cohorts to see how widely applicable the concept was. Methods and Results: In the first study, 134 stroke survivors were prospectively recruited and had 12-lead ECGs and Nuclear myocardial perfusion scanning. QT peak was measured in lead I of a 12-lead ECG and heart rate corrected by Bazett’s formula (QTpc). QTpc prolongation to 360ms or more was 92% specific at diagnosing severe myocardial ischaemia. This hypothesis-generating study led us to perform a second prospective study in a different cohort of patients who were referred for dobutamine stress echocardiography. 13 of 102 patients had significant myocardial ischaemia. Significant myocardial ischaemia was associated with QT peak prolongation at rest (mean 354ms, 95% CI 341-367ms, compared with mean 332ms, 95% CI 327-337ms in those without significant ischaemia; p=0.002). QT peak prolongation to 360ms or more was 88% specific at diagnosing significant myocardial ischaemia in the stress echocardiography study. QT peak prolongation to 360ms or more was associated with over 4-fold increase odds ratio of significant myocardial ischaemia. The Mantel- Haenszel Common Odds Ratio Estimate=4.4, 95% CI=1.2-16.0, p=0.023. Conclusion: QT peak (QTpc) prolongation to 360ms or more should make us suspect the presence of significant myocardial ischaemia. Such patients merit further investigations for potentially treatable ischaemic heart disease to reduce their risk of subsequent death or non-fatal MI

Tayside Screening For Cardiac Events (TASCFORCE) study : a prospective cardiovascular risk screening study

This study was funded by Chest Heart and Stroke (Scotland) and the Souter Foundation.Purpose: Risk factor-based models struggle to accurately predict the development of cardiovascular disease (CVD) at the level of the individual. Ways of identifying people with low predicted risk who will develop CVD would allow stratified advice and support informed treatment decisions about the initiation or adjustment of preventive medication, and this is the aim of this prospective cohort study. Participants: The Tayside Screening for Cardiac Events (TASCFORCE) study recruited men and women aged≥40 years, free from known CVD, with a predicted 10-year risk of coronary heart disease<20%. If B-type natriuretic peptide (BNP) was greater than their gender median, participants were offered a whole-body contrast-enhanced MRI (WBCE-MRI) scan (cardiac imaging, whole-body angiography to determine left ventricular parameters, delayed gadolinium enhancement, atheroma burden). Blood, including DNA, was stored for future biomarker assays. Participants are being followed up using electronic record-linkage cardiovascular outcomes. Findings to date: 4423 (1740, 39.3% men) were recruited. Mean age was 52.3 years with a median BNP of 7.50 ng/L and 15.30 ng/L for men and women, respectively. 602 had a predicted 10-year risk of 10%-19.9%, with the remainder<10%. Age, female sex, ex-smoking status, lower heart rate, higher high-density lipoprotein and lower total cholesterol were independently associated with higher log10 BNP levels. Mean left ventricular mass was 129.2 g and 87.0 g in men and women, respectively. Future plans: The TASCFORCE study is investigating the ability of a screening programme, using BNP and WBCE-MRI, at the time of enrolment, to evaluate prediction of CVD in a population at low/intermediate risk. Blood stored for future biomarker analyses will allow testing/development of novel biomarkers. We believe this could be a new UK Framingham study allowing study for many years to come. Clinical Trial Registration: ISRCTN38976321.Publisher PDFPeer reviewe

Effect of vitamin D supplementation on blood pressure:a systematic review and meta-analysis incorporating individual patient data

D-PRESSURE Collaboration: et al.[Importance]: Low levels of vitamin D are associated with elevated blood pressure (BP) and future cardiovascular events. Whether vitamin D supplementation reduces BP and which patient characteristics predict a response remain unclear.[Objective]: To systematically review whether supplementation with vitamin D or its analogues reduce BP.[Data Sources]: We searched MEDLINE, CINAHL, EMBASE, Cochrane Central Register of Controlled Trials, and http://www.ClinicalTrials.com augmented by a hand search of references from the included articles and previous reviews. Google was searched for gray literature (ie, material not published in recognized scientific journals). No language restrictions were applied. The search period spanned January 1, 1966, through March 31, 2014.[Study Selection]: We included randomized placebo-controlled clinical trials that used vitamin D supplementation for a minimum of 4 weeks for any indication and reported BP data. Studies were included if they used active or inactive forms of vitamin D or vitamin D analogues. Cointerventions were permitted if identical in all treatment arms.[Data Extraction and Synthesis]: We extracted data on baseline demographics, 25-hydroxyvitamin D levels, systolic and diastolic BP (SBP and DBP), and change in BP from baseline to the final follow-up. Individual patient data on age, sex, medication use, diabetes mellitus, baseline and follow-up BP, and 25-hydroxyvitamin D levels were requested from the authors of the included studies. For trial-level data, between-group differences in BP change were combined in a random-effects model. For individual patient data, between-group differences in BP at the final follow up, adjusted for baseline BP, were calculated before combining in a random-effects model.[Main Outcomes and Measures]: Difference in SBP and DBP measured in an office setting.[Results]: We included 46 trials (4541 participants) in the trial-level meta-analysis. Individual patient data were obtained for 27 trials (3092 participants). At the trial level, no effect of vitamin D supplementation was seen on SBP (effect size, 0.0 [95% CI, −0.8 to 0.8] mm Hg; P = .97; I2 = 21%) or DBP (effect size, −0.1 [95% CI, −0.6 to 0.5] mm Hg; P = .84; I2 = 20%). Similar results were found analyzing individual patient data for SBP (effect size, −0.5 [95% CI, −1.3 to 0.4] mm Hg; P = .27; I2 = 0%) and DBP (effect size, 0.2 [95% CI, −0.3 to 0.7] mm Hg; P = .38; I2 = 0%). Subgroup analysis did not reveal any baseline factor predictive of a better response to therapy.[Conclusions and Relevance]: Vitamin D supplementation is ineffective as an agent for lowering BP and thus should not be used as an antihypertensive agent.Peer reviewe

Xanthine oxidase inhibition for the improvement of long-term outcomes following ischaemic stroke and transient ischaemic attack (XILO-FIST) - Protocol for a randomised double blind placebo-controlled clinical trial

Background: Allopurinol, a xanthine oxidase inhibitor, reduced progression of carotid-intima media thickness and lowered blood pressure in a small clinical trial in people with ischaemic stroke. Xanthine oxidase inhibition for improvement of long-term outcomes following ischaemic stroke and transient ischaemic attack (XILO-FIST) aims to assess the effect of allopurinol treatment on white matter hyperintensity progression and blood pressure after stroke. This paper describes the XILO-FIST protocol. Methods: XILO-FIST is a multicentre randomised double-blind, placebo-controlled, parallel group clinical trial funded by the British Heart Foundation and the Stroke Association. The trial has been adopted by the Scottish Stroke Research Network and the UK Clinical Research Network. The trial is registered in clinicaltrials.gov (registration number NCT02122718). XILO-FIST will randomise 464 participants, aged greater than 50 years, with ischaemic stroke within the past month, on a 1:1 basis, to two years treatment with allopurinol 300 mg twice daily or placebo. Participants will undergo brain magnetic resonance imaging, cognitive assessment, ambulatory blood pressure monitoring and blood sampling at baseline and after two years treatment. The primary outcome will be white matter hyperintensity progression, measured using the Rotterdam progression scale. Secondary outcomes will include change in white matter hyperintensity volume, mean day-time systolic blood pressure and measures of cognitive function. Up to 100 will undergo additional cardiac magnetic resonance imaging in a sub-study of left ventricular mass. Discussion: If white matter hyperintensity progression is reduced, allopurinol could be an effective preventative treatment for patients with ischaemic stroke and clinical endpoint studies would be needed. If allopurinol reduces blood pressure after stroke, then it could be used to help patients reach blood pressure targets