The Riesz-Sobolev inequality provides a sharp upper bound for a trilinear expression involving convolution of indicator functions of sets. Equality is known to hold only for indicator functions of ...appropriately situated intervals. We characterize ordered triples of subsets of ℝ
1
that nearly realize equality, with quantitative bounds of power law form with the optimal exponent.
Objectives The purpose of this study was to examine the incremental value of copeptin for rapid rule out of acute myocardial infarction (AMI). Background The rapid and reliable exclusion of AMI is a ...major unmet clinical need. Copeptin, the C-terminal part of the vasopressin prohormone, as a marker of acute endogenous stress may be useful in this setting. Methods In 487 consecutive patients presenting to the emergency department with symptoms suggestive of AMI, we measured levels of copeptin at presentation, using a novel sandwich immunoluminometric assay in a blinded fashion. The final diagnosis was adjudicated by 2 independent cardiologists using all available data. Results The adjudicated final diagnosis was AMI in 81 patients (17%). Copeptin levels were significantly higher in AMI patients compared with those in patients having other diagnoses (median 20.8 pmol/l vs. 6.0 pmol/l, p < 0.001). The combination of troponin T and copeptin at initial presentation resulted in an area under the receiver-operating characteristic curve of 0.97 (95% confidence interval: 0.95 to 0.98), which was significantly higher than the 0.86 (95% confidence interval: 0.80 to 0.92) for troponin T alone (p < 0.001). A copeptin level <14 pmol/l in combination with a troponin T ≤0.01 μg/l correctly ruled out AMI with a sensitivity of 98.8% and a negative predictive value of 99.7%. Conclusions The additional use of copeptin seems to allow a rapid and reliable rule out of AMI already at presentation and may thereby obviate the need for prolonged monitoring and serial blood sampling in the majority of patients. (Advantageous Predictors of Acute Coronary Syndromes Evaluation APACE; NCT00470587 )
An analogue of the Riesz-Sobolev convolution inequality is formulated and proved for arbitrary compact connected Abelian groups. Maximizers are characterized, and a quantitative stability theorem is ...proved, under natural hypotheses. A corresponding stability theorem for sets whose sumset has nearly minimal measure is also proved, sharpening recent results of other authors. For the special case of the group $\Bbb{R}/\Bbb{Z}$, a continuous deformation of sets is developed, under which a scaled Riesz-Sobolev functional is shown to be nondecreasing.
Aims
Considerable differences in the long‐term trends of heart failure (HF) exist between different countries. To extend the existing knowledge on HF epidemiology in Germany, we analysed trends of ...HF‐related hospitalizations, hospital days and in‐hospital deaths during a 14‐year period (2000–2013).
Methods and results
Data were derived from the official German Federal Health Monitoring System, which includes an annual and complete enumeration of inpatients at the time of discharge from the hospital. HF cases were identified by the primary diagnosis code for HF (I50). From 2000 to 2013, the absolute number of HF‐related hospitalizations increased by 65.4% (239 694–396 380 cases) and by 28.4% after age‐standardization (261–335 per 100 000 population). Accordingly, the absolute number of HF‐related hospital days increased by 22.1% (3.4–4.2 million hospital days), despite a marked decrease by 25.9% in average length of stay (14.3–10.6 days). With approximately 35 000 in‐hospital deaths (∼45 per 100 000 population), the annual number of HF‐related in‐hospital deaths remained consistently high, and in‐hospital mortality rate in HF patients constituted 9.3% in 2013. Patients aged >65 years were disproportionately affected. In 2013, HF was the leading cause of disease‐related hospitalizations and in‐hospital deaths, representing 2.1% and 8.8% of all cases, respectively.
Conclusion
In Germany, the burden of HF is growing further, and the risk of death in HF remains high. These trends can only be partly attributed to demographic developments suggesting an exigent need for increased awareness and enhanced efforts in the prevention and management of HF.
Study objective We aim to prospectively validate the diagnostic accuracy of the recently developed 0-h/1-h algorithm, using high-sensitivity cardiac troponin T (hs-cTnT) for the early rule-out and ...rule-in of acute myocardial infarction. Methods We enrolled patients presenting with suspected acute myocardial infarction and recent (<6 hours) onset of symptoms to the emergency department in a global multicenter diagnostic study. Hs-cTnT (Roche Diagnostics) and sensitive cardiac troponin I (Siemens Healthcare) were measured at presentation and after 1 hour, 2 hours, and 4 to 14 hours in a central laboratory. Patient triage according to the predefined hs-cTnT 0-hour/1-hour algorithm (hs-cTnT below 12 ng/L and Δ1 hour below 3 ng/L to rule out; hs-cTnT at least 52 ng/L or Δ1 hour at least 5 ng/L to rule in; remaining patients to the “observational zone”) was compared against a centrally adjudicated final diagnosis by 2 independent cardiologists (reference standard). The final diagnosis was based on all available information, including coronary angiography and echocardiography results, follow-up data, and serial measurements of sensitive cardiac troponin I, whereas adjudicators remained blinded to hs-cTnT. Results Among 1,282 patients enrolled, acute myocardial infarction was the final diagnosis for 213 (16.6%) patients. Applying the hs-cTnT 0-hour/1-hour algorithm, 813 (63.4%) patients were classified as rule out, 184 (14.4%) were classified as rule in, and 285 (22.2%) were triaged to the observational zone. This resulted in a negative predictive value and sensitivity for acute myocardial infarction of 99.1% (95% confidence interval CI 98.2% to 99.7%) and 96.7% (95% CI 93.4% to 98.7%) in the rule-out zone (7 patients with false-negative results), a positive predictive value and specificity for acute myocardial infarction of 77.2% (95% CI 70.4% to 83.0%) and 96.1% (95% CI 94.7% to 97.2%) in the rule-in zone, and a prevalence of acute myocardial infarction of 22.5% in the observational zone. Conclusion The hs-cTnT 0-hour/1-hour algorithm performs well for early rule-out and rule-in of acute myocardial infarction.
Abstract
In acute heart failure (AHF) syndromes significant respiratory failure (RF) is essentially seen in patients with acute cardiogenic pulmonary oedema (ACPE) or cardiogenic shock (CS). ...Non-invasive ventilation (NIV), the application of positive intrathoracic pressure through an interface, has shown to be useful in the treatment of moderate to severe RF in several scenarios. There are two main modalities of NIV: continuous positive airway pressure (CPAP) and pressure support ventilation (NIPSV) with positive end expiratory pressure. Appropriate equipment and experience is needed for NIPSV, whereas CPAP may be administered without a ventilator, not requiring special training. Both modalities have shown to be effective in ACPE, by a reduction of respiratory distress and the endotracheal intubation rate compared to conventional oxygen therapy, but the impact on mortality is less conclusive. Non-invasive ventilation is also indicated in patients with AHF associated to pulmonary disease and may be considered, after haemodynamic stabilization, in some patients with CS. There are no differences in the outcomes in the studies comparing both techniques, but CPAP is a simpler technique that may be preferred in low-equipped areas like the pre-hospital setting, while NIPSV may be preferable in patients with significant hypercapnia. The new modality ‘high-flow nasal cannula’ seems promising in cases of AHF with less severe RF. The correct selection of patients and interfaces, early application of the technique, the achievement of a good synchrony between patients and the ventilator avoiding excessive leakage, close monitoring, proactive management, and in some cases mild sedation, may warrant the success of the technique.
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