The Heterogeneous Multiscale Method for dispersive Maxwell systems

In this work, we apply the finite element heterogeneous multiscale method to a class of dispersive first-order time-dependent Maxwell systems. For this purpose, we use an analytic homogenization result, which shows that the effective system contains additional dispersive effects. We provide a careful study of the (time-dependent) micro problems, including $\mathrm{H}^2$ and micro errors estimates. Eventually, we prove a semi-discrete error estimate for the method.Comment: 26 page

The heterogeneous multiscale method for dispersive Maxwell systems

In this work, we apply the finite element heterogeneous multiscale method to a class of dispersive first-order time-dependent Maxwell systems. For this purpose, we use an analytic homogenization result, which shows that the effective system contains additional dispersive effects. We provide a careful study of the (time-dependent) micro problems, including $H^2$ and micro errors estimates. Eventually, we prove a semi-discrete error estimate for the method

Numerical homogenization of time-dependent Maxwell\u27s equations with dispersion effects

This thesis studies the propagation of electromagnetic waves in heterogeneous structures such as metamaterials. The governing equations for this problem are Maxwell\u27s equations with highly oscillatory parameters. We use an analytic homogenization result which yields an effective Maxwell system that involves a convolution integral. This convolution represents dispersive effects that result from the interaction of the wave with the (locally) periodic microscopic structure. We discretize in space using the Finite Element Heterogeneous Multiscale Method (FE-HMM) and provide a semi-discrete error estimate. The rigorous error analysis in space is supplemented by a rather standard time discretization at the end of which an efficient, fully discrete method is proposed. This method uses a recursive approximation of the convolution that relies on the assumption that the convolution kernel is an exponential function. Eventually, we present numerical experiments both for the microscopic and the macroscopic scale

Super-localized orthogonal decomposition for high-frequency Helmholtz problems

We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for time-harmonic scattering problems of Helmholtz type with high wavenumber $\kappa$. On a coarse mesh of width $H$, the proposed method identifies local finite element source terms that yield rapidly decaying responses under the solution operator. They can be constructed to high accuracy from independent local snapshot solutions on patches of width $\ell H$ and are used as problem-adapted basis functions in the method. In contrast to the classical LOD and other state-of-the-art multi-scale methods, the localization error decays super-exponentially as the oversampling parameter $\ell$ is increased. This implies that optimal convergence is observed under the substantially relaxed over-sampling condition $\ell\gtrsim(\log \frac{\kappa}{H})^{(d-1)/d}$ with $d$ denoting the spatial dimension. Numerical experiments demonstrate the significantly improved offline and online performance of the method also in the case of heterogeneous media and perfectly matched layers

Computational multiscale methods for nondivergence-form elliptic partial differential equations

This paper proposes novel computational multiscale methods for linear second-order elliptic partial differential equations in nondivergence-form with heterogeneous coefficients satisfying a Cordes condition. The construction follows the methodology of localized orthogonal decomposition (LOD) and provides operator-adapted coarse spaces by solving localized cell problems on a fine scale in the spirit of numerical homogenization. The degrees of freedom of the coarse spaces are related to nonconforming and mixed finite element methods for homogeneous problems. The rigorous error analysis of one exemplary approach shows that the favorable properties of the LOD methodology known from divergence-form PDEs, i.e., its applicability and accuracy beyond scale separation and periodicity, remain valid for problems in nondivergence-form.Comment: 21 page

Early diagnosis of acute myocardial infarction in the elderly using more sensitive cardiac troponin assays

Aims To examine the diagnostic accuracy of sensitive cardiac troponin (cTn) assays in elderly patients, since elevated levels with sensitive cTn assays were reported in 20% of elderly patients without acute myocardial infarction (AMI). Methods and results In this multi-centre study, we included 1098 consecutive patients presenting with symptoms suggestive of AMI, 406 (37%) were >70 years old. Measurement of three investigational sensitive cTn assays [Roche high-sensitive cTnT (hs-cTnT), Siemens cTnI-Ultra, and Abbott-Architect cTnI) and the standard assay (Roche cTnT) was performed in a blinded fashion. The final diagnosis was adjudicated by two independent cardiologists. Acute myocardial infarction was the adjudicated final diagnosis in 24% of elderly patients. Among elderly patients without AMI, baseline cTn levels were elevated above the 99th percentile in 51% with Roche hs-cTnT, in 17% with Siemens TnI-Ultra, and 13% with Abbott-Architect cTnI. The diagnostic accuracy as quantified by the area under the receiver operating characteristic (ROC) curve (AUC) was significantly greater for the sensitive cTn assays compared with the standard assay (AUC for Roche hs-cTnT, 0.94; Siemens cTnI-Ultra, 0.95; and Abbott-Architect cTnI, 0.95 vs. AUC for the standard assay, 0.90; P < 0.05 for comparisons). The best cut-offs for the sensitive cTn-assays determined by the ROC-curve in elderly patients differed clearly from those in younger patients. Furthermore, the prognostic value regarding 90-day mortality varied among the sensitive cTn assays. Conclusion Sensitive cTn assays have high diagnostic accuracy also in the elderly. Mild elevations are common in elderly non-AMI patients, therefore the optimal cut-off levels are substantially higher in elderly as compared with younger patients. Furthermore, sensitive cTn assays yielded different prognostic value (ClinicalTrials.gov number, NCT00470587

Early diagnosis of acute myocardial infarction in patients with pre-existing coronary artery disease using more sensitive cardiac troponin assays

Aims We sought to examine the diagnostic and prognostic utility of sensitive cardiac troponin (cTn) assays in patients with pre-existing coronary artery disease (CAD). Methods and results We conducted a multicentre study to examine the diagnostic accuracy of one high-sensitive and two sensitive cTn assays in 1098 consecutive patients presenting with symptoms suggestive of acute myocardial infarction (AMI), of whom 401 (37%) had pre-existing CAD. Measurements of Roche high-sensitive cTnT (hs-cTnT), Siemens cTnI-Ultra, Abbott-Architect cTnI and the standard assay (Roche cTnT) were performed in a blinded fashion. The final diagnosis was adjudicated by two independent cardiologists. Acute myocardial infarction was the final diagnosis in 19% of CAD patients. Among patients with diagnoses other than AMI, baseline cTn levels were elevated above the 99th percentile with Roche hs-cTnT in 40%, with Siemens TnI-Ultra in 15%, and Abbott-Architect cTnI in 13% of them. In patients with pre-existing CAD, the diagnostic accuracy at presentation, quantified by the area under the receiver operator characteristic curve (AUC), was significantly greater for the sensitive cTn assays compared with the standard assay (AUC for Roche hs-cTnT, 0.92; Siemens cTnI-Ultra, 0.94; and Abbott-Architect cTnI, 0.93 vs. AUC for the standard assay, 0.87; P < 0.01 for all comparisons). Elevated levels of cTn measured with the sensitive assays predicted mortality irrespective of pre-existing CAD, age, sex, and cardiovascular risk factors. Conclusion Sensitive cTn assays have high-diagnostic accuracy also in CAD patients. Mild elevations are common in non-AMI patients and test-specific optimal cut-off levels tend to be higher in CAD patients than in patients without history of CAD. Sensitive cTn assays also retain prognostic value. (ClinicalTrials.gov number, NCT00470587

Risk stratification in patients with acute chest pain using three high-sensitivity cardiac troponin assays

Aims Several high-sensitivity cardiac troponin (hs-cTn) assays have recently been developed. It is unknown which hs-cTn provides the most accurate prognostic information and to what extent early changes in hs-cTn predict mortality. Methods and results In a prospective, international multicentre study, cTn was simultaneously measured with three novel [high-sensitivity cardiac Troponin T (hs-cTnT), Roche Diagnostics; hs-cTnI, Beckman-Coulter; hs-cTnI, Siemens] and a conventional assay (cTnT, Roche Diagnostics) in a blinded fashion in 1117 unselected patients with acute chest pain. Patients were followed up 2 years regarding mortality. Eighty-two (7.3%) patients died during the follow-up. The 2-year prognostic accuracy of hs-cTn was most accurate for hs-cTnT [area under the receivers operating characteristic curve (AUC) 0.78 (95% CI: 0.73-0.83) and outperformed both hs-cTnI (Beckman-Coulter, 0.71 (95% CI: 0.65-0.77; P = 0.001 for comparison), hs-cTnI (Siemens) 0.70 (95% CI: 0.64-0.76; P < 0.001 for comparison)] and cTnT 0.67 (95% CI: 0.61-0.74; P < 0.001 for comparison). Absolute changes of hs-cTnT were more accurate than relative changes in predicting mortality, but inferior to presentation values of hs-cTnT. Combining changes of hs-cTnT within the first 6 h with their presentation values did not further improve prognostic accuracy. Similar results were obtained for both hs-cTnI assays regarding the incremental value of changes. Hs-cTn concentrations remained predictors of death in clinically challenging subgroups such as patients with pre-existing coronary artery disease, impaired renal function, and patients older than 75 years. Conclusion High-sensitivity cardiac Troponin T is more accurate than hs-cTnI in the prediction of long-term mortality. Changes of hs-cTn do not seem to further improve risk stratification beyond initial presentation value

Effect of phosphodiesterase-5 inhibition on SystEmic Right VEntricular size and function - a multi-center, double-blind, randomized, placebo-controlled trial - SERVE.

BACKGROUND AND AIMS In adults with congenital heart disease and systemic right ventricles, progressive right ventricular systolic dysfunction is common and is associated with adverse outcomes. Our aim was to assess the impact of the phosphodiesterase-5-inhibitor tadalafil on right ventricular systolic function. METHODS AND RESULTS This was a double-blind, randomized, placebo-controlled, multi-center superiority trial (NCT03049540) involving 100 adults with systemic right ventricles (33 women, mean age: 40.7 years, SD 10.7), comparing tadalafil 20mg once daily versus placebo (1:1-ratio). Primary endpoint was the change in right ventricular endsystolic volume after three years of therapy. Secondary endpoints were changes in right ventricular ejection fraction, exercise capacity and NT-proBNP-concentration. Primary endpoint assessment by intention to treat analysis at three years of follow up was possible in 83 patients (42 patients in the tadalafil group and 41 patients in the placebo group). No significant changes over time in right ventricular endsystolic volumes were observed in the tadalafil and the placebo-group, and no significant differences between treatment groups (3.4ml, 95% CI, -4.3 to 11.0, p=0.39). No significant changes over time were observed for the pre-specified secondary endpoints for the entire study population, without differences between the tadalafil and the placebo-group. CONLCUSIONS In this trial in adults with systemic right ventricles, right ventricular systolic function, exercise capacity and neuro-hormonal activation remained stable over a three-year follow-up period. No significant treatment effect of tadalafil was observed. Further research is needed to find effective treatment for improvement of ventricular function in adults with systemic right ventricles. This article is protected by copyright. All rights reserved

Effect of phosphodiesterase-5 inhibition on SystEmic Right VEntricular size and function - A multicentre, double-blind, randomized, placebo-controlled trial - SERVE

AIMS In adults with congenital heart disease and systemic right ventricles, progressive right ventricular systolic dysfunction is common and is associated with adverse outcomes. Our aim was to assess the impact of the phosphodiesterase-5-inhibitor tadalafil on right ventricular systolic function. METHODS AND RESULTS This was a double-blind, randomized, placebo-controlled, multicentre superiority trial (NCT03049540) involving 100 adults with systemic right ventricles (33 women, mean age: 40.7 ± 10.7 years), comparing tadalafil 20 mg once daily versus placebo (1:1 ratio). The primary endpoint was the change in right ventricular end-systolic volume after 3 years of therapy. Secondary endpoints were changes in right ventricular ejection fraction, exercise capacity and N-terminal pro-B-type natriuretic peptide concentration. Primary endpoint assessment by intention to treat analysis at 3 years of follow-up was possible in 83 patients (42 patients in the tadalafil group and 41 patients in the placebo group). No significant changes over time in right ventricular end-systolic volumes were observed in the tadalafil and the placebo group, and no significant differences between treatment groups (3.4 ml, 95% confidence interval -4.3 to 11.0, p = 0.39). No significant changes over time were observed for the pre-specified secondary endpoints for the entire study population, without differences between the tadalafil and the placebo group. CONCLUSIONS In this trial in adults with systemic right ventricles, right ventricular systolic function, exercise capacity and neuro-hormonal activation remained stable over a 3-year follow-up period. No significant treatment effect of tadalafil was observed. Further research is needed to find effective treatment for improvement of ventricular function in adults with systemic right ventricles