Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

Optical properties of a nanomatch-like plasmonic structure

The optical properties of a match-like plasmonic nanostructure are numerically investigated using full-wave finite-difference time-domain analysis in conjunction with dispersive material models. This work is mainly motivated by the developed technique enabling reproducible fabrication of nanomatch structures as well as the growing applications that utilize the localized field enhancement in plasmonic nanostructures. Our research revealed that due to the pronounced field enhancement and larger resonance tunabilities, some nanomatch topologies show potentials for various applications in the field of, e.g., sensing as well as a novel scheme for highly reproducible tips in scanning near field optical microscopy, among others. Despite the additional degrees of freedom that are offered by the composite nature of the proposed nanomatch topology, the paper also reflects on a fundamental complication intrinsic to the material interfaces especially in the nanoscale: stoichiometric mixing. We conclude that the specificity in material modeling will become a significant issue in future research on functionalized composite nanostructures.

A numerical model for inert gas transport in the lung based on fractal airway morphology

Patients suffering from cystic fibrosis (CF) show thick secretions, mucus plugging and bronchiectasis in bronchial and alveolar ducts. This results in substantial structural changes of the airway morphology and heterogeneous ventilation. Disease progression and treatment effects are monitored by so-called gas washout tests, where the change in concentration of an inert gas is measured over a single or multiple breaths. The result of the tests based on the profile of the measured concentration is a marker for the severity of the ventilation inhomogeneity strongly affected by the airway morphology. However, it is hard to localize underlying obstructions to specific parts of the airways, especially if occurring in the lung periphery. In order to support the analysis of lung function tests (e.g. multi-breath washout), we developed a numerical model of the entire airway tree, coupling a lumped parameter model for the lung ventilation with a 4th-order accurate finite difference model of a 1D advection-diffusion equation for the transport of an inert gas. The boundary conditions for the flow problem comprise the pressure and flow profile at the mouth, which is typically known from clinical washout tests. The natural asymmetry of the lung morphology is approximated by a generic, fractal, asymmetric branching scheme which we applied for the conducting airways. A conducting airway ends when its dimension falls below a predefined limit. A model acinus is then connected to each terminal airway. The morphology of an acinus unit comprises a network of expandable cells. A regional, linear constitutive law describes the pressure-volume relation between the pleural gap and the acinus. The cyclic expansion (breathing) of each acinus unit depends on the resistance of the feeding airway and on the flow resistance and stiffness of the cells themselves. Special care was taken in the development of a conservative numerical scheme for the gas transport across bifurcations, handling spatially and temporally varying advective and diffusive fluxes over a wide range of scales. Implicit time integration was applied to account for the numerical stiffness resulting from the discretized transport equation. Local or regional modification of the airway dimension, resistance or tissue stiffness are introduced to mimic pathological airway restrictions typical for CF. This leads to a more heterogeneous ventilation of the model lung. As a result the concentration in some distal parts of the lung model remains increased for a longer duration. The inert gas concentration at the mouth towards the end of the expirations is composed of gas from regions with very different washout efficiency. This results in a steeper slope of the corresponding part of the washout profile.

Bounding Standard Gaussian Tail Probabilities

We review various inequalities for Mills' ratio (1 - Φ)= Ø, where Ø and Φ denote the standard Gaussian density and distribution function, respectively. Elementary considerations involving finite continued fractions lead to a general approximation scheme which implies and refines several known bounds.

Extraordinary transmission through a single coaxial aperture in a thin metal film

We investigate experimentally the transmission properties of single sub-wavelength coaxial apertures in thin metal films (t = 110 nm). Enhanced transmission through a single sub-wavelength coaxial aperture illuminated with a strongly focused radially polarized light beam is reported. In our experiments we achieved up to four times enhanced transmission through a single coaxial aperture as compared to a (hollow) circular aperture with the same outer diameter.We attribute this enhancement of transmission to the excitation of a TEM-mode for illumination with radially polarized light inside the single coaxial aperture. A strong polarization contrast is observed between the transmission for radially and azimuthally polarized illumination. Furthermore, the observed transmission through a single coaxial aperture can be strongly reduced if surface plasmons are excited. The experimental results are in good agreement with finite difference time domain (FDTD) simulations.

Quantitative Myocardial Contrast Echocardiography during Pharmacological Stress for Diagnosis of Coronary Artery Disease: A Systematic Review and Meta-analysis of Diagnostic Accuracy Studies

AIMS: We conducted a meta-analysis to evaluate the accuracy of quantitative stress myocardial contrast echocardiography (MCE) in coronary artery disease (CAD). METHODS AND RESULTS: Database search was performed through January 2008. We included studies evaluating accuracy of quantitative stress MCE for detection of CAD compared with coronary angiography or single-photon emission computed tomography (SPECT) and measuring reserve parameters of A, beta, and Abeta. Data from studies were verified and supplemented by the authors of each study. Using random effects meta-analysis, we estimated weighted mean difference (WMD), likelihood ratios (LRs), diagnostic odds ratios (DORs), and summary area under curve (AUC), all with 95% confidence interval (CI). Of 1443 studies, 13 including 627 patients (age range, 38-75 years) and comparing MCE with angiography (n = 10), SPECT (n = 1), or both (n = 2) were eligible. WMD (95% CI) were significantly less in CAD group than no-CAD group: 0.12 (0.06-0.18) (P < 0.001), 1.38 (1.28-1.52) (P < 0.001), and 1.47 (1.18-1.76) (P < 0.001) for A, beta, and Abeta reserves, respectively. Pooled LRs for positive test were 1.33 (1.13-1.57), 3.76 (2.43-5.80), and 3.64 (2.87-4.78) and LRs for negative test were 0.68 (0.55-0.83), 0.30 (0.24-0.38), and 0.27 (0.22-0.34) for A, beta, and Abeta reserves, respectively. Pooled DORs were 2.09 (1.42-3.07), 15.11 (7.90-28.91), and 14.73 (9.61-22.57) and AUCs were 0.637 (0.594-0.677), 0.851 (0.828-0.872), and 0.859 (0.842-0.750) for A, beta, and Abeta reserves, respectively. CONCLUSION: Evidence supports the use of quantitative MCE as a non-invasive test for detection of CAD. Standardizing MCE quantification analysis and adherence to reporting standards for diagnostic tests could enhance the quality of evidence in this field.

Stent Thrombosis in Drug-Eluting or Bare-Metal Stents in Patients Receiving Dual Antiplatelet Therapy

OBJECTIVES This study sought to compare rates of stent thrombosis and major adverse cardiac and cerebrovascular events (MACCE) (composite of death, myocardial infarction, or stroke) after coronary stenting with drug-eluting stents (DES) versus bare-metal stents (BMS) in patients who participated in the DAPT (Dual Antiplatelet Therapy) study, an international multicenter randomized trial comparing 30 versus 12 months of dual antiplatelet therapy in subjects undergoing coronary stenting with either DES or BMS. BACKGROUND Despite antirestenotic efficacy of coronary DES compared with BMS, the relative risk of stent thrombosis and adverse cardiovascular events is unclear. Many clinicians perceive BMS to be associated with fewer adverse ischemic events and to require shorter-duration dual antiplatelet therapy than DES. METHODS Prospective propensity-matched analysis of subjects enrolled into a randomized trial of dual antiplatelet therapy duration was performed. DES- and BMS-treated subjects were propensity-score matched in a many-to-one fashion. The study design was observational for all subjects 0 to 12 months following stenting. A subset of eligible subjects without major ischemic or bleeding events were randomized at 12 months to continued thienopyridine versus placebo; all subjects were followed through 33 months. RESULTS Among 10,026 propensity-matched subjects, DES-treated subjects (n = 8,308) had a lower rate of stent thrombosis through 33 months compared with BMS-treated subjects (n = 1,718, 1.7% vs. 2.6%; weighted risk difference -1.1%, p = 0.01) and a noninferior rate of MACCE (11.4% vs. 13.2%, respectively, weighted risk difference -1.8%, p = 0.053, noninferiority p < 0.001). CONCLUSIONS DES-treated subjects have long-term rates of stent thrombosis that are lower than BMS-treated subjects. (The Dual Antiplatelet Therapy Study [DAPT study]; NCT00977938).

Precipitation isoscape of high reliefs: interpolation scheme designed and tested for monthly resolved precipitation oxygen isotope records of an Alpine domain

Stable oxygen isotope composition of atmospheric precipitation (δ18Op) was scrutinized from 39 stations distributed over Switzerland and its border zone. Monthly amount-weighted δ18Op values averaged over the 1995–2000 period showed the expected strong linear altitude dependence (−0.15 to −0.22‰ per 100 m) only during the summer season (May–September). Steeper gradients (~ −0.56 to −0.60‰ per 100 m) were observed for winter months over a low elevation belt, while hardly any altitudinal difference was seen for high elevation stations. This dichotomous pattern could be explained by the characteristically shallower vertical atmospheric mixing height during winter season and provides empirical evidence for recently simulated effects of stratified atmospheric flow on orographic precipitation isotopic ratios. This helps explain "anomalous" deflected altitudinal water isotope profiles reported from many other high relief regions. Grids and isotope distribution maps of the monthly δ18Op have been calculated over the study region for 1995–1996. The adopted interpolation method took into account both the variable mixing heights and the seasonal difference in the isotopic lapse rate and combined them with residual kriging. The presented data set allows a point estimation of δ18Op with monthly resolution. According to the test calculations executed on subsets, this biannual data set can be extended back to 1992 with maintained fidelity and, with a reduced station subset, even back to 1983 at the expense of faded reliability of the derived δ18Op estimates, mainly in the eastern part of Switzerland. Before 1983, reliable results can only be expected for the Swiss Plateau since important stations representing eastern and south-western Switzerland were not yet in operation.

Effect of vascular targeting agent in rat tumor model: dynamic contrast-enhanced versus diffusion-weighted MR imaging

PURPOSE: To compare dynamic contrast material-enhanced magnetic resonance (MR) imaging and diffusion-weighted MR imaging for noninvasive evaluation of early and late effects of a vascular targeting agent in a rat tumor model. MATERIALS AND METHODS: The study protocol was approved by the local ethics committee for animal care and use. Thirteen rats with one rhabdomyosarcoma in each flank (26 tumors) underwent dynamic contrast-enhanced imaging and diffusion-weighted echo-planar imaging in a 1.5-T MR unit before intraperitoneal injection of combretastatin A4 phosphate and at early (1 and 6 hours) and later (2 and 9 days) follow-up examinations after the injection. Histopathologic examination was performed at each time point. The apparent diffusion coefficient (ADC) of each tumor was calculated separately on the basis of diffusion-weighted images obtained with low b gradient values (ADC(low); b = 0, 50, and 100 sec/mm(2)) and high b gradient values (ADC(high); b = 500, 750, and 1000 sec/mm(2)). The difference between ADC(low) and ADC(high) was used as a surrogate measure of tissue perfusion (ADC(low) - ADC(high) = ADC(perf)). From the dynamic contrast-enhanced MR images, the volume transfer constant k and the initial slope of the contrast enhancement-time curve were calculated. For statistical analyses, a paired two-tailed Student t test and linear regression analysis were used. RESULTS: Early after administration of combretastatin, all perfusion-related parameters (k, initial slope, and ADC(perf)) decreased significantly (P < .001); at 9 days after combretastatin administration, they increased significantly (P < .001). Changes in ADC(perf) were correlated with changes in k (R(2) = 0.46, P < .001) and the initial slope (R(2) = 0.67, P < .001). CONCLUSION: Both dynamic contrast-enhanced MR imaging and diffusion-weighted MR imaging allow monitoring of perfusion changes induced by vascular targeting agents in tumors. Diffusion-weighted imaging provides additional information about intratumoral cell viability versus necrosis after administration of combretastatin.

Thermal 2-loop master spectral function at finite momentum

When considering NLO corrections to thermal particle production in the “relativistic” regime, in which the invariant mass squared of the produced particle is K2 ~ (πT)2, then the production rate can be expressed as a sum of a few universal “master” spectral functions. Taking the most complicated 2-loop master as an example, a general strategy for obtaining a convergent 2-dimensional integral representation is suggested. The analysis applies both to bosonic and fermionic statistics, and shows that for this master the non-relativistic approximation is only accurate for K2 ~(8πT)2, whereas the zero-momentum approximation works surprisingly well. Once the simpler masters have been similarly resolved, NLO results for quantities such as the right-handed neutrino production rate from a Standard Model plasma or the dilepton production rate from a QCD plasma can be assembled for K2 ~ (πT)2.

Living Renal Allograft Transplantation: Diffusion-weighted MR Imaging in Longitudinal Follow-up of the Donated and the Remaining Kidney.

Purpose To determine whether diffusion-weighted (DW) magnetic resonance (MR) imaging in living renal allograft donation allows monitoring of potential changes in the nontransplanted remaining kidney of the donor because of unilateral nephrectomy and changes in the transplanted kidney before and after transplantation in donor and recipient, respectively, and whether DW MR parameters are correlated in the same kidney before and after transplantation. Materials and Methods The study protocol was approved by the local ethics committee; written informed consent was obtained. Thirteen healthy kidney donors and their corresponding recipients prospectively underwent DW MR imaging (multiple b values) in donors before donation and in donors and recipients at day 8 and months 3 and 12 after donation. Total apparent diffusion coefficient (ADCT) values were determined; contribution of microcirculation was quantified in perfusion fraction (FP). Longitudinal changes of diffusion parameters were compared (repeated-measures one-way analysis of variance with post hoc pairwise comparisons). Correlations were tested (linear regression). Results ADCT values in nontransplanted kidney of donors increased from a preexplantation value of (188 ± 9 [standard deviation]) to (202 ± 11) × 10(-5) mm(2)/sec in medulla and from (199 ± 11) to (210 ± 13) × 10(-5) mm(2)/sec in cortex 1 week after donation (P < .004). Medullary, but not cortical, ADCT values stayed increased up to 1 year. ADCT values in allografts in recipients were stable. Compared with values obtained before transplantation in donors, the corticomedullary difference was reduced in allografts (P < .03). Cortical ADCT values correlated with estimated glomerular filtration rate in recipients (R = 0.56, P < .001) but not donors. Cortical ADCT values in the same kidney before transplantation in donors correlated with those in recipients on day 8 after transplantation (R = 0.77, P = .006). FP did not show significant changes. Conclusion DW MR imaging depicts early adaptations in the remaining nontransplanted kidney of donors after nephrectomy. All diffusion parameters remained constant in allograft recipients after transplantation. This method has potential monitoring utility, although assessment of clinical relevance is needed. © RSNA, 2013 Online supplemental material is available for this article.

Finite Element Based Nonlinear Normalization of Human Lumbar Intervertebral Disc Stiffness to Account for Its Morphology

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.

Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.