Development and validation of a gene expression test to identify hard-to-heal chronic venous leg ulcers

Background: Chronic venous leg ulcers pose a significant burden to healthcare systems, and predicting wound healing is challenging. The aim of this study was to develop a genetic test to evaluate the propensity of a chronic ulcer to heal. Methods: Sequential refinement and testing of a gene expression signature was conducted using three distinct cohorts of human wound tissue. The expression of candidate genes was screened using a cohort of acute and chronic wound tissue and normal skin with quantitative transcript analysis. Genes showing significant expression differences were combined and examined, using receiver operating characteristic (ROC) curve analysis, in a controlled prospective study of patients with venous leg ulcers. A refined gene signature was evaluated using a prospective, blinded study of consecutive patients with venous ulcers. Results: The initial gene signature, comprising 25 genes, could identify the outcome (healing versus non‐healing) of chronic venous leg ulcers (area under the curve (AUC) 0·84, 95 per cent c.i. 0·73 to 0·94). Subsequent refinement resulted in a final 14‐gene signature (WD14), which performed equally well (AUC 0·88, 0·80 to 0·97). When examined in a prospective blinded study, the WD14 signature could also identify wounds likely to demonstrate signs of healing (AUC 0·73, 0·62 to 0·84). Conclusion: A gene signature can identify people with chronic venous leg ulcers that are unlikely to heal

First-Order System Least Squares and the Energetic Variational Approach for Two-Phase Flow

This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen-Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques.Comment: 22 pages, 8 figures submitted to Journal of Computational Physic

A Scheme to Numerically Evolve Data for the Conformal Einstein Equation

This is the second paper in a series describing a numerical implementation of the conformal Einstein equation. This paper deals with the technical details of the numerical code used to perform numerical time evolutions from a "minimal" set of data. We outline the numerical construction of a complete set of data for our equations from a minimal set of data. The second and the fourth order discretisations, which are used for the construction of the complete data set and for the numerical integration of the time evolution equations, are described and their efficiencies are compared. By using the fourth order scheme we reduce our computer resource requirements --- with respect to memory as well as computation time --- by at least two orders of magnitude as compared to the second order scheme.Comment: 20 pages, 12 figure

Kapazitive pH-Sensoren auf der Basis von makroporösem Silizium mit Doppelisolatorschicht aus thermisch oxidiertem SiO2 und LPCVD-Si3N4

Halbleitersensoren für den Ionennachweis in wässrigen Lösungen lassen sich einfach und kostengünstig als kapazitive Feldeffektstrukturen in Form von sogenannten EIS- (Elektrolyt-Isolator-Silizium) Sensoren realisieren. Allerdings sind solche Sensoren begrenzt miniaturisierbar, da ihre geometrische Fläche direkt proportional in das Meßsignal, die Kapazitätsänderung, eingeht. Um diesen Nachteil zu umgehen, haben wir auf dem ersten BioSensorSymposium in München (1999) einen neuartigen Lösungsansatz vorgeschlagen, bei dem makroporöses Silizium als Basismaterial für verschiedene sensoraktive Substanzen, wie z.B. pH-sensitive Schichten und Enzyme eingesetzt werden kann. Bei der Verwendung von makroporösem Silizium als Transducermaterial hat die durch den Herstellungsprozeß bedingte Vergrößerung der sensoraktiven Oberfläche nämlich eine Zunahme der Meßkapazität zur Folge. Aufgrund der Ätzanordnung zur Herstellung von porösem Silizium war es bisher allerdings nur möglich, Niedertemperaturprozesse, wie das PECVD (Plasma-Enhanced-Chemical-Vapour-Deposition)-Verfahren, zur Abscheidung von SiO2 als Isolatorschicht und Si3N4 als pH-sensitiver Schicht zu verwenden. Solche Sensoren besitzen allerdings keine hohe Langzeitstabilität im Meßbetrieb (ca. 2 Monate), da die dielektrischen Schichten unzureichende Korrosionseigenschaften aufweisen. Zur Verbesserung der Langzeitstabilität von Sensoren aus porösem Silizium bietet sich die Verwendung von thermisch oxidiertem Silizium als Isolatorschicht und das Abscheiden von Siliziumnitrid als pH-sensitive Schicht mittels LPCVD (Low-Pressure- Chemical-Vapour-Deposition)-Verfahren an. Vorangegangene Arbeiten aus unserer Arbeitsgruppe hatten gezeigt, daß planare Sensoren mit LPCVD-Nitrid als Transducermaterial über einen Zeitraum von sieben Monaten konstant hohe Sensitivitäten nahe dem Nernst-Idealwert aufweisen

Boundary critical behaviour at mm-axial Lifshitz points: the special transition for the case of a surface plane parallel to the modulation axes

The critical behaviour of $d$-dimensional semi-infinite systems with $n$-component order parameter $\bm{\phi}$ is studied at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of $\mathbb{R}^d$. Field-theoretic renormalization group methods are utilised to examine the special surface transition in the case where the $m$ potential modulation axes, with $0\leq m\leq d-1$, are parallel to the surface. The resulting scaling laws for the surface critical indices are given. The surface critical exponent $\eta_\|^{\rm sp}$, the surface crossover exponent $\Phi$ and related ones are determined to first order in \epsilon=4+\case{m}{2}-d. Unlike the bulk critical exponents and the surface critical exponents of the ordinary transition, $\Phi$ is $m$-dependent already at first order in $\epsilon$. The \Or(\epsilon) term of $\eta_\|^{\rm sp}$ is found to vanish, which implies that the difference of $\beta_1^{\rm sp}$ and the bulk exponent $\beta$ is of order $\epsilon^2$.Comment: 21 pages, one figure included as eps file, uses IOP style file

Modified critical correlations close to modulated and rough surfaces

Correlation functions are sensitive to the presence of a boundary. Surface modulations give rise to modified near surface correlations, which can be measured by scattering probes. To determine these correlations, we develop a perturbative calculation in deformations in height from a flat surface. The results, combined with a renormalization group around four dimensions, are also used to predict critical behavior near a self-affinely rough surface. We find that a large enough roughness exponent can modify surface critical behavior.Comment: 4 pages, 1 figure. Revised version as published in Phys. Rev. Lett. 86, 4596 (2001

Renormalized couplings and scaling correction amplitudes in the N-vector spin models on the sc and the bcc lattices

For the classical N-vector model, with arbitrary N, we have computed through order \beta^{17} the high temperature expansions of the second field derivative of the susceptibility \chi_4(N,\beta) on the simple cubic and on the body centered cubic lattices. (The N-vector model is also known as the O(N) symmetric classical spin Heisenberg model or, in quantum field theory, as the lattice O(N) nonlinear sigma model.) By analyzing the expansion of \chi_4(N,\beta) on the two lattices, and by carefully allowing for the corrections to scaling, we obtain updated estimates of the critical parameters and more accurate tests of the hyperscaling relation d\nu(N) +\gamma(N) -2\Delta_4(N)=0 for a range of values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the classical Heisenberg model]. Using the recently extended series for the susceptibility and for the second correlation moment, we also compute the dimensionless renormalized four point coupling constants and some universal ratios of scaling correction amplitudes in fair agreement with recent renormalization group estimates.Comment: 23 pages, latex, no figure

Correlation functions near Modulated and Rough Surfaces

In a system with long-ranged correlations, the behavior of correlation functions is sensitive to the presence of a boundary. We show that surface deformations strongly modify this behavior as compared to a flat surface. The modified near surface correlations can be measured by scattering probes. To determine these correlations, we develop a perturbative calculation in the deformations in height from a flat surface. Detailed results are given for a regularly patterned surface, as well as for a self-affinely rough surface with roughness exponent $\zeta$. By combining this perturbative calculation in height deformations with the field-theoretic renormalization group approach, we also estimate the values of critical exponents governing the behavior of the decay of correlation functions near a self-affinely rough surface. We find that for the interacting theory, a large enough $\zeta$ can lead to novel surface critical behavior. We also provide scaling relations between roughness induced critical exponents for thermodynamic surface quantities.Comment: 31 pages, 2 figure

Casimir forces in binary liquid mixtures

If two ore more bodies are immersed in a critical fluid critical fluctuations of the order parameter generate long ranged forces between these bodies. Due to the underlying mechanism these forces are close analogues of the well known Casimir forces in electromagnetism. For the special case of a binary liquid mixture near its critical demixing transition confined to a simple parallel plate geometry it is shown that the corresponding critical Casimir forces can be of the same order of magnitude as the dispersion (van der Waals) forces between the plates. In wetting experiments or by direct measurements with an atomic force microscope the resulting modification of the usual dispersion forces in the critical regime should therefore be easily detectable. Analytical estimates for the Casimir amplitudes Delta in d=4-epsilon are compared with corresponding Monte-Carlo results in d=3 and their quantitative effect on the thickness of critical wetting layers and on force measurements is discussed.Comment: 34 pages LaTeX with revtex and epsf style, to appear in Phys. Rev.

Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems

High-temperature series are computed for a generalized $3d$ Ising model with arbitrary potential. Two specific ``improved'' potentials (suppressing leading scaling corrections) are selected by Monte Carlo computation. Critical exponents are extracted from high-temperature series specialized to improved potentials, achieving high accuracy; our best estimates are: $\gamma=1.2371(4)$, $\nu=0.63002(23)$, $\alpha=0.1099(7)$, $\eta=0.0364(4)$, $\beta=0.32648(18)$. By the same technique, the coefficients of the small-field expansion for the effective potential (Helmholtz free energy) are computed. These results are applied to the construction of parametric representations of the critical equation of state. A systematic approximation scheme, based on a global stationarity condition, is introduced (the lowest-order approximation reproduces the linear parametric model). This scheme is used for an accurate determination of universal ratios of amplitudes. A comparison with other theoretical and experimental determinations of universal quantities is presented.Comment: 65 pages, 1 figure, revtex. New Monte Carlo data by Hasenbusch enabled us to improve the determination of the critical exponents and of the equation of state. The discussion of several topics was improved and the bibliography was update