Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena

In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion process-based mechanisms motivated by applications from cell biology. Previous investigations that focussed on relaxing the independence assumption have been limited to studying initially-uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterised by moving fronts. Here we propose generalised methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

Depth-dependent biomechanical and biochemical properties of fetal, newborn, and tissue-engineered articular cartilage

Adult articular cartilage has depth-dependent mechanical and biochemical properties which contribute to zone-specific functions. The compressive moduli of immature cartilage and tissue-engineered cartilage are known to be lower than those of adult cartilage. The objective of this study was to determine if such tissues exhibit depth-dependent compressive properties, and how these depth-varying properties were correlated with cell and matrix composition of the tissue. The compressive moduli of fetal and newborn bovine articular cartilage increased with depth (p < 0.05) by a factor of 4-5 from the top 0.1 mm (28 +/- 13 kPa, 141 +/- 10 kPa, respectively) to 1 mm deep into the tissue. Likewise, the glycosaminoglycan and collagen content increased with depth (both p < 0.001), and correlated with the modulus (both p < 0.01). In contrast, tissue-engineered cartilage formed by either layering or mixing cells from the superficial and middle zone of articular cartilage exhibited similarly soft regions at both construct surfaces, as exemplified by large equilibrium strains. The properties of immature cartilage may provide a template for developing tissue-engineered cartilage which aims to repair cartilage defects by recapitulating the natural development and growth processes. These results suggest that while depth-dependent properties may be important to engineer into cartilage constructs, issues other than cell heterogeneity must be addressed to generate such tissues. (c) 2005 Elsevier Ltd. All rights reserved.

Modulation of depth-dependent properties in tissue-engineered cartilage with a semi-permeable membrane and perfusion : a continuum model of matrix metabolism and transport

The functional properties of cartilaginous tissues are determined predominantly by the content, distribution, and organization of proteoglycan and collagen in the extracellular matrix. Extracellular matrix accumulates in tissue-engineered cartilage constructs by metabolism and transport of matrix molecules, processes that are modulated by physical and chemical factors. Constructs incubated under free-swelling conditions with freely permeable or highly permeable membranes exhibit symmetric surface regions of soft tissue. The variation in tissue properties with depth from the surfaces suggests the hypothesis that the transport processes mediated by the boundary conditions govern the distribution of proteoglycan in such constructs. A continuum model (DiMicco and Sah in Transport Porus Med 50:57-73, 2003) was extended to test the effects of membrane permeability and perfusion on proteoglycan accumulation in tissue-engineered cartilage. The concentrations of soluble, bound, and degraded proteoglycan were analyzed as functions of time, space, and non-dimensional parameters for several experimental configurations. The results of the model suggest that the boundary condition at the membrane surface and the rate of perfusion, described by non-dimensional parameters, are important determinants of the pattern of proteoglycan accumulation. With perfusion, the proteoglycan profile is skewed, and decreases or increases in magnitude depending on the level of flow-based stimulation. Utilization of a semi-permeable membrane with or without unidirectional flow may lead to tissues with depth-increasing proteoglycan content, resembling native articular cartilage.

The relationship between building characteristics and the chemical composition of surface films found on glass windows in Brisbane, Australia

Films found on the windows of residential buildings have been studied. The main aim of the paper was to assess the roles of the films in the accumulation of potentially toxic chemicals in residential buildings. Thus the elemental and polycyclic aromatic hydrocarbon compositions of the surface films from the glass windows of eighteen residential buildings were examined. The presence of sample amounts of inorganic elements (4.0–1.2 × 106 μg m−2) and polycyclic aromatic hydrocarbons in the films (BDL - 620.1 ng m−2) has implications for human exposure and the fate of pollutants in the urban environment. To facilitate the interpretation of the results, data matrices consisting of the chemical composition of the films and the building characteristics were subjected to multivariate data analysis methods, and these revealed that the accumulation of the chemicals was strongly dependent on building characteristics such as the type of glass used for the window, the distance from a major road, age of the building, distance from an industrial activity, number of smokers in the building and frequency of cooking in the buildings. Thus, building characteristics which minimize the accumulation of pollutants on the surface films need to be encouraged.

Cholesterol enhances phospholipid-dependent activated protein C anticoagulant activity

The influence of cholesterol on activated protein C (APC) anticoagulant activity in plasma and on factor Va inactivation was investigated. Anticoagulant and procoagulant activities of phosphatidylcholine/phosphatidylserine (PC/PS) vesicles containing cholesterol were assessed in the presence and absence of APC using factor Xa-1-stage clotting and factor Va inactivation assays. Cholesterol at approximate physiological membrane levels (30%) in PC/PS (60%/10% w/w) vesicles prolonged the factor Xa-1-stage clotting time dose-dependently in the presence of APC but not in the absence of APC. APC-mediated cleavage of purified recombinant factor Va variants that were modified at specific APC cleavage sites (Q306/Q679-factor Va; Q506/Q679-factor Va) was studied to define the effects of cholesterol on APC cleavage at R506 and R306. When compared to control PC/PS vesicles, cholesterol in PC/PS vesicles enhanced factor Va inactivation and the rate of APC cleavage at both R506 and R306. Cholesterol also enhanced APC cleavage rates at R306 in the presence of the APC cofactor, protein S. In summary, APC anticoagulant activity in plasma and factor Va inactivation as a result of cleavages at R506 and R306 by APC is markedly enhanced by cholesterol in phospholipid vesicles. These results suggest that cholesterol in a membrane surface may selectively enhance APC activities. © 2005 International Society on Thrombosis and Haemostasis.

Use of first nucleotide change technology to determine the frequency of factor V Leiden in a population of Australian blood donors

Activated protein C resistance (APCR), the most common risk factor for venous thrombosis, is the result of a G to A base substitution at nucleotide 1691 (R506Q) in the factor V gene. Current techniques to detect the factor V Leiden mutation, such as determination of restriction length polymorphisms, do not have the capacity to screen large numbers of samples in a rapid, cost- effective test. The aim of this study was to apply the first nucleotide change (FNC) technology, to the detection of the factor V Leiden mutation. After preliminary amplification of genomic DNA by polymerase chain reaction (PCR), an allele-specific primer was hybridised to the PCR product and extended using fluorescent terminating dideoxynucleotides which were detected by colorimetric assay. Using this ELISA-based assay, the prevalence of the factor V Leiden mutation was determined in an Australian blood donor population (n = 500). A total of 18 heterozygotes were identified (3.6%) and all of these were confirmed with conventional MnlI restriction digest. No homozygotes for the variant allele were detected. We conclude from this study that the frequency of 3.6% is compatible with others published for Caucasian populations. In addition, the FNC technology shows promise as the basis for a rapid, automated DNA based test for factor V Leiden.

Dual-frequency decoupling networks for compact antenna arrays

Decoupling networks can alleviate the effects of mutual coupling in antenna arrays. Conventional decoupling networks can provide decoupled and matched ports at a single frequency. This paper describes dual-frequency decoupling which is achieved by using a network of series or parallel resonant circuits instead of single reactive elements.

Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres

A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modelled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyse the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multi-layered drug delivery device is suggested, which allows for more flexible control of drug release.

The effect of temperature dependent viscosity on MHD natural convection flow from an isothermal sphere

Laminar magnetohydrodynamic (MHD) natural convection flow from an isothermal sphere immersed in a fluid with viscosity proportional to linear function of temperature has been studied. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations are reduced to convenient form which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and temperature distribution, streamlines and isotherms of the fluid as well as heat transfer characteristics, namely the local skin-friction coefficients and the local heat transfer rate for a wide range of magnetohydrodynamic paramagnet and viscosity-variation parameter.