Chlamydial infection and spatial ascension of the female genital tract : a novel hybrid cellular automata and continuum mathematical model

Sexually transmitted chlamydial infection initially establishes in the endocervix in females, but if the infection ascends the genital tract, significant disease, including infertility, can result. Many of the mechanisms associated with chlamydial infection kinetics and disease ascension are unknown. We attempt to elucidate some of these processes by developing a novel mathematical model, using a cellular automata–partial differential equation model. We matched our model outputs to experimental data of chlamydial infection of the guinea-pig cervix and carried out sensitivity analyses to determine the relative influence of model parameters. We found that the rate of recruitment and action of innate immune cells to clear extracellular chlamydial particles and the rate of passive movement of chlamydial particles are the dominant factors in determining the early course of infection, magnitude of the peak chlamydial time course and the time of the peak. The rate of passive movement was found to be the most important factor in determining whether infection would ascend to the upper genital tract. This study highlights the importance of early innate immunity in the control of chlamydial infection and the significance of motility-diffusive properties and the adaptive immune response in the magnitude of infection and in its ascension.

Application of a continuum theory to vertical vibrations of a layer of granular material

Many interesting phenomena have been observed in layers of granular materials subjected to vertical oscillations; these include the formation of a variety of standing wave patterns, and the occurrence of isolated features called oscillons, which alternately form conical heaps and craters oscillating at one-half of the forcing frequency. No continuum-based explanation of these phenomena has previously been proposed. We apply a continuum theory, termed the double-shearing theory, which has had success in analyzing various problems in the flow of granular materials, to the problem of a layer of granular material on a vertically vibrating rigid base undergoing vertical oscillations in plane strain. There exists a trivial solution in which the layer moves as a rigid body. By investigating linear perturbations of this solution, we find that at certain amplitudes and frequencies this trivial solution can bifurcate. The time dependence of the perturbed solution is governed by Mathieu’s equation, which allows stable, unstable and periodic solutions, and the observed period-doubling behaviour. Several solutions for the spatial velocity distribution are obtained; these include one in which the surface undergoes vertical velocities that have sinusoidal dependence on the horizontal space dimension, which corresponds to the formation of striped standing waves, and is one of the observed patterns. An alternative continuum theory of granular material mechanics, in which the principal axes of stress and rate-of-deformation are coincident, is shown to be incapable of giving rise to similar instabilities.

Creating cultural change in education : A proposal for a continuum for evaluating the effectiveness of sustainable schools implementation strategies in Australia

Networks are increasingly recognised as advantageous when creating and embedding cultural change within organisations. This paper explores andproblematises ideas around networks for education for sustainability (EfS), Australian Sustainable Schools Initiative (AuSSI), a national, whole-school approach to EfS. In three Australian states - New South Wales, Victoria and Queensland – AuSSI has been implemented in different ways. In examining the use of products, facilitators and networks to embed initiatives such as AuSSI in Australian schools, we propose a “continuum of cultural change strategies” as a framework for thinking about each of these approaches to creating organisational and cultural change for sustainability. We anticipate that such a framework may assist where choices need to be made in relation to the kinds of capacity building processes that might best achieve “deep and wide” change within schools hoping to engender significant cultural change.

Theory-of-Mind Continuum Model: Why Mind Matters in Philosophy, Psychology and Education

Theory-of-Mind has been defined as the ability to explain and predict human behaviour by imputing mental states, such as attention, intention, desire, emotion, perception and belief, to the self and others (Astington & Barriault, 2001). Theory-of-Mind study began with Piaget and continued through a tradition of meta-cognitive research projects (Flavell, 2004). A study by Baron-Cohen, Leslie and Frith (1985) of Theory-of-Mind abilities in atypically developing children reported major difficulties experienced by children with autism spectrum disorder (ASD) in imputing mental states to others. Since then, a wide range of follow-up research has been conducted to confirm these results. Traditional Theory-of-Mind research on ASD has been based on an either-or assumption that Theory-of-Mind is something one either possesses or does not. However, this approach fails to take account of how the ASD population themselves experience Theory-of-Mind. This paper suggests an alternative approach, Theory-of-Mind continuum model, to understand the Theory-of-Mind experience of people with ASD. The Theory-of-Mind continuum model will be developed through a comparison of subjective and objective aspects of mind, and phenomenal and psychological concepts of mind. This paper will demonstrate the importance of balancing qualitative and quantitative research methods in investigating the minds of people with ASD. It will enrich our theoretical understanding of Theory-of-Mind, as well as contain methodological implications for further studies in Theory-of-Mind

Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

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.

Continuum of police crime : an empirical study of court cases

The great majority of police officers are committed to honourable and competent public service and consistently demonstrate integrity and accountability in carrying out the often difficult, complex and sometimes dangerous, activities involved in policing by consent. However, in every police agency there exists an element of dishonesty, lack of professionalism and criminal behaviour. This article is based on archival research of criminal behaviour in the Norwegian police force. A total of 60 police employees were prosecuted in court because of misconduct and crime from 2005 to 2010. Court cases were coded as two potential predictors of court sentence in terms of imprisonment days, ie, type of deviance and level of deviance. Categories of police crime and levels were organised according to a conceptual framework developed for assessing and managing police deviance. Empirical findings support the hypothesis that as the seriousness of police crime increases in breadth and depth so also does the severity of the court sentence as measured by time in prison.

A continuum model of the growth of engineered epidermal skin substitutes

We present a porous medium model of the growth and deterioration of the viable sublayers of an epidermal skin substitute. It consists of five species: cells, intracellular and extracellular calcium, tight junctions, and a hypothesised signal chemical emanating from the stratum corneum. The model is solved numerically in Matlab using a finite difference scheme. Steady state calcium distributions are predicted that agree well with the experimental data. Our model also demonstrates epidermal skin substitute deterioration if the calcium diffusion coefficient is reduced compared to reported values in the literature.

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.