Modelling photochemical production of fine particulates in a toluene/NOx/water vapour system

This work investigates the computer modelling of the photochemical formation of smog products such as ozone and aerosol, in a system containing toluene, NOx and water vapour. In particular, the problem of modelling this process in the Commonwealth Scientific and Industrial Research Organization (CSIRO) smog chambers, which utilize outdoor exposure, is addressed. The primary requirement for such modelling is a knowledge of the photolytic rate coefficients. Photolytic rate coefficients of species other than N02 are often related to JNo2 (rate coefficient for the photolysis ofN02) by a simple factor, but for outdoor chambers, this method is prone to error as the diurnal profiles may not be similar in shape. Three methods for the calculation of diurnal JNo2 are investigated. The most suitable method for incorporation into a general model, is found to be one which determines the photolytic rate coefficients for N02, as well as several other species, from actinic flux, absorption cross section and quantum yields. A computer model was developed, based on this method, to calculate in-chamber photolysis rate coefficients for the CSIRO smog chambers, in which ex-chamber rate coefficients are adjusted by accounting for variation in light intensity by transmittance through the Teflon walls, albedo from the chamber floor and radiation attenuation due to clouds. The photochemical formation of secondary aerosol is investigated in a series of toluene-NOx experiments, which were performed in the CSIRO smog chambers. Three stages of aerosol formation, in plots of total particulate volume versus time, are identified: a delay period in which no significant mass of aerosol is formed, a regime of rapid aerosol formation (regime 1) and a second regime of slowed aerosol formation (regime 2). Two models are presented which were developed from the experimental data. One model is empirically based on observations of discrete stages of aerosol formation and readily allows aerosol growth profiles to be calculated. The second model is based on an adaptation of published toluene photooxidation mechanisms and provides some chemical information about the oxidation products. Both models compare favorably against the experimental data. The gross effects of precursor concentrations (toluene, NOx and H20) and ambient conditions (temperature, photolysis rate) on the formation of secondary aerosol are also investigated, primarily using the mechanism model. An increase in [NOx]o results in increased delay time, rate of aerosol formation in regime 1 and volume of aerosol formed in regime 1. This is due to increased formation of dinitrocresol and furanone products. An increase in toluene results in a decrease in the delay time and an increase in the rate of aerosol formation in regime 1, due to enhanced reactivity from the toluene products, such as the radicals from the photolysis of benzaldehyde. Water vapor has very little effect on the formation of aerosol volume, except that rates are slightly increased due to more OH radicals from reaction with 0(1D) from ozone photolysis. Increased temperature results in increased volume of aerosol formed in regime 1 (increased dinitrocresol formation), while increased photolysis rate results in increased rate of aerosol formation in regime 1. Both the rate and volume of aerosol formed in regime 2 are increased by increased temperature or photolysis rate. Both models indicate that the yield of secondary particulates from hydrocarbons (mass concentration aerosol formed/mass concentration hydrocarbon precursor) is proportional to the ratio [NOx]0/[hydrocarbon]0

Pathogenicity of Plesiomonas shigelloides : interactions with eukaryotic host cells in vitro

Diarrhoea is one of the leading causes of morbidity and mortality in populations in developing countries and is a significant health issue throughout the world. Despite the frequency and the severity of the diarrhoeal disease, mechanisms of pathogenesis for many of the causative agents have been poorly characterised. Although implicated in a number of intestinal and extra-intestinal infections in humans, Plesiomonas shigelloides generally has been dismissed as an enteropathogen due to the lack of clearly demonstrated virulence-associated properties such as production of cytotoxins and enterotoxins or invasive abilities. However, evidence from a number of sources has indicated that this species may be the cause of a number of clinical infections. The work described in this thesis seeks to resolve this discrepancy by investigating the pathogenic potential of P. shigelloides using in vitro cell models. The focus of this research centres on how this organism interacts with human host cells in an experimental model. Very little is known about the pathogenic potential of P. shigel/oides and its mechanisms in human infections and disease. However, disease manifestations mimic those of other related microorganisms. Chapter 2 reviews microbial pathogenesis in general, with an emphasis on understanding the mechanisms resulting from infection with bacterial pathogens and the alterations in host cell biology. In addition, this review analyses the pathogenic status of a poorly-defined enteropathogen, P. shigelloides. Key stages of pathogenicity must occur in order for a bacterial pathogen to cause disease. Such stages include bacterial adherence to host tissue, bacterial entry into host tissues (usually required), multiplication within host tissues, evasion of host defence mechanisms and the causation of damage. In this study, these key strategies in infection and disease were sought to help assess the pathogenic potential of P. shigelloides (Chapter 3). Twelve isolates of P. shigelloides, obtained from clinical cases of gastroenteritis, were used to infect monolayers of human intestinal epithelial cells in vitro. Ultrastructural analysis demonstrated that P. shigelloides was able to adhere to the microvilli at the apical surface of the epithelial cells and also to the plasma membranes of both apical and basal surfaces. Furthermore, it was demonstrated that these isolates were able to enter intestinal epithelial cells. Internalised bacteria often were confined within vacuoles surrounded by single or multiple membranes. Observation of bacteria within membranebound vacuoles suggests that uptake of P. shigelloides into intestinal epithelial cells occurs via a process morphologically comparable to phagocytosis. Bacterial cells also were observed free in the host cell cytoplasm, indicating that P. shige/loides is able to escape from the surrounding vacuolar membrane and exist within the cytosol of the host. Plesiomonas shigelloides has not only been implicated in gastrointestinal infections, but also in a range of non-intestinal infections such as cholecystitis, proctitis, septicaemia and meningitis. The mechanisms by which P. shigelloides causes these infections are not understood. Previous research was unable to ascertain the pathogenic potential of P. shigel/oides using cells of non-intestinal origin (HEp-2 cells derived from a human larynx carcinoma and Hela cells derived from a cervical carcinoma). However, with the recent findings (from this study) that P. shigelloides can adhere to and enter intestinal cells, it was hypothesised, that P. shigel/oides would be able to enter Hela and HEp-2 cells. Six clinical isolates of P. shigelloides, which previously have been shown to be invasive to intestinally derived Caco-2 cells (Chapter 3) were used to study interactions with Hela and HEp-2 cells (Chapter 4). These isolates were shown to adhere to and enter both nonintestinal host cell lines. Plesiomonas shigelloides were observed within vacuoles surrounded by single and multiple membranes, as well as free in the host cell cytosol, similar to infection by P. shigelloides of Caco-2 cells. Comparisons of the number of bacteria adhered to and present intracellularly within Hela, HEp-2 and Caco-2 cells revealed a preference of P. shigelloides for Caco-2 cells. This study conclusively showed for the first time that P. shigelloides is able to enter HEp-2 and Hela cells, demonstrating the potential ability to cause an infection and/or disease of extra-intestinal sites in humans. Further high resolution ultrastructural analysis of the mechanisms involved in P. shigelloides adherence to intestinal epithelial cells (Chapter 5) revealed numerous prominent surface features which appeared to be involved in the binding of P. shige/loides to host cells. These surface structures varied in morphology from small bumps across the bacterial cell surface to much longer filaments. Evidence that flagella might play a role in bacterial adherence also was found. The hypothesis that filamentous appendages are morphologically expressed when in contact with host cells also was tested. Observations of bacteria free in the host cell cytosol suggests that P. shigelloides is able to lyse free from the initial vacuolar compartment. The vacuoles containing P. shigel/oides within host cells have not been characterised and the point at which P. shigelloides escapes from the surrounding vacuolar compartment has not been determined. A cytochemical detection assay for acid phosphatase, an enzymatic marker for lysosomes, was used to analyse the co-localisation of bacteria-containing vacuoles and acid phosphatase activity (Chapter 6). Acid phosphatase activity was not detected in these bacteria-containing vacuoles. However, the surface of many intracellular and extracellular bacteria demonstrated high levels of acid phosphatase activity, leading to the proposal of a new virulence factor for P. shigelloides. For many pathogens, the efficiency with which they adhere to and enter host cells is dependant upon the bacterial phase of growth. Such dependency reflects the timing of expression of particular virulence factors important for bacterial pathogenesis. In previous studies (Chapter 3 to Chapter 6), an overnight culture of P. shigelloides was used to investigate a number of interactions, however, it was unknown whether this allowed expression of bacterial factors to permit efficient P. shigelloides attachment and entry into human cells. In this study (Chapter 7), a number of clinical and environmental P. shigelloides isolates were investigated to determine whether adherence and entry into host cells in vitro was more efficient during exponential-phase or stationary-phase bacterial growth. An increase in the number of adherent and intracellular bacteria was demonstrated when bacteria were inoculated into host cell cultures in exponential phase cultures. This was demonstrated clearly for 3 out of 4 isolates examined. In addition, an increase in the morphological expression of filamentous appendages, a suggested virulence factor for P. shigel/oides, was observed for bacteria in exponential growth phase. These observations suggest that virulence determinants for P. shigel/oides may be more efficiently expressed when bacteria are in exponential growth phase. This study demonstrated also, for the first time, that environmental water isolates of P. shigelloides were able to adhere to and enter human intestinal cells in vitro. These isolates were seen to enter Caco-2 host cells through a process comparable to the clinical isolates examined. These findings support the hypothesis of a water transmission route for P. shigelloides infections. The results presented in this thesis contribute significantly to our understanding of the pathogenic mechanisms involved in P. shigelloides infections and disease. Several of the factors involved in P. shigelloides pathogenesis have homologues in other pathogens of the human intestine, namely Vibrio, Aeromonas, Salmonella, Shigella species and diarrhoeaassociated strains of Escherichia coli. This study emphasises the relevance of research into Plesiomonas as a means of furthering our understanding of bacterial virulence in general. As well it provides tantalising clues on normal and pathogenic host cell mechanisms.

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.

Important omitted spatial variables in safety models: Understanding contributing crash causes at intersections

Advances in safety research—trying to improve the collective understanding of motor vehicle crash causation—rests upon the pursuit of numerous lines of inquiry. The research community has focused on analytical methods development (negative binomial specifications, simultaneous equations, etc.), on better experimental designs (before-after studies, comparison sites, etc.), on improving exposure measures, and on model specification improvements (additive terms, non-linear relations, etc.). One might think of different lines of inquiry in terms of ‘low lying fruit’—areas of inquiry that might provide significant improvements in understanding crash causation. It is the contention of this research that omitted variable bias caused by the exclusion of important variables is an important line of inquiry in safety research. In particular, spatially related variables are often difficult to collect and omitted from crash models—but offer significant ability to better understand contributing factors to crashes. This study—believed to represent a unique contribution to the safety literature—develops and examines the role of a sizeable set of spatial variables in intersection crash occurrence. In addition to commonly considered traffic and geometric variables, examined spatial factors include local influences of weather, sun glare, proximity to drinking establishments, and proximity to schools. The results indicate that inclusion of these factors results in significant improvement in model explanatory power, and the results also generally agree with expectation. The research illuminates the importance of spatial variables in safety research and also the negative consequences of their omissions.

Advanced mathematical modelling and experimental investigation of new torque arms for shaft-mounted drives

Shaft-mounted gearboxes are widely used in industry. The torque arm that holds the reactive torque on the housing of the gearbox, if properly positioned creates the reactive force that lifts the gearbox and unloads the bearings of the output shaft. The shortcoming of these torque arms is that if the gearbox is reversed the direction of the reactive force on the torque arm changes to opposite and added to the weight of the gearbox overloads the bearings shortening their operating life. In this paper, a new patented design of torque arms that develop a controlled lifting force and counteract the weight of the gearbox regardless of the direction of the output shaft rotation is described. Several mathematical models of the conventional and new torque arms were developed and verified experimentally on a specially built test rig that enables modelling of the radial compliance of the gearbox bearings and elastic elements of the torque arms. Comparison showed a good agreement between theoretical and experimental results.

Mathematical modelling of chronic wound healing

Chronicwounds fail to proceed through an orderly process to produce anatomic and functional integrity and are a significant socioeconomic problem. There is much debate about the best way to treat these wounds. In this thesis we review earlier mathematical models of angiogenesis and wound healing. Many of these models assume a chemotactic response of endothelial cells, the primary cell type involved in angiogenesis. Modelling this chemotactic response leads to a system of advection-dominated partial differential equations and we review numerical methods to solve these equations and argue that the finite volume method with flux limiting is best-suited to these problems. One treatment of chronic wounds that is shrouded with controversy is hyperbaric oxygen therapy (HBOT). There is currently no conclusive data showing that HBOT can assist chronic wound healing, but there has been some clinical success. In this thesis we use several mathematical models of wound healing to investigate the use of hyperbaric oxygen therapy to assist the healing process - a novel threespecies model and a more complex six-species model. The second model accounts formore of the biological phenomena but does not lend itself tomathematical analysis. Bothmodels are then used tomake predictions about the efficacy of hyperbaric oxygen therapy and the optimal treatment protocol. Based on our modelling, we are able to make several predictions including that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds, treatment should continue until healing is complete and finding the right protocol for an individual patient is crucial if HBOT is to be effective. Analysis of the models allows us to derive constraints for the range of HBOT protocols that will stimulate healing, which enables us to predict which patients are more likely to have a positive response to HBOT and thus has the potential to assist in improving both the success rate and thus the cost-effectiveness of this therapy.

A framework for integrating disadvantaged analysis into transportation planning models

This research paper aims to develop a method to explore the travel behaviour differences between disadvantaged and non-disadvantaged populations. It also aims to develop a modelling approach or a framework to integrate disadvantage analysis into transportation planning models (TPMs). The methodology employed identifies significantly disadvantaged groups through a cluster analysis and the paper presents a disadvantage-integrated TPM. This model could be useful in determining areas with concentrated disadvantaged population and also developing and formulating relevant disadvantage sensitive policies. (a) For the covering entry of this conference, please see ITRD abstract no. E214666.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Students’ approaches to learning a new mathematical model

In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quanti- tative data based around the students’ approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to under- standing a new mathematical model: gathering information for the task of understanding the model, practising with and using the model, and finding interrelationships between elements of the model. We found that the students appreciate mathematical models that have a real world application and that this can be used to engage students in higher level learning approaches.

Contextual models and the non-Newtonian paradigm

Biological systems exhibit a wide range of contextual effects, and this often makes it difficult to construct valid mathematical models of their behaviour. In particular, mathematical paradigms built upon the successes of Newtonian physics make assumptions about the nature of biological systems that are unlikely to hold true. After discussing two of the key assumptions underlying the Newtonian paradigm, we discuss two key aspects of the formalism that extended it, Quantum Theory (QT). We draw attention to the similarities between biological and quantum systems, motivating the development of a similar formalism that can be applied to the modelling of biological processes.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.