Mathematical modelling of tumour-induced angiogenesis

The growth of solid tumours beyond a critical size is dependent upon angiogenesis, the formation of new blood vessels from an existing vasculature. Tumours may remain dormant at microscopic sizes for some years before switching to a mode in which growth of a supportive vasculature is initiated. The new blood vessels supply nutrients, oxygen, and access to routes by which tumour cells may travel to other sites within the host (metastasize). In recent decades an abundance of biological research has focused on tumour-induced angiogenesis in the hope that treatments targeted at the vasculature may result in a stabilisation or regression of the disease: a tantalizing prospect. The complex and fascinating process of angiogenesis has also attracted the interest of researchers in the field of mathematical biology, a discipline that is, for mathematics, relatively new. The challenge in mathematical biology is to produce a model that captures the essential elements and critical dependencies of a biological system. Such a model may ultimately be used as a predictive tool. In this thesis we examine a number of aspects of tumour-induced angiogenesis, focusing on growth of the neovasculature external to the tumour. Firstly we present a one-dimensional continuum model of tumour-induced angiogenesis in which elements of the immune system or other tumour-cytotoxins are delivered via the newly formed vessels. This model, based on observations from experiments by Judah Folkman et al., is able to show regression of the tumour for some parameter regimes. The modelling highlights a number of interesting aspects of the process that may be characterised further in the laboratory. The next model we present examines the initiation positions of blood vessel sprouts on an existing vessel, in a two-dimensional domain. This model hypothesises that a simple feedback inhibition mechanism may be used to describe the spacing of these sprouts with the inhibitor being produced by breakdown of the existing vessel's basement membrane. Finally, we have developed a stochastic model of blood vessel growth and anastomosis in three dimensions. The model has been implemented in C++, includes an openGL interface, and uses a novel algorithm for calculating proximity of the line segments representing a growing vessel. This choice of programming language and graphics interface allows for near-simultaneous calculation and visualisation of blood vessel networks using a contemporary personal computer. In addition the visualised results may be transformed interactively, and drop-down menus facilitate changes in the parameter values. Visualisation of results is of vital importance in the communication of mathematical information to a wide audience, and we aim to incorporate this philosophy in the thesis. As biological research further uncovers the intriguing processes involved in tumourinduced angiogenesis, we conclude with a comment from mathematical biologist Jim Murray, Mathematical biology is : : : the most exciting modern application of mathematics.

Use of a zeolite synthesised from alkali treated kaolin as a K fertiliser : glasshouse experiments on leaching and uptake of K by wheat plants in sandy soil

Zeolite N, a zeolite referred to in earlier publications as MesoLite, is made by caustic reaction of kaolin at temperatures between 80 °C and 95 °C. This material has a very high cation exchange capacity (CEC ≈ 500 meq/100 g). Soil column leaching experiments have shown that K-zeolite N additions greatly reduce leaching of NH4+ fertilisers but the agronomic effectiveness of the retained K+ and NH4+ is unknown. To measure the bioavailability of K in this zeolite, wheat was grown in a glasshouse with K-zeolite N as the K fertiliser in highly-leached and non-leached pots for four weeks and compared with a soluble K fertiliser (KCl). The plants grown in non-leached pots and fertilised with K-zeolite N were slightly larger than those grown with KCl. The elemental compositions in the plants were similar except for Si being significantly more concentrated in the plants supplied with K-zeolite N. Thus K-zeolite N may be an effective K-fertiliser. Plants grown in highly-leached pots were significantly smaller than those grown in non-leached pots. Plants grown in highly-leached pots were severely K deficient as half of the K from both KCl and K-zeolite N was leached from the pots within three days.

Solder joint defects classification using the Log-Gabor Filter, the Discrete Wavelet Transform and the Discrete Cosine Transform

Inspection of solder joints has been a critical process in the electronic manufacturing industry to reduce manufacturing cost, improve yield, and ensure project quality and reliability. This paper proposes the use of the Log-Gabor filter bank, Discrete Wavelet Transform and Discrete Cosine Transform for feature extraction of solder joint images on Printed Circuit Boards (PCBs). A distance based on the Mahalanobis Cosine metric is also presented for classification of five different types of solder joints. From the experimental results, this methodology achieved high accuracy and a well generalised performance. This can be an effective method to reduce cost and improve quality in the production of PCBs in the manufacturing industry.

Factors of process model comprehension : findings from a series of experiments

In order to make good decisions about the design of information systems, an essential skill is to understand process models of the business domain the system is intended to support. Yet, little knowledge to date has been established about the factors that affect how model users comprehend the content of process models. In this study, we use theories of semiotics and cognitive load to theorize how model and personal factors influence how model viewers comprehend the syntactical information of process models. We then report on a four-part series of experiments, in which we examined these factors. Our results show that additional semantical information impedes syntax comprehension, and that theoretical knowledge eases syntax comprehension. Modeling experience further contributes positively to comprehension efficiency, measured as the ratio of correct answers to the time taken to provide answers. We discuss implications for practice and research.

Tax concessions for charities : competitive neutrality, the tax base and "public goods" choice

It is argued that concerns arise about the integrity and fairness of the taxation regime where charitable organizations, which avail themselves of the tax exemption status while undertaking commercial activities, compete directly with the for-profit sector. The appropriateness of the tax concessions granted to charitable organizations is considered in respect of income derived from commercial activities. It is principally argued that the traditional line of reasoning for imposing limitations on tax concessions focuses on an incorrect underlying inquiry. Traditionally, it is argued that limitations should be imposed because of unfair competition, lack of competitive neutrality, or an arbitrary decision relating to a lack of deserving. However, it is argued that a more appropriate question from which to base any limitations is one which considers the value attached to the integrity of the taxation regime as a whole, and the tax base specifically compared to the public good of charities. When the correct underlying question is asked, sound taxation policy ensues, as a less arbitrary approach may be adopted to limit the scope of tax concessions available to charitable organizations.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Outsourcing and cutting choice in private hospital menus – does it impact on patient foodservice satisfaction?

Patient satisfaction with foodservices is multidimensional. It is well recognised that food and other aspects of foodservice delivery are important elements of patients overall perception of the hospital experience. This study aimed to determine whether menu changes in 2008 at an acute private hospital, considered negative by the dietetic staff, would affect patient satisfaction with the foodservice. Changes to the menu, secondary to the refurbishment of the foodservice facilities decreased the number of choices at breakfast from six to four, and altered the dessert menu to include a larger proportion of commercially produced products. The Acute Care Hospital Foodservice Patient Satisfaction Questionnaire (ACHFPSQ) was utilised to assess patient satisfaction with the menu changes, as it has proven accuracy and reliability in measuring patient satisfaction. Results of the survey (n=306) were compared to data with previous ACHFPSQ surveys conducted annually since 2003. Data analysed included overall foodservice satisfaction and four dimensions of foodservice satisfaction: food quality, meal service quality, staff/service issues and the physical environment. Satisfaction targets were set at 4 (scale 1–5) for each foodservice dimension. Analysis showed that despite changes to the menu, overall foodservice satisfaction rated high, with a score of 4.3. Eighty-six percent of patients rated the foodservice as either ‘very good’ or ‘good’. The four foodservice dimensions were rated highly (4.2–4.8). Findings were consistent with previous survey results, demonstrating a high level of patient satisfaction across all dimensions of the foodservice, despite changes to the menu. The annual ACHFPSQ was of value to this practice question.

Intrinsic kinetics of titania photocatalysis : simplified models for their investigation

Even though titanium dioxide photocatalysis has been promoted as a leading green technology for water purification, many issues have hindered its application on a large commercial scale. For the materials scientist the main issues have centred the synthesis of more efficient materials and the investigation of degradation mechanisms; whereas for the engineers the main issues have been the development of appropriate models and the evaluation of intrinsic kinetics parameters that allow the scale up or re-design of efficient large-scale photocatalytic reactors. In order to obtain intrinsic kinetics parameters the reaction must be analysed and modelled considering the influence of the radiation field, pollutant concentrations and fluid dynamics. In this way, the obtained kinetic parameters are independent of the reactor size and configuration and can be subsequently used for scale-up purposes or for the development of entirely new reactor designs. This work investigates the intrinsic kinetics of phenol degradation over titania film due to the practicality of a fixed film configuration over a slurry. A flat plate reactor was designed in order to be able to control reaction parameters that include the UV irradiance, flow rates, pollutant concentration and temperature. Particular attention was paid to the investigation of the radiation field over the reactive surface and to the issue of mass transfer limited reactions. The ability of different emission models to describe the radiation field was investigated and compared to actinometric measurements. The RAD-LSI model was found to give the best predictions over the conditions tested. Mass transfer issues often limit fixed film reactors. The influence of this phenomenon was investigated with specifically planned sets of benzoic acid experiments and with the adoption of the stagnant film model. The phenol mass transfer coefficient in the system was calculated to be km,phenol=8.5815x10-7Re0.65(ms-1). The data obtained from a wide range of experimental conditions, together with an appropriate model of the system, has enabled determination of intrinsic kinetic parameters. The experiments were performed in four different irradiation levels (70.7, 57.9, 37.1 and 20.4 W m-2) and combined with three different initial phenol concentrations (20, 40 and 80 ppm) to give a wide range of final pollutant conversions (from 22% to 85%). The simple model adopted was able to fit the wide range of conditions with only four kinetic parameters; two reaction rate constants (one for phenol and one for the family of intermediates) and their corresponding adsorption constants. The intrinsic kinetic parameters values were defined as kph = 0.5226 mmol m-1 s-1 W-1, kI = 0.120 mmol m-1 s-1 W-1, Kph = 8.5 x 10-4 m3 mmol-1 and KI = 2.2 x 10-3 m3 mmol-1. The flat plate reactor allowed the investigation of the reaction under two different light configurations; liquid and substrate side illumination. The latter of particular interest for real world applications where light absorption due to turbidity and pollutants contained in the water stream to be treated could represent a significant issue. The two light configurations allowed the investigation of the effects of film thickness and the determination of the catalyst optimal thickness. The experimental investigation confirmed the predictions of a porous medium model developed to investigate the influence of diffusion, advection and photocatalytic phenomena inside the porous titania film, with the optimal thickness value individuated at 5 ìm. The model used the intrinsic kinetic parameters obtained from the flat plate reactor to predict the influence of thickness and transport phenomena on the final observed phenol conversion without using any correction factor; the excellent match between predictions and experimental results provided further proof of the quality of the parameters obtained with the proposed method.

Scenes, quarters and clusters : new experiments in the formation and governance of creative places in China

This thesis examines the formation and governance patterns of the social and spatial concentration of creative people and creative business in cities. It develops a typology for creative places, adding the terms 'scene' and 'quarter' to 'clusters', to fill in the literature gap of partial emphasis on the 'creative clusters' model as an organising mechanism for regional and urban policy. In this framework, a cluster is the gathering of firms with a core focus on economic benefits; a quarter is the urban milieu usually driven by a growth coalition consisting of local government, real estate agents and residential communities; and a scene is the spontaneous assembly of artists, performers and fans with distinct cultural forms. The framework is applied to China, specifically to Hangzhou – a second-tier city in central eastern China that is ambitious to become a 'national cultural and creative industries centre'. The thesis selects three cases – Ideal & Silian 166 Creative Industries Park, White-horse Lake Eco-creative City and LOFT49 Creative Industries Park – to represent scene, quarter and cluster respectively. Drawing on in-depth interviews with initiators, managers and creative professionals of these places, together with extensive documentary analysis, the thesis investigates the composition of actors, characteristics of the locality and the diversity of activities. The findings illustrate that, in China, planning and government intervention is the key to the governance of creative space; spontaneous development processes exist, but these need a more tolerant environment, a greater diversity of cultural forms and more time to develop. Moreover, the main business development model is still real estate based: this model needs to incorporate more mature business models and an enhanced IP protection system. The thesis makes a contribution to literature on economic and cultural geography, urban planning and creative industries theory. It advocates greater attention to self-management, collaborative governance mechanisms and business strategies for scenes, quarters and clusters. As intersections exist in the terms discussed, a mixed toolkit of the three models is required to advance the creative city discourse in China.

Practical stability of approximating discrete-time filters with respect to model mismatch

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Practical stability is established in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

The role of organisational concern for workplace fairness in the choice of a performance mesaurement system

Prior studies linking performance management systems (PMS) and organisational justice have examined how PMS influence procedural fairness. Our investigation differs from these studies. First, it examines fairness as an antecedent (instead of as a consequence) of the choice of PMS. Second, instead of conceptualising organisational fairness as procedural fairness, it relies on the impression management interpretation of organisational fairness. Hence, the study investigates how the need of senior managers to cultivate an impression of being fair is related to the choice of PMS systems and employee outcomes. Based on a sample of 276 employees, the results indicate that the need of senior management to cultivate an impression of being fair is associated with employee performance. They also indicate that a substantial component of these effects is indirect through the choice of comprehensive performance measures (CPM) and employee job satisfaction. These findings highlight the importance of organisational concern for workplace fairness as an antecedent of choice of CPM. From a theoretical perspective, the adoption of the impression management interpretation of organisational fairness contributes by providing new insights into the relationship between fairness and choice of PMS from a perspective that is different from those used in prior management accounting research.

Studies on bending limitations for the optimal fit of orthopaedic bone plates

Distal tibial fractures are now commonly treated via intermedullary plate fixation due to higher rates of union and lower rates of postoperative complications. However, patient specific bone morphology demands manual deformation of the plate to ensure appropriate fit along the bone Distal tibial fractures are now commonly treated via intermedullary plate fixation due to higher rates of union and lower rates of postoperative complications. However, patient specific bone morphology demands manual deformation of the plate to ensure appropriate fit along the bone contours, and depending on the material of the plate, different outcomes have been reported along with postoperative complications. A comparative analysis of Stainless Steel 316L and Ti-6Al-4V alloys was carried to estimate the safe bending limit for appropriate fits. The results from the ANSYS FEA simulations were validated with experiments based on ASTM F382-99. It is found that SS316L is better suited for large deformations (up to 16˚ in proximal tip and 7.5˚ in distal end) and Ti for smaller deformation contours (up to 3˚ in proximal tip and 1.8˚ in distal end). The results of this study have profound implications for the choice of plates based on preliminary radiographical fracture examinations to ensure better fixation and higher rates of union of distal tibial fractures.

Beat phenomena in metal nanowires, and their implications for resonance-based elastic property measurements

The elastic properties of 1D nanostructures such as nanowires are often measured experimentally through actuation of the nanowire at its resonance frequency, and then relating the resonance frequency to the elastic stiffness using elementary beam theory. In the present work, we utilize large scale molecular dynamics simulations to report a novel beat phenomenon in [110]oriented Ag nanowires. The beat phenomenon is found to arise from the asymmetry of the lattice spacing in the orthogonal elementary directions of the [110] nanowire, i.e. the [-110] and [001] directions, which results in two different principal moments of inertia. Because of this, actuations imposed along any other direction are found to decompose into two orthogonal vibrational components based on the actuation angle relative to these two elementary directions, with this phenomenon being generalizable to <110> FCC nanowires of different materials (Cu, Au, Ni, Pd and Pt). The beat phenomenon is explained using a discrete moment of inertia model based on the hard sphere assumption, the model is utilized to show that surface effects enhance the beat phenomenon, while the effect is reduced with increasing nanowires cross-sectional size or aspect ratio. Most importantly, due to the existence of the beat phenomena, we demonstrate that in resonance experiments only a single frequency component is expected to be observed, particularly when the damping ratio is relatively large or very small. Furthermore, for a large range of actuation angles, the lower frequency is more likely to be detected than the higher one, which implies that experimental predictions of Young’s modulus obtained from resonance may in fact be under predictions. The present study therefore has significant implications for experimental interpretations of Young’s modulus as obtained via resonance testing.