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.

Application of Geographic Modeling Techniques to Quantify Spatial Access to Health Services Before and After an Acute Cardiac Event: The Cardiac ARIA Project

Background: Access to cardiac services is essential for appropriate implementation of evidence-based therapies to improve outcomes. The Cardiac Accessibility and Remoteness Index for Australia (Cardiac ARIA) aimed to derive an objective, geographic measure reflecting access to cardiac services. Methods: An expert panel defined an evidence-based clinical pathway. Using Geographic Information Systems (GIS), a numeric/alpha index was developed at two points along the continuum of care. The acute category (numeric) measured the time from the emergency call to arrival at an appropriate medical facility via road ambulance. The aftercare category (alpha) measured access to four basic services (family doctor, pharmacy, cardiac rehabilitation, and pathology services) when a patient returned to their community. Results: The numeric index ranged from 1 (access to principle referral center with cardiac catheterization service ≤ 1 hour) to 8 (no ambulance service, > 3 hours to medical facility, air transport required). The alphabetic index ranged from A (all 4 services available within 1 hour drive-time) to E (no services available within 1 hour). 13.9 million (71%) Australians resided within Cardiac ARIA 1A locations (hospital with cardiac catheterization laboratory and all aftercare within 1 hour). Those outside Cardiac 1A were over-represented by people aged over 65 years (32%) and Indigenous people (60%). Conclusion: The Cardiac ARIA index demonstrated substantial inequity in access to cardiac services in Australia. This methodology can be used to inform cardiology health service planning and the methodology could be applied to other common disease states within other regions of the world.

Mathematical modelling of the drying of sol gel microspheres

This thesis presents a mathematical model of the evaporation of colloidal sol droplets suspended within an atmosphere consisting of water vapour and air. The main purpose of this work is to investigate the causes of the morphologies arising within the powder collected from a spray dryer into which the precursor sol for Synroc™ is sprayed. The morphology is of significant importance for the application to storage of High Level Liquid Nuclear Waste. We begin by developing a model describing the evaporation of pure liquid droplets in order to establish a framework. This model is developed through the use of continuum mechanics and thermodynamic theory, and we focus on the specific case of pure water droplets. We establish a model considering a pure water vapour atmosphere, and then expand this model to account for the presence of an atmospheric gas such as air. We model colloidal particle-particle interactions and interactions between colloid and electrolyte using DLVO Theory and reaction kinetics, then incorporate these interactions into an expression for net interaction energy of a single particle with all other particles within the droplet. We account for the flow of material due to diffusion, advection, and interaction between species, and expand the pure liquid droplet models to account for the presence of these species. In addition, the process of colloidal agglomeration is modelled. To obtain solutions for our models, we develop a numerical algorithm based on the Control Volume method. To promote numerical stability, we formulate a new method of convergence acceleration. The results of a MATLAB™ code developed from this algorithm are compared with experimental data collected for the purposes of validation, and further analysis is done on the sensitivity of the solution to various controlling parameters.

The younger audience : children and broadcasting in New Zealand

The role and influence of media in the lives of children are ongoing sources of public, political and academic debates. These debates move back and forth along a care-control continuum (Cohen, 1997), and reflect a commitment both to educate children and to regulate their media experiences. Rapid advancements in computer technologies have vastly expanded the range of media experiences available to children. The development of Internet information and the rapid expansion of channels as a result of digital television have created increasingly accessible and diverse sources of media for children. These media are instantaneous and, in some circumstances, constantly available. As a result, a substantial body of international research has emerged that examines the influence of media consumption on children. How much time do children spend interacting with media? What sorts of media do they access? Are media harmful or beneficial to children? If so, in which contexts? Do media influence children�s personal development? And what role should governments, broadcasters and independent producers play in the regulation of the media? These questions remain central to contemporary debates about children and the media.

Using mobile social media and GIS in health and place research

This paper presents new research methods that combine the use of location-based, social media on mobile phones with geographic information systems (GIS) to explore connections between people, place and health. It discusses the feasibility, limitations, and benefits of using these methods, which enable real-time, location-based, quantitative data to be collected on the recreation, consumption, and physical activity patterns of urban residents in Brisbane, Queensland. The study employs mechanisms already inherent in popular mobile social media applications (Facebook, Twitter and Foursquare) to collect this data. The research methods presented in this paper are innovative and potentially applicable to an increasing number of academic research areas, as well as to a growing range of service providers that benefit from monitoring consumer behaviour, and responding to emerging changes in these patterns and trends. The ability to both collect and map objective, real-time data about the consumption, leisure, recreation, and physical activity patterns amongst urban communities has direct implications for a range of research disciplines including media studies, advertising, health promotion, social marketing, public health inequalities, and urban design.

Critical time scales for advection–diffusion–reaction processes

The concept of local accumulation time (LAT) was introduced by Berezhkovskii and coworkers in 2010–2011 to give a finite measure of the time required for the transient solution of a reaction–diffusion equation to approach the steady–state solution (Biophys J. 99, L59 (2010); Phys Rev E. 83, 051906 (2011)). Such a measure is referred to as a critical time. Here, we show that LAT is, in fact, identical to the concept of mean action time (MAT) that was first introduced by McNabb in 1991 (IMA J Appl Math. 47, 193 (1991)). Although McNabb’s initial argument was motivated by considering the mean particle lifetime (MPLT) for a linear death process, he applied the ideas to study diffusion. We extend the work of these authors by deriving expressions for the MAT for a general one–dimensional linear advection–diffusion–reaction problem. Using a combination of continuum and discrete approaches, we show that MAT and MPLT are equivalent for certain uniform–to-uniform transitions; these results provide a practical interpretation for MAT, by directly linking the stochastic microscopic processes to a meaningful macroscopic timescale. We find that for more general transitions, the equivalence between MAT and MPLT does not hold. Unlike other critical time definitions, we show that it is possible to evaluate the MAT without solving the underlying partial differential equation (pde). This makes MAT a simple and attractive quantity for practical situations. Finally, our work explores the accuracy of certain approximations derived using the MAT, showing that useful approximations for nonlinear kinetic processes can be obtained, again without treating the governing pde directly.

Grounding the internet : categorising the geographies of locative media

Taxonometrical uncertainty is prevalent in the field of locative media, which has been variously referred to as “the geomobile web” (Crawford and Goggin, 2009), “the geoweb” (Lake et al., 2004), “Where 2.0” (O’Reilly, 2008:1), and “DigiPlace” (Zook and Graham, 2007). However, it is not only the rapid development of the technology, or the various academic disciplinary approaches to it, that have resulted in this uncertainty but also the deeply ideological debates and concerns about what locative media should and should not be. The intention of this article is to provide an overview of existing literature and research in this field in order to develop a synthetic overview of the various types of locative media, and the geographies arising from them. Not only will such taxonomy clarify communication about locative media, it will identify for developers, users, policy-makers and scholars the specific contours and affordances of the different types of locative media, as well as the issues associated with them.

Relaxed phylogenetics and dating with confidence

In phylogenetics, the unrooted model of phylogeny and the strict molecular clock model are two extremes of a continuum. Despite their dominance in phylogenetic inference, it is evident that both are biologically unrealistic and that the real evolutionary process lies between these two extremes. Fortunately, intermediate models employing relaxed molecular clocks have been described. These models open the gate to a new field of “relaxed phylogenetics.” Here we introduce a new approach to performing relaxed phylogenetic analysis. We describe how it can be used to estimate phylogenies and divergence times in the face of uncertainty in evolutionary rates and calibration times. Our approach also provides a means for measuring the clocklikeness of datasets and comparing this measure between different genes and phylogenies. We find no significant rate autocorrelation among branches in three large datasets, suggesting that autocorrelated models are not necessarily suitable for these data. In addition, we place these datasets on the continuum of clocklikeness between a strict molecular clock and the alternative unrooted extreme. Finally, we present analyses of 102 bacterial, 106 yeast, 61 plant, 99 metazoan, and 500 primate alignments. From these we conclude that our method is phylogenetically more accurate and precise than the traditional unrooted model while adding the ability to infer a timescale to evolution.

Fatigue crack growth and fatigue life evaluation for welded steel bridge members with initial crack

Initial crack widely exists in the welded members of steel bridge induced by the welding procedure or by the fatigue damage crack initiation. The behavior of crack growth with a view to fatigue damage accumulation on the tip of cracks is discussed. Fatigue life of welded components with initial crack in bridges under traffic loading is investigated. Based on existing fatigue experiment results of welded members with initial crack and the fatigue experiment results of welded bridge members under constant stress cycles, the crack would keep semi-elliptical shape with variable ratio of a/c during the crack propagation. Based on the concept of continuum damage accumulated on the tip of fatigue cracks,the fatigue damage law suitable for steel bridge members under traffic loading is modified to consider the crack growth.The virtual crack growth method and the semi-elliptical crack shape assumption are proposed in this paper to deduce a new model of fatigue crack growth rate for welded bridge members under traffic loading. And the calculated method of the stress intensity factor necessary for evaluation of the fatigue life of welded bridge members with cracks is discussed.The proposed fatigue crack growth model is then applied to calculate the crack growth and the fatigue life of existing welded members with fatigue experimental results. The fatigue crack propagation computation results show that the ratio of crack depth to the half crack surface length a/c is variable during crack propagation process and the stress cycle increases with the increase of a0/c0 with certain a0/t0 .The calculated and measured fatigue lives are generally in good agreement,at some initial conditions of cracking, for welded members widely used in steel bridges.

Numerical analysis of the time variable fractional order mobile-immobile advection-dispersion model

Many physical processes exhibit fractional order behavior that varies with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider the time variable fractional order mobile-immobile advection-dispersion model. Numerical methods and analyses of stability and convergence for the fractional partial differential equations are quite limited and difficult to derive. This motivates us to develop efficient numerical methods as well as stability and convergence of the implicit numerical methods for the fractional order mobile immobile advection-dispersion model. In the paper, we use the Coimbra variable time fractional derivative which is more efficient from the numerical standpoint and is preferable for modeling dynamical systems. An implicit Euler approximation for the equation is proposed and then the stability of the approximation are investigated. As for the convergence of the numerical scheme we only consider a special case, i.e. the time fractional derivative is independent of time variable t. The case where the time fractional derivative depends both the time variable t and the space variable x will be considered in the future work. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

A unified description language for human to automated services

Through the rise of cloud computing, on-demand applications, and business networks, services are increasingly being exposed and delivered on the Internet and through mobile communications. So far, services have mainly been described through technical interface descriptions. The description of business details, such as pricing, service-level, or licensing, has been neglected and is therefore hard to automatically process by service consumers. Also, third-party intermediaries, such as brokers, cloud providers, or channel partners, are interested in the business details in order to extend services and their delivery and, thus, further monetize services. In this paper, the constructivist design of the UnifiedServiceDescriptionLanguage (USDL), aimed at describing services across the human-to-automation continuum, is presented. The proposal of USDL follows well-defined requirements which are expressed against a common service discourse and synthesized from currently available servicedescription efforts. USDL's concepts and modules are evaluated for their support of the different requirements and use cases.

Molecular investigation of the mechanical properties of single actin filaments based on vibration analyses

The mechanical vibration properties of single actin filaments from 50 to 288 nm are investigated by the molecular dynamics simulation in this study. The natural frequencies obtained from the molecular simulations agree with those obtained from the analytical solution of the equivalent Euler–Bernoulli beam model. Through the convergence study of the mechanical properties with respect to the filament length, it was found that the Euler–Bernoulli beam model can only be reliably used when the single actin filament is of the order of hundreds of nanometre scale. This molecular investigation not only provides the evidence for the use of the continuum beam model in characterising the mechanical properties of single actin filaments, but also clarifies the criteria for the effective use of the Euler–Bernoulli beam model.

Tolerance, Freedom, Justice and Peace?: Britain, Australia and anti-Muslim Racism in the UK and Australia before 11 September 2001

Since 11 September 2001, Muslim minorities have experienced intensive "othering" in “Western” countries, above all in those US-led anglophone nations which invaded Afghanistan and Iraq to prosecute their "war on terror". This paper examines the cases of Britain and Australia, where whole communities of Muslims have been criminalised as "evil" and a "fifth column" enemy within by media, politicians, the security services and the criminal justice system. Although constituted by disparate ethnic groups, the targeted communities in each of these nations have experienced similar treatment in the State's anti-terrorist measures, as well as ideological responses and everyday racism, making comparable the two cases.

The performance and politics of practice for New Graduate Nurses

The change from nursing student to Registered Nurse (RNs) is both a desirable and anticipated event for New Graduate Nurses (NGNs). Having completed their formal education, most NGNs approach the threshold of their professional career with mixed emotions. While excited about the future and eagerly awaiting the commencement of employment, many are aware that this change also signifies a time of personal upheaval, professional insecurity and further personal learning. In the nursing professions’ enthusiasm to facilitate a smooth passage for NGNs a vast literature now addresses preparation-for-practice degrees, as well as the perceived workplace deficits and support needs of NGNs. However, the importance this change from working as a student to working as a NGN is not well conceptualised, theorised or understood as this largely instrumental literature essentially reduces the problematisation of the NGN transition experience to the problematisation of the individual by identifying NGNs as ‘the’ problem. Subsequently it fails to expose or challenge the normative assumptions underpinning processes that have formerly been considered solutions, or, the impact of such processes in a workplace that frames itself as “supportive”. Conspicuously absent is an exploration of how the NGN role is performed by former students, now beginning RNs undergoing the very personal transition of “becoming registered nurses”. Using Goffman’s (1956) theorisation of performance in everyday life exploring how process and meaning in mundane interactions present themselves in the “regular” lives of people at large, and Margaret Archer’s (2000) work emphasising the significance of the inner dialogue for managing the emotions that emerge out of situations that confront us, this paper draws upon data collected during a study of NGNs’ experience of transition to practice (Malouf 2010). It focuses on an emergent understanding of the need to differentiate the performance of ‘student’ from that of ‘NGN’ role. Further, it explores how these roles have become conflated into a conceptual continuum and viewed as a slide from student to NGN performance, rather than a significant moment of change involving roles that need to be distinctly defined as a necessary precursor to enhancing and supporting the professional and personal development of beginning practitioners.

Multimodal and monomodal discourses of marketization in higher education : power, ideology, and the absence of the image

The ubiquity of multimodality in hypermedia environments is undeniable. Bezemer and Kress (2008) have argued that writing has been displaced by image as the central mode for representation. Given the current technical affordances of digital technology and user-friendly interfaces that enable the ease of multimodal design, the conspicuous absence of images in certain domains of cyberspace is deserving of critical analysis. In this presentation, I examine the politics of discourses implicit within hypertextual spaces, drawing textual examples from a higher education website. I critically examine the role of writing and other modes of production used in what Fairclough (1993) refers to as discourses of marketisation in higher education, tracing four pervasive discourses of teaching and learning in the current economy: i) materialization, ii) personalization, iii) technologisation, and iv) commodification (Fairclough, 1999). Each of these arguments is supported by the critical analysis of multimodal texts. The first is a podcast highlighting the new architectonic features of a university learning space. The second is a podcast and transcript of a university Open Day interview with prospective students. The third is a time-lapse video showing the construction of a new science and engineering precinct. These three multimodal texts contrast a final web-based text that exhibits a predominance of writing and the powerful absence or silencing of the image. I connect the weightiness of words and the function of monomodality in the commodification of discourses, and its resistance to the multimodal affordances of web-based technologies, and how this is used to establish particular sets of subject positions and ideologies through which readers are constrained to occupy. Applying principles of critical language study by theorists that include Fairclough, Kress, Lemke, and others whose semiotic analysis of texts focuses on the connections between language, power, and ideology, I demonstrate how the denial of image and the privileging of written words in the multimodality of cyberspace is an ideological effect to accentuate the dominance of the institution.