Modelling the interaction of keratinocytes and fibroblasts during normal and abnormal wound healing processes

The crosstalk between fibroblasts and keratinocytes is a vital component of the wound healing process, and involves the activity of a number of growth factors and cytokines. In this work, we develop a mathematical model of this crosstalk in order to elucidate the effects of these interactions on the regeneration of collagen in a wound that heals by second intention. We consider the role of four components that strongly affect this process: transforming growth factor-beta, platelet-derived growth factor, interleukin-1 and keratinocyte growth factor. The impact of this network of interactions on the degradation of an initial fibrin clot, as well as its subsequent replacement by a matrix that is mainly comprised of collagen, is described through an eight-component system of nonlinear partial differential equations. Numerical results, obtained in a two-dimensional domain, highlight key aspects of this multifarious process such as reepithelialisation. The model is shown to reproduce many of the important features of normal wound healing. In addition, we use the model to simulate the treatment of two pathological cases: chronic hypoxia, which can lead to chronic wounds; and prolonged inflammation, which has been shown to lead to hypertrophic scarring. We find that our model predictions are qualitatively in agreement with previously reported observations, and provide an alternative pathway for gaining insight into this complex biological process.

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.

Water–rock interactions : an investigation of the relationships between mineralogy and groundwater composition and flow in a subtropical basalt aquifer

A holistic study of the composition of the basalt groundwaters of the Atherton Tablelands region in Queensland, Australia was undertaken to elucidate possible mechanisms for the evolution of these very low salinity, silica- and bicarbonate-rich groundwaters. It is proposed that aluminosilicate mineral weathering is the major contributing process to the overall composition of the basalt groundwaters. The groundwaters approach equilibrium with respect to the primary minerals with increasing pH and are mostly in equilibrium with the major secondary minerals (kaolinite and smectite), and other secondary phases such as goethite, hematite, and gibbsite, which are common accessory minerals in the Atherton basalts. The mineralogy of the basalt rocks, which has been examined using X-ray diffraction and whole rock geochemistry methods, supports the proposed model for the hydrogeochemical evolution of these groundwaters: precipitation + CO 2 (atmospheric + soil) + pyroxene + feldspars + olivine yields H 4SiO 4, HCO 3 -, Mg 2+, Na +, Ca 2+ + kaolinite and smectite clays + amorphous or crystalline silica + accessory minerals (hematite, goethite, gibbsite, carbonates, zeolites, and pyrite). The variations in the mineralogical content of these basalts also provide insights into the controls on groundwater storage and movement in this aquifer system. The fresh and weathered vesicular basalts are considered to be important in terms of zones of groundwater occurrence, while the fractures in the massive basalt are important pathways for groundwater movement.

Relative entropy rate based model selection for linear hybrid system filters of uncertain nonlinear systems

Hybrid system representations have been exploited in a number of challenging modelling situations, including situations where the original nonlinear dynamics are too complex (or too imprecisely known) to be directly filtered. Unfortunately, the question of how to best design suitable hybrid system models has not yet been fully addressed, particularly in the situations involving model uncertainty. This paper proposes a novel joint state-measurement relative entropy rate based approach for design of hybrid system filters in the presence of (parameterised) model uncertainty. We also present a design approach suitable for suboptimal hybrid system filters. The benefits of our proposed approaches are illustrated through design examples and simulation studies.

An improved model of tumour-immune system interactions

The immune system plays an important role in defending the body against tumours and other threats. Currently, mechanisms involved in immune system interactions with tumour cells are not fully understood. Here we develop a mathematical tool that can be used in aiding to address this shortfall in understanding. This paper de- scribes a hybrid cellular automata model of the interaction between a growing tumour and cells of the innate and specific immune system including the effects of chemokines that builds on previous models of tumour-immune system interactions. In particular, the model is focused on the response of immune cells to tumour cells and how the dynamics of the tumour cells change due to the immune system of the host. We present results and predictions of in silico experiments including simulations of Kaplan-Meier survival-like curves.

Linear and nonlinear propagation of localised plasmon in metallic nanostructures

A major challenge in modern photonics and nano-optics is the diffraction limit of light which does not allow field localisation into regions with dimensions smaller than half the wavelength. Localisation of light into nanoscale regions (beyond its diffraction limit) has applications ranging from the design of optical sensors and measurement techniques with resolutions as high as a few nanometres, to the effective delivery of optical energy into targeted nanoscale regions such as quantum dots, nano-electronic and nano-optical devices. This field has become a major research direction over the last decade. The use of strongly localised surface plasmons in metallic nanostructures is one of the most promising approaches to overcome this problem. Therefore, the aim of this thesis is to investigate the linear and non-linear propagation of surface plasmons in metallic nanostructures. This thesis will focus on two main areas of plasmonic research –– plasmon nanofocusing and plasmon nanoguiding. Plasmon nanofocusing – The main aim of plasmon nanofocusing research is to focus plasmon energy into nanoscale regions using metallic nanostructures and at the same time achieve strong local field enhancement. Various structures for nanofocusing purposes have been proposed and analysed such as sharp metal wedges, tapered metal films on dielectric substrates, tapered metal rods, and dielectric V-grooves in metals. However, a number of important practical issues related to nanofocusing in these structures still remain unclear. Therefore, one of the main aims of this thesis is to address two of the most important of issues which are the coupling efficiency and heating effects of surface plasmons in metallic nanostructures. The method of analysis developed throughout this thesis is a general treatment that can be applied to a diversity of nanofocusing structures, with results shown here for the specific case of sharp metal wedges. Based on the geometrical optics approximation, it is demonstrated that the coupling efficiency from plasmons generated with a metal grating into the nanofocused symmetric or quasi-symmetric modes may vary between ~50% to ~100% depending on the structural parameters. Optimal conditions for nanofocusing with the view to minimise coupling and dissipative losses are also determined and discussed. It is shown that the temperature near the tip of a metal wedge heated by nanosecond plasmonic pulses can increase by several hundred degrees Celsius. This temperature increase is expected to lead to nonlinear effects, self-influence of the focused plasmon, and ultimately self-destruction of the metal tip. This thesis also investigates a different type of nanofocusing structure which consists of a tapered high-index dielectric layer resting on a metal surface. It is shown that the nanofocusing mechanism that occurs in this structure is somewhat different from other structures that have been considered thus far. For example, the surface plasmon experiences significant backreflection and mode transformation at a cut-off thickness. In addition, the reflected plasmon shows negative refraction properties that have not been observed in other nanofocusing structures considered to date. Plasmon nanoguiding – Guiding surface plasmons using metallic nanostructures is important for the development of highly integrated optical components and circuits which are expected to have a superior performance compared to their electronicbased counterparts. A number of different plasmonic waveguides have been considered over the last decade including the recently considered gap and trench plasmon waveguides. The gap and trench plasmon waveguides have proven to be difficult to fabricate. Therefore, this thesis will propose and analyse four different modified gap and trench plasmon waveguides that are expected to be easier to fabricate, and at the same time acquire improved propagation characteristics of the guided mode. In particular, it is demonstrated that the guided modes are significantly screened by the extended metal at the bottom of the structure. This is important for the design of highly integrated optics as it provides the opportunity to place two waveguides close together without significant cross-talk. This thesis also investigates the use of plasmonic nanowires to construct a Fabry-Pérot resonator/interferometer. It is shown that the resonance effect can be achieved with the appropriate resonator length and gap width. Typical quality factors of the Fabry- Pérot cavity are determined and explained in terms of radiative and dissipative losses. The possibility of using a nanowire resonator for the design of plasmonic filters with close to ~100% transmission is also demonstrated. It is expected that the results obtained in this thesis will play a vital role in the development of high resolution near field microscopy and spectroscopy, new measurement techniques and devices for single molecule detection, highly integrated optical devices, and nanobiotechnology devices for diagnostics of living cells.

Dynamics of rod and cone photoreceptor interactions under mesopic light levels

Visual adaptation regulates contrast sensitivity during dynamically changing light conditions (Crawford, 1947; Hecht, Haig & Chase, 1937). These adaptation dynamics are unknown under dim (mesopic) light levels when the rod (R) and long (L), medium (M) and short (S) wavelength cone photoreceptor classes contribute to vision via interactions in shared non-opponent Magnocellular (MC), chromatically opponent Parvocellular (PC) and Koniocellular (KC) visual pathways (Dacey, 2000). This study investigated the time-course of adaptation and post-receptoral pathways mediating receptor specific rod and cone interactions under mesopic illumination. A four-primary photostimulator (Pokorny, Smithson & Quinlan, 2004) was used to independently control the activity of the four photoreceptor classes and their post-receptoral visual athways in human observers. In the first experiment, the contrast sensitivity and time-course of visual adaptation under mesopic illumination were measured for receptoral (L, S, R) and post-receptoral (LMS, LMSR, L-M) stimuli. An incremental (Rapid-ON) sawtooth conditioning pulse biased detection to ON-cells within the visual pathways and sensitivity was assayed relative to pulse onset using a briefly presented incremental probe that did not alter adaptation. Cone.Cone interactions with luminance stimuli (L cone, LMS, LMSR) reduced sensitivity by 15% and the time course of recovery was 25± 5ms-1 (μ ± SEM). PC mediated (+L-M) chromatic stimuli sensitivity loss was less (8%) than for luminance and recovery was slower (μ = 2.95 ± 0.05 ms-1), with KC mediated (S cone) chromatic stimuli showing a high sensitivity loss (38%) and the slowest recovery time (1.6 ± 0.2 ms-1). Rod-Rod interactions increased sensitivity by 20% and the time course of recovery was 0.7 ± 0.2 ms-1 (μ ± SD). Compared to these interaction types, Rod-Cone interactions reduced sensitivity to a lesser degree (5%) and showed the fastest recovery (μ = 43 ± 7 ms-1). In the second experiment, rod contribution to the magnocellular, parvocellular and koniocellular post-receptoral pathways under mesopic illumination was determined as a function of incremental stimulus duration and waveform (rectangular; sawtooth) using a rod colour match procedure (Cao, Pokorny & Smith, 2005; Cao, Pokorny, Smith & Zele, 2008a). For a 30% rod increment, a cone match required a decrease in [L/(L+M)] and an increase in [L+M] and [S/(L+M)], giving a greenish-blue and brighter appearance for probe durations of 75 ms or longer. Probe durations less than 75 ms showed an increase in [L+M] and no change in chromaticity [L/(L+M) or S/(L+M)], uggesting mediation by the MC pathway only for short duration rod stimuli. s We advance previous studies by determining the time-course and nature of photoreceptor specific retinal interactions in the three post-receptoral pathways under mesopic illumination. In the first experiment, the time-course of adaptation for ON cell processing was determined, revealing opponent cell facilitation in chromatic PC and KC pathways. The Rod-Rod and Rod-Cone data identify previously unknown interaction types that act to maintain contrast sensitivity during dynamically changing light conditions and improve the speed of light adaptation under mesopic light levels. The second experiment determined the degree of rod contribution to the inferred post-eceptoral pathways as a function of the temporal properties of the rod signal. r The understanding of the mechanisms underlying interactions between photoreceptors under mesopic illumination has implications for the study of retinal disease. Visual function has been shown to be reduced in persons with age-related maculopathy (ARM) risk genotypes prior to clinical signs of the disease (Feigl, Cao, Morris & Zele, 2011) and disturbances in rod-mediated adaptation have been shown in early phases of ARM (Dimitrov, Guymer, Zele, Anderson & Vingrys, 2008; Feigl, Brown, Lovie-Kitchin & Swann, 2005). Also, the understanding of retinal networks controlling vision enables the development of international lighting standards to optimise visual performance nder dim light levels (e.g. work-place environments, transportation).

A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.

Assessment of interactions between alluvial, Great Artesian Basin (GAB) and volcanic aquifers using 3D visualisation and environmental tracers, Lockyer Valley, southeast Queensland, Australia

A detailed 3D lithological model framework was developed using GOCAD software to understand interactions between alluvial, volcanic and GAB aquifers and the spatial and temporal distribution of groundwater recharge to the alluvium of the Lockyer Valley. Groundwater chemistry, isotope data (H20-δ2H and δ18O , 87Sr/86Sr, 3H and 14C) and groundwater level time-series data from approximately 550 observation wells were integrated into the catchment-wide 3D model to assess the recharge processes involved. This approach enabled the identification of zones where recharge to the alluvium primarily occurs from stream water during episodic flood events. Importantly, the study also demonstrates that in some sections of the alluvium recharge is also from storm rainfall and seepage discharge from the underlying GAB aquifers. These other sources of recharge are indicated by (a) the absence of a response of groundwater levels to flooding in some areas, (b) old radiocarbon ages, and (c) distinct bedrock water chemistry and δ2H and δ18O signatures in alluvial groundwater at these locations. Integration of isotopes, water chemistry and time-series displays of groundwater levels before and after the 2010/2011 flood into the 3D model suggest that the spatial variations in the alluvial groundwater response are mostly controlled by valley morphology and lithological (i.e. permeability) variations within the alluvium. Examination of the groundwater level variations in the 3D model also enabled quantification of the volumetric change of groundwater stored in the unconfined alluvial aquifer prior to and post-flood events.

Nonlinear H_infinity control of UAVs for collision avoidance in gusty environments

This paper proposes a nonlinear H_infinity controller for stabilization of velocities, attitudes and angular rates of a fixed-wing unmanned aerial vehicle (UAV) in a windy environment. The suggested controller aims to achieve a steady-state flight condition in the presence of wind gusts such that the host UAV can be maneuvered to avoid collision with other UAVs during cruise flight with safety guarantees. This paper begins with building a proper model capturing flight aerodynamics of UAVs. Then a nonlinear controller is developed with gust attenuation and rapid response properties. Simulations are conducted for the Shadow UAV to verify performance of the proposed con- troller. Comparative studies with the proportional-integral-derivative (PID) controllers demonstrate that the proposed controller exhibits great performance improvement in a gusty environment, making it suitable for integration into the design of flight control systems for cruise flight of UAVs.

The interactions between insulin and androgens in progression to castrate resistant prostate cancer

An association between the metabolic syndrome and reduced testosterone levels has been identified, and a specific inverse relationship between insulin and testosterone levels suggests that an important metabolic crosstalk exists between these two hormonal axes; however, the mechanisms by which insulin and androgens may be reciprocally regulated are not well described. Androgen-dependant gene pathways regulate the growth and maintenance of both normal and malignant prostate tissue, and androgen-deprivation therapy (ADT) in patients exploits this dependence when used to treat recurrent and metastatic prostate cancer resulting in tumour regression. A major systemic side effect of ADT includes induction of key features of the metabolic syndrome and the consistent feature of hyperinsulinaemia. Recent studies have specifically identified a correlation between elevated insulin and high-grade PCa and more rapid progression to castrate resistant disease. This paper examines the relationship between insulin and androgens in the context of prostate cancer progression. Prostate cancer patients present a promising cohort for the exploration of insulin stabilising agents as adjunct treatments for hormone deprivation or enhancers of chemosensitivity for treatment of advanced prostate cancer.