Mathematical modelling of tumour growth and interaction with host tissue and the immune system

In this thesis, three mathematical models describing the growth of solid tumour incorporating the host tissue and the immune system response are developed and investigated. The initial model describes the dynamics of the growing tumour and immune response before being extended in the second model by introducing a time-varying dendritic cell-based treatment strategy. Finally, in the third model, we present a mathematical model of a growing tumour using a hybrid cellular automata. These models can provide information to pre-experimental work to assist in designing more effective and efficient laboratory experiments related to tumour growth and interactions with the immune system and immunotherapy.

Three-dimensional geological modelling of the Galilee and central Eromanga basins, Australia: New insights into aquifer/aquitard geometry and potential influence of faults on inter-connectivity

Study region The Galilee and Eromanga basins are located in central Queensland, Australia. Both basins are components of the Great Artesian Basin which host some of the most significant groundwater resources in Australia. Study focus This study evaluates the influence of regional faults on groundwater flow in an aquifer/aquitard interbedded succession that form one of the largest Artesian Basins in the world. In order to assess the significance of regional faults as potential barriers or conduits to groundwater flow, vertical displacements of the major aquifers and aquitards were studied at each major fault and the general hydraulic relationship of units that are juxtaposed by the faults were considered. A three-dimensional (3D) geological model of the Galilee and Eromanga basins was developed based on integration of well log data, seismic surfaces, surface geology and elevation data. Geological structures were mapped in detail and major faults were characterised. New hydrological insights for the region Major faults that have been described in previous studies have been confirmed within the 3D geological model domain and a preliminary assessment of their hydraulic significance has been conducted. Previously unknown faults such as the Thomson River Fault (herein named) have also been identified in this study.

Atheroma: Is calcium important or not? A modelling study of stress within the atheromatous fibrous cap in relation to position and size of calcium deposits

Atheromatous plaque rupture h the cause of the majority of strokes and heart attacks in the developed world. The role of calcium deposits and their contribution to plaque vulnerability are controversial. Some studies have suggested that calcified plaque tends to be more stable whereas others have suggested the opposite. This study uses a finite element model to evaluate the effect of calcium deposits on the stress within the fibrous cap by varying their location and size. Plaque fibrous cap, lipid pool and calcification were modeled as hyperelastic, Isotropic, (nearly) incompressible materials with different properties for large deformation analysis by assigning time-dependent pressure loading on the lumen wall. The stress and strain contours were illustrated for each condition for comparison. Von Mises stress only increases up to 1.5% when varying the location of calcification in the lipid pool distant to the fibrous cap. Calcification in the fibrous cap leads to a 43% increase of Von Mises stress when compared with that in the lipid pool. An increase of 100% of calcification area leads to a 15% stress increase in the fibrous cap. Calcification in the lipid pool does not increase fibrous cap stress when it is distant to the fibrous cap, whilst large areas of calcification close to or in the fibrous cap may lead to a high stress concentration within the fibrous cap, which may cause plaque rupture. This study highlights the application of a computational model on a simulation of clinical problems, and it may provide insights into the mechanism of plaque rupture.

Thermal requirements, field mortality and population phenology modelling of Paropsis atomaria Olivier, an emergent pest in subtropical hardwood plantations

Paropsis atomaria is a recently emerged pest of eucalypt plantations in subtropical Australia. Its broad host range of at least 20 eucalypt species and wide geographical distribution provides it the potential to become a serious forestry pest both within Australia and, if accidentally introduced, overseas. Although populations of P. atomaria are genetically similar throughout its range, population dynamics differ between regions. Here, we determine temperature-dependent developmental requirements using beetles sourced from temperate and subtropical zones by calculating lower temperature thresholds, temperature-induced mortality, and day-degree requirements. We combine these data with field mortality estimates of immature life stages to produce a cohort-based model, ParopSys, using DYMEX™ that accurately predicts the timing, duration, and relative abundance of life stages in the field and number of generations in a spring–autumn (September–May) field season. Voltinism was identified as a seasonally plastic trait dependent upon environmental conditions, with two generations observed and predicted in the Australian Capital Territory, and up to four in Queensland. Lower temperature thresholds for development ranged between 4 and 9 °C, and overall development rates did not differ according to beetle origin. Total immature development time (egg–adult) was approximately 769.2 ± S.E. 127.8 DD above a lower temperature threshold of 6.4 ± S.E. 2.6 °C. ParopSys provides a basic tool enabling forest managers to use the number of generations and seasonal fluctuations in abundance of damaging life stages to estimate the pest risk of P. atomaria prior to plantation establishment, and predict the occurrence and duration of damaging life stages in the field. Additionally, by using local climatic data the pest potential of P. atomaria can be estimated to predict the risk of it establishing if accidentally introduced overseas. Improvements to ParopSys’ capability and complexity can be made as more biological data become available.

Rule-based modelling of iron homeostasis in tuberculosis

To establish itself within the host system, Mycobacterium tuberculosis (Mtb) has formulated various means of attacking the host system. One such crucial strategy is the exploitation of the iron resources of the host system. Obtaining and maintaining the required concentration of iron becomes a matter of contest between the host and the pathogen, both trying to achieve this through complex molecular networks. The extent of complexity makes it important to obtain a systems perspective of the interplay between the host and the pathogen with respect to iron homeostasis. We have reconstructed a systems model comprising 92 components and 85 protein-protein or protein-metabolite interactions, which have been captured as a set of 194 rules. Apart from the interactions, these rules also account for protein synthesis and decay, RBC circulation and bacterial production and death rates. We have used a rule-based modelling approach, Kappa, to simulate the system separately under infection and non-infection conditions. Various perturbations including knock-outs and dual perturbation were also carried out to monitor the behavioral change of important proteins and metabolites. From this, key components as well as the required controlling factors in the model that are critical for maintaining iron homeostasis were identified. The model is able to re-establish the importance of iron-dependent regulator (ideR) in Mtb and transferrin (Tf) in the host. Perturbations, where iron storage is increased, appear to enhance nutritional immunity and the analysis indicates how they can be harmful for the host. Instead, decreasing the rate of iron uptake by Tf may prove to be helpful. Simulation and perturbation studies help in identifying Tf as a possible drug target. Regulating the mycobactin (myB) concentration was also identified as a possible strategy to control bacterial growth. The simulations thus provide significant insight into iron homeostasis and also for identifying possible drug targets for tuberculosis.

Computational modelling and characterisation of nanoparticle-based tuneable photonic crystal sensors

Photonic crystals are materials that are used to control or manipulate the propagation of light through a medium for a desired application. Common fabrication methods to prepare photonic crystals are both costly and intricate. However, through a cost-effective laser-induced photochemical patterning, one-dimensional responsive and tuneable photonic crystals can easily be fabricated. These structures act as optical transducers and respond to external stimuli. These photonic crystals are generally made of a responsive hydrogel that can host metallic nanoparticles in the form of arrays. The hydrogel-based photonic crystal has the capability to alter its periodicity in situ but also recover its initial geometrical dimensions, thereby rendering it fully reversible and reusable. Such responsive photonic crystals have applications in various responsive and tuneable optical devices. In this study, we fabricated a pH-sensitive photonic crystal sensor through photochemical patterning and demonstrated computational simulations of the sensor through a finite element modelling technique in order to analyse its optical properties on varying the pattern and characteristics of the nanoparticle arrays within the responsive hydrogel matrix. Both simulations and experimental results show the wavelength tuneability of the sensor with good agreement. Various factors, including nanoparticle size and distribution within the hydrogel-based responsive matrices that directly affect the performance of the sensors, are also studied computationally. © 2014 The Royal Society of Chemistry.

Modelling raindrop impact and splash erosion processes within a spatial cell: a stochastic approach

A new approach is proposed to simulate splash erosion on local soil surfaces. Without the effect of wind and other raindrops, the impact of free-falling raindrops was considered as an independent event from the stochastic viewpoint. The erosivity of a single raindrop depending on its kinetic energy was computed by an empirical relationship in which the kinetic energy was expressed as a power function of the equivalent diameter of the raindrop. An empirical linear function combining the kinetic energy and soil shear strength was used to estimate the impacted amount of soil particles by a single raindrop. Considering an ideal local soil surface with size of I m x I m, the expected number of received free-failing raindrops with different diameters per unit time was described by the combination of the raindrop size distribution function and the terminal velocity of raindrops. The total splash amount was seen as the sum of the impact amount by all raindrops in the rainfall event. The total splash amount per unit time was subdivided into three different components, including net splash amount, single impact amount and re-detachment amount. The re-detachment amount was obtained by a spatial geometric probability derived using the Poisson function in which overlapped impacted areas were considered. The net splash amount was defined as the mass of soil particles collected outside the splash dish. It was estimated by another spatial geometric probability in which the average splashed distance related to the median grain size of soil and effects of other impacted soil particles and other free-falling raindrops were considered. Splash experiments in artificial rainfall were carried out to validate the availability and accuracy of the model. Our simulated results suggested that the net splash amount and re-detachment amount were small parts of the total splash amount. Their proportions were 0.15% and 2.6%, respectively. The comparison of simulated data with measured data showed that this model could be applied to simulate the soil-splash process successfully and needed information of the rainfall intensity and original soil properties including initial bulk intensity, water content, median grain size and some empirical constants related to the soil surface shear strength, the raindrop size distribution function and the average splashed distance. Copyright (c) 2007 John Wiley & Sons, Ltd.