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Full Text, Thesis (PhD Doctorate), Doctor of Philosophy (PhD), School of Environment and Sc, Science, Environment, Engineering and Technology, Coarctation of the Aorta (CoA) is a disease that is present in newborns and is commonly described as a short section of narrowing in the aorta. This thesis uses mathematical and numerical modelling to investigate both pre- and post-treatment issues experienced by CoA patients, by examining the effect of the coarctation, some associated cardiovascular abnormalities, as well as treatments for CoA, on blood flow properties. CoA is a serious congenital heart disease, and the mean age of mortality has been estimated to be 34 years. Treatments generally focus on resolving the physical restriction in the aorta, which is the coarctation, although CoA is associated with many cardiovascular abnormalities. Despite the availability of several treatments, treated CoA patients experience late hypertension and have a decreased life expectancy compared to normal people. Two examples of treatments are resection and end-to-end anastomosis (REA) and stents. REA is a surgical treatment that involves excising the coarctation and suturing the remaining aorta together. Stents are a catheter-based intervention where a catheter is inserted into the artery and used to expand a metal stent into the coarctation. It is unclear whether a particular treatment is superior, as there is insufficient long-term data for some treatments. Several reviews of treatments for CoA have concluded that additional data are required to understand whether these recently utilised treatments result in superior long-term outcomes. Numerical simulation of mathematical models of blood flow in arteries can be used to investigate and compare treatments where clinical data are lacking, and difficult or expensive to obtain. This thesis uses existing one-dimensional mathematical models of blood flow in arteries, which have been shown to reproduce the main features of hemodynamics. Equations are developed to implement altered arterial properties, such as artery wall stiffness and cross-sectional luminal area, in the models.

Full Text, Thesis (PhD Doctorate), Doctor of Philosophy (PhD), School of Environment and Sc, Science, Environment, Engineering and Technology, Infectious diseases are a serious problem throughout the world and are responsible for a large number of deaths annually. It is estimated that tuberculosis was respon- sible for 1.3 million deaths in 2016 worldwide. Malaria, a vector-transmitted dis- ease (transmitted to humans by mosquitoes), is responsible for almost half a million deaths annually. There are also many sexually transmitted diseases, such as chlamy- dia, genital herpes and gonorrhea, as well as the much more serious HIV/AIDS. In order to help prevent the spread of an infectious disease, we rst need to understand how the disease is spreading through the population, as well as how fast it is spreading. To do this, we need to build mathematical models for the disease. These are referred to as epidemic models. These models can also help predict the e ectiveness of interventions, such as treatment and vaccines. One of the most widely used methods for constructing an epidemic model is the use of compartmental models. Each person within the population is assigned to a speci c compartment, based upon their current status with regard to the disease. As their status changes, for example, if they contract the disease, they are moved to the appropriate compartment. Using the compartment model, a system of ordinary di erential equations can be derived that models the disease. As the system of ordinary di erential equations is usually non-linear, numerical solvers often need to be used as an analytic solution is rarely obtainable. While it is usually a relatively easy process to derive a model for a particular dis- ease, the parameters within these compartment models are rarely known and usually have to be estimated. Even for well-studied or seasonal diseases, these parameter values are usually not known with certainty and are instead given as probability distributions or simply as a plausible range of values. Since the parameter values are not known with certainty, it is important for this uncertainty to be incl

Full Text, Thesis (PhD Doctorate), Doctor of Philosophy (PhD), School of Environment and Sc, Science, Environment, Engineering and Technology, Tissue engineering is one of the most rapidly developing areas in healthcare. A variety of different fabrication techniques, types of biomaterials, and their modification approaches have been studied lately. Significant progress in the design of artificial matrices has led to an evolution from a simple supporting scaffold to a more sophisticated biomaterial environment. Bioabsorbable materials can be employed to fabricate such complex systems. Ideally, these materials should allow for the prevention of further surgeries in order to avoid the removal of scaffolds, as well as allow for the delivery of desired drugs or growth factors to accelerate body tissue recovery. Polymeric scaffolds as drug delivery carriers play a crucial role in the development of tissue engineering. Targeted drug delivery at a specific site with controlled release rates can lead to the reduction of the required dosage and thus fewer side effects. Bioabsorbable polymers should degrade with the desired rate, eluting the drug at predetermined times, and keeping the drug concentration within the therapeutic window in the release medium. The design of the controlled release device may vary significantly due to the local anatomy and microenvironment. Nevertheless, the microstructure of the scaffolds is preferred to be fibrous for better integration in the body. Moreover, the high surface area to volume ratio of the fibrous scaffolds allows high drug loading amount per unit mass. To gain new knowledge in the field of polymeric drug delivery carriers, this study has been divided into two sections. The first direction of the study is the employment of mathematical modeling for the purpose of studying drug release kinetics from various materials which can be potentially used as drug delivery carriers in tissue engineering. The second direction is the investigation of surface modification approaches for controlling drug release from polymeric materials. The notion of combining theoretical and experimenta

Full Text, Thesis (PhD Doctorate), Doctor of Philosophy (PhD), School of Natural Sciences, Science, Environment, Engineering and Technology, Atherosclerosis is a condition whereby fatty material is deposited in the walls of arteries resulting in a thickening of the wall. It is the leading cause of morbidity and mortality in much of the world, including Australia. Some of the clinical manifestations of atherosclerosis include acute ischaemic syndromes such as heart attacks and strokes. Despite continuous eorts over the past four decades, the biology of atherosclerosis and its clinical manifestations are still poorly understood. According to the response-to-injury hypothesis, this disease is initiated by an injury to or dysfunctionality of the inner lining of the artery (the endothelium) and progresses through multiple dynamical cell processes. Mathematical models that take into account the initiation of atherosclerosis can be used to provide an integrated description of the mechanisms of the formation of an early atherosclerotic lesion. Such models may have signicant utility for designing future clinical and experimental studies, as well as in the development of therapeutic hypotheses and the provision of preventative advice for an individual or group of patients. This thesis aims to develop models of the cellular dynamics of the process of early atherosclerosis, which will enhance the understanding of the cellular mechanics behind the formation of an early atherosclerotic lesion. In order to address the aims of the thesis, we present increasingly more realistic models.

Full Text, Thesis (PhD Doctorate), Doctor of Philosophy (PhD), School of Natural Sciences, Science, Environment, Engineering and Technology, Molecular modelling plays an important and complementary role to experimental studies. In this thesis we use molecular dynamic simulations and time correlation functions to examine the isomerization of n-butane and to perform a proof-of-concept demonstration, applying the dissipation theorem to calculating transport properties. Equilibrium molecular dynamics are used to determine the solvent shift and rate constants in the isomerization process of n-butane. Furthermore the effects of confining n-butane to a nanopore are examined and compared to in two different wall-models. The structure and dynamics of a fluid can be affected when confined to pores of nanometre widths. An understanding of the effects of confinement on the equilibrium composition of reacting mixtures, diffusion and adsorption rates, can lead to improvements in industrial processes such as in the food and pharmaceutical industry. A known effect of confinement is wetting of the walls due to interactions between the wall and the fluid. Examination of the local molecular fluid density across the pore has shown that the degree of wetting is a function of pore width, mean fluid density and wall surface density.

Full Text, Thesis (PhD Doctorate), Doctor of Philosophy (PhD), School of Biomolecular and Physical Sciences., Science, Environment, Engineering and Technology, Computer simulations have become an important tool for modeling the electrical behaviour of ischaemia in the heart, in order to better understand the processes involved and increase accuracy in patient diagnosis. Unfortunately, there is still not a complete understanding of the relationship between the electrical and physical properties of a heart which contains ischaemia. The work presented here focuses on obtaining a better understanding of the electrical behaviour at the epicardium due to localised ischaemia during the ST segment. This is achieved by solving the bidomain equations using both steady state and transient methods. Three separate models of increasing complexity are used to represent the cardiac geometry: a rectangular slab of ventricular tissue resting on a large volume of blood; a half-ellipsoid shape, which represents the left ventricle (filled with blood) and a final model (which contains both the left and right ventricles) that is based on experimental measurements of a dog heart.

Full Text, Thesis (PhD Doctorate), Doctor of Philosophy (PhD), School of Biomolecular and Physical Sciences, Science, Environment, Engineering and Technology, Knowledge of free-energy differences for states of a system provides an essential component in understanding many processes, including solubility, reaction rates, and phase changes. Therefore, the development of efficient, accurate free-energy calculation routines has long been of interest within the field of molecular modelling. Until recently, thermodynamic integration, free-energy perturbation and slow-change techniques were the only approaches available for the calculation of free-energy differences between two states of a system. However, with the discovery of non-equilibrium free-energy relations in the late nineties, new calculation approaches are now possible. This thesis demonstrates the application of these new relations by deriving them from statistical mechanical concepts and applying them to a variety of systems. Although other types of systems are considered, the focus of this work is on the investigation of density changes, as the density of a system is one of its fundamental intrinsic properties, and expansion and compression phenomena are central to many thermodynamic investigations. To investigate the convergence properties of the free-energy calculation methods prior to their application to systems undergoing a density change, a novel transformation between Lennard-Jones systems possessing different potentials is developed and simulations are completed for a variety of transformation parameters. In particular, the accuracy of free-energy calculations as a function of transformation rate is considered, along with a detailed analysis of free-energy convergence as a function of the number of transformations completed.

We present an analytic solution for the d-dimensional (d > 1) hard-sphere free flight trajectories in a thermostatted colour field. The solution shows that particles can only reach a finite distance in the direction perpendicular to the field in the absence of collisions. Using a numerical algorithm we designed to simulate many-body hard-sphere systems with curved trajectories, we study the onset of the instability leading to phase separation in the two-dimensional case for a range of field strengths and three densities. For the two fluid densities we find that phase separation occurs for sufficiently strong fields regardless of the initial configuration, and that the phase-separated state eventually becomes a collisionless, non-ergodic steady state. For solid densities the phase-separated configuration is stable and conducting, but is not an attractor for other charge distributions because of the impossibility of particle rearrangement.

The analytical solutions for collision free trajectories in an N particle thermostatted hard-sphere system undergoing homogeneous shear were discussed. The solutions led to the equivalence of constant temperature and constant energy ensembles in the thermodynamic limit in equilibrium and the conditions for the nature of heat exchange with the environment in the system. The condition for appearance of the artificial string phase also followed from the solutions.

A new method of thermostatting non-equilibrium molecular dynamics (NEMD) simulations is described. The thermostat is based on a recently developed, entirely configurational expression for the temperature. To demonstrate this method, thermostatted NEMD simulations are performed on WCA atoms, linear, freely jointed Lennard-Jones 8-mer chains and a united-atom model of n-decane under a constant applied strain rate. The results of simulations thermostatted kinetically (the standard method) and configurationally are compared. As expected, both types of thermostat yield identical system properties for low strain rates. For higher strain rates, both thermostats yield the same qualitative dependence of system properties on applied strain rate. The great advantage of the configurational thermostat is that no a priori knowledge of the streaming velocity is required. For molecular systems and atomic systems in most flow geometries, the analytical form for the atomic streaming velocity is not known. This makes the implementation of standard kinetic thermostats highly problematic.

We show that arbitrary phase space vector fields can be used to generate phase functions whose ensemble averages give the thermodynamic temperature. We describe conditions for the validity of these functions in periodic boundary systems and the molecular

Non-equilibrium molecular dynamics (NEMD) simulations are used to study the generation of heat fluxes in systems with spatially varying shear rates. We show that the kinetic temperature, when used in Fourier's law of heat conduction, does not correctly account for the heat flux, and that the normal temperature as described by Rugh (1997, Phys. Rev. Lett., 78, 772), should be used. Only in the absence of normal temperature gradients can heat fluxes due to strain rate coupling be correctly calculated.

[Unable to convert symbols, please look at PDF version for symbols] A new diagnostic that is useful for checking the algorithmic correctness of Monte Carlo computer programs is presented. The check is made by comparing the Boltzmann temperature, which is input to the program and used to accept or reject moves, with a configurational temperature k T B config [unable to convert symbol, please see PDF]. Here, F is the potential energy of the system and [symbal]represents the dimensionless gradient operator with respect to the particle positions [symbol]. We show, using a simulation of Lennard-Jones particles, that the configurational temperature rapidly and accurately tracks changes made to the input temperature even when the system is not in global thermodynamic equilibrium. Coding and/or algorithmic errors can be detected by checking that the input temperature and Tconfig agree. The effects of system size and continuity of F and its first derivative on Tconfig are also discussed.