Numerical simulation of anomalous diffusion with application to medical imaging

The first objective of this project is to develop new efficient numerical methods and supporting error and convergence analysis for solving fractional partial differential equations to study anomalous diffusion in biological tissue such as the human brain. The second objective is to develop a new efficient fractional differential-based approach for texture enhancement in image processing. The results of the thesis highlight that the fractional order analysis captured important features of nuclear magnetic resonance (NMR) relaxation and can be used to improve the quality of medical imaging.

Harmonic quality of multilevel cascade inverters with random carrier phase pulse width modulation

The output harmonic quality of N series connected full-bridge dc-ac inverters is investigated. The inverters are pulse width modulated using a common reference signal but randomly phased carrier signals. Through analysis and simulation, probability distributions for inverter output harmonics and vector representations of N carrier phases are combined and assessed. It is concluded that a low total harmonic distortion is most likely to occur and will decrease further as N increases.

Metrological performances of a diffusion charger particle counter for personal monitoring

Airborne particles have been shown to be associated with a wide range of adverse health effects, which has led to a recent increase in medical research to gain better insight into their health effects. However, accurate evaluation of the exposure-dose-response relationship is highly dependent on the ability to track actual exposure levels of people to airborne particles. This is quite a complex task, particularly in relation to submicrometer and ultrafine particles, which can vary quite significantly in terms of particle surface area and number concentrations. Therefore, suitable monitors that can be worn for measuring personal exposure to these particles are needed. This paper presents an evaluation of the metrological performance of six diffusion charger sensors, NanoTracer (Philips Aerasense) monitors, when measuring particle number and surface area concentrations, as well as particle number distribution mean when compared to reference instruments. Tests in the laboratory (by generating monodisperse and polydisperse aerosols) and in the field (using natural ambient particles) were designed to evaluate the response of these devices under both steady-state and dynamics conditions. Results showed that the NanoTracers performed well when measuring steady state aerosols, however they strongly underestimated actual concentrations during dynamic response testing. The field experiments also showed that, when the majority of the particles were smaller than 20 nm, which occurs during particle formation events in the atmosphere, the NanoTracer underestimated number concentration quite significantly. Even though the NanoTracer can be used for personal monitoring of exposure to ultrafine particles, it also has limitations which need to be considered in order to provide meaningful results.

Application of kaolin amorphous derivative as a nitrogen carrier

Sandy soils have low nutrient holding capacity and high water conductivity. Consequently, nutrients applied as highly soluble chemical fertilisers are prone to leaching, particularly in heavily irrigated environments such as horticultural soils and golf courses. Amorphous derivatives of kaolin with high cation exchange capacity may be loaded with desired nutrients and applied as controlledrelease fertilisers. Kaolin is an abundant mineral, which can be converted to a meso-porous amorphous derivative (KAD) using facile chemical processes. KAD is currently being used to sequester ammonium from digester effluent in sewage treatment plants in a commercial environment. This material is also known in Australia by the trade name MesoLite. The ammonium-saturated form of KAD may be applied to soils as a nitrogen fertiliser. Up to 7% N can be loaded onto KAD by contacting it with high-ammonia concentration wastewater from sewerage treatment plants. This poster paper demonstrates plant uptake of nitrogen from KAD and compares its efficiency as a fertiliser with NH4SO4. Rye grass was grown in 1kg pots in a glass-house. Nitrogen was applied at a range of rates using NH4SO4 and two KAD materials carrying 7% and 3% nitrogen, respectively. All other nutrients were applied in adequate amounts. All treatments were replicated three times. Plants were harvested after four weeks. Dry mass and N concentrations were determined by standard methods. At all N application rates, ammonium-loaded KAD produced significantly higher plant mass than for NH4SO4. The lower fertiliser effectiveness of NH4SO4 is attributed to possible loss of some N through volatilisation. Of the two KAD types, the material with lower CEC value supported slightly higher plant yields. The KAD materials did not show any adverse effect on availability of trace elements, as evidenced by lack of deficiency symptoms and plant analyses. Clearly, nitrogen loaded on to KAD in the form of ammonium is likely to be protected from leaching, but is still available to plants. These data suggest that KAD-based fertilisers may be suitable substitutes for water soluble N, K and other cation fertilisers for leaching soils.

Harmonic quality of multilevel cascade inverters with random carrier phase pulse width modulation

The output harmonic quality of N series connected full-bridge dc-ac inverters is investigated. The inverters are pulse width modulated using a common reference signal but randomly phased carrier signals. Through analysis and simulation, probability distributions for inverter output harmonics and vector representations of N carrier phases are combined and assessed. It is concluded that a low total harmonic distortion is most likely to occur and will decrease further as N increases.

A simplified approach for calculating the moments of action for linear reaction-diffusion equations

The mean action time is the mean of a probability density function that can be interpreted as a critical time, which is a finite estimate of the time taken for the transient solution of a reaction-diffusion equation to effectively reach steady state. For high-variance distributions, the mean action time under-approximates the critical time since it neglects to account for the spread about the mean. We can improve our estimate of the critical time by calculating the higher moments of the probability density function, called the moments of action, which provide additional information regarding the spread about the mean. Existing methods for calculating the nth moment of action require the solution of n nonhomogeneous boundary value problems which can be difficult and tedious to solve exactly. Here we present a simplified approach using Laplace transforms which allows us to calculate the nth moment of action without solving this family of boundary value problems and also without solving for the transient solution of the underlying reaction-diffusion problem. We demonstrate the generality of our method by calculating exact expressions for the moments of action for three problems from the biophysics literature. While the first problem we consider can be solved using existing methods, the second problem, which is readily solved using our approach, is intractable using previous techniques. The third problem illustrates how the Laplace transform approach can be used to study coupled linear reaction-diffusion equations.

Diffusion tensor of water in partially aligned fibre networks

Monte Carlo simulations were used to investigate the relationship between the morphological characteristics and the diffusion tensor (DT) of partially aligned networks of cylindrical fibres. The orientation distributions of the fibres in each network were approximately uniform within a cone of a given semi-angle (θ0). This semi-angle was used to control the degree of alignment of the fibres. The networks studied ranged from perfectly aligned (θ0 = 0) to completely disordered (θ0 = 90°). Our results are qualitatively consistent with previous numerical models in the overall behaviour of the DT. However, we report a non-linear relationship between the fractional anisotropy (FA) of the DT and collagen volume fraction, which is different to the findings from previous work. We discuss our results in the context of diffusion tensor imaging of articular cartilage. We also demonstrate how appropriate diffusion models have the potential to enable quantitative interpretation of the experimentally measured diffusion-tensor FA in terms of collagen fibre alignment distributions.

Investigations of the physical origins of etching LiNbO3 during Ti in-diffusion

We investigate the physical origins of etching observed during Ti diffusion. The relationship between observed etch depth and water vapor content in the annealing environment is quantified. The dynamics of the etching process are also identified. It is discovered that water vapor content is essential for etching and that there is a characteristic delay before etching is observed. From these observations we can conclude that the process is electrochemical in nature with ionic defects diffusing into the Ti strip from the lithium niobate and these defects catalyzing the dissociation of water into reactive ions.

Diffusion of extreme weather-proofing technology in the built environment

This study addresses the research question: ‘What are the diffusion determinants for extreme weather-proofing technology in the Australian built environment?’ In order to effectively identify diffusion determinants, a synthesis of literature in both technical and management fields was conducted from a system-wide perspective. Review results where then interpreted through an innovation system framework, drawn from innovation systems literature, in order to map the current state of extreme weather-proofing technology diffusion in the Australian built environment industry. Drivers and obstacles to optimal diffusion are presented. Results show the important role to be played by Australian governments in facilitating improved weather proofing technology diffusion. This applies to governments in their various roles, but particularly as regulators, clients/owners and investors in research & development and education. In the role as regulators, findings suggest Australian governments should be encouraging the application of innovative finance options and positive end-user incentives to promote the uptake of weather proofing technology. Additionally, in their role as clients/owners, diffusion can be improved by adjusting building and infrastructure specifications to encourage designers and constructors to incorporate extreme weather proofing technology in new and redeveloped built assets. Finally, results suggest greater investment is required in research and development and improved knowledge sharing across the construction supply chain to further mitigate risks associated with greater incidences of extreme weather events.

Influence of drying conditions on the moisture diffusion and fluidization quality during multi-stage fluidized bed drying of bovine intestine for pet food

In order to establish the influence of the drying air characteristics on the drying performance and fluidization quality of bovine intestine for pet food, several drying tests have been carried out in a laboratory scale heat pump assisted fluid bed dryer. Bovine intestine samples were heat pump fluidized bed dried at atmospheric pressure and at temperatures below and above the materials freezing points, equipped with a continuous monitoring system. The investigation of the drying characteristics have been conducted in the temperature range −10 to 25 ◦C and the airflow in the range 1.5–2.5 m/s. Some experiments were conducted as single temperature drying experiments and others as two stage drying experiments employing two temperatures. An Arrhenius-type equation was used to interpret the influence of the drying air temperature on the effective diffusivity, calculated with the method of slopes in terms of energy activation, and this was found to be sensitive to the temperature. The effective diffusion coefficient of moisture transfer was determined by the Fickian method using uni-dimensional moisture movement in both moisture, removal by evaporation and combined sublimation and evaporation. Correlations expressing the effective moisture diffusivity and drying temperature are reported. Bovine particles were characterized according to the Geldart classification and the minimum fluidization velocity was calculated using the Ergun Equation and generalized equation for all drying conditions at the beginning and end of the trials. Walli’s model was used to categorize stability of the fluidization at the beginning and end of the dryingv for each trial. The determined Walli’s values were positive at the beginning and end of all trials indicating stable fluidization at the beginning and end for each drying condition.

Diffusion-sensitive magnetic resonance spectroscopy and imaging in biomedical sciences

We present a mini-review of the development and contemporary applications of diffusion-sensitive nuclear magnetic resonance (NMR) techniques in biomedical sciences. Molecular diffusion is a fundamental physical phenomenon present in all biological systems. Due to the connection between experimentally measured diffusion metrics and the microscopic environment sensed by the diffusing molecules, diffusion measurements can be used for characterisation of molecular size, molecular binding and association, and the morphology of biological tissues. The emergence of magnetic resonance was instrumental to the development of biomedical applications of diffusion. We discuss the fundamental physical principles of diffusion NMR spectroscopy and diffusion MR imaging. The emphasis is placed on conceptual understanding, historical evolution and practical applications rather than complex technical details. Mathematical description of diffusion is presented to the extent that it is required for the basic understanding of the concepts. We present a wide range of spectroscopic and imaging applications of diffusion magnetic resonance, including colloidal drug delivery vehicles; protein association; characterisation of cell morphology; neural fibre tractography; cardiac imaging; and the imaging of load-bearing connective tissues. This paper is intended as an accessible introduction into the exciting and growing field of diffusion magnetic resonance.

Inferring diffusion in single live cells at the single-molecule level

The movement of molecules inside living cells is a fundamental feature of biological processes. The ability to both observe and analyse the details of molecular diffusion in vivo at the single-molecule and single-cell level can add significant insight into understanding molecular architectures of diffus- ing molecules and the nanoscale environment in which the molecules diffuse. The tool of choice for monitoring dynamic molecular localization in live cells is fluorescence microscopy, especially so combining total internal reflection fluorescence with the use of fluorescent protein (FP) reporters in offering exceptional imaging contrast for dynamic processes in the cell mem- brane under relatively physiological conditions compared with competing single-molecule techniques. There exist several different complex modes of diffusion, and discriminating these from each other is challenging at the mol- ecular level owing to underlying stochastic behaviour. Analysis is traditionally performed using mean square displacements of tracked particles; however, this generally requires more data points than is typical for single FP tracks owing to photophysical instability. Presented here is a novel approach allowing robust Bayesian ranking of diffusion processes to dis-criminate multiple complex modes probabilistically. It is a computational approach that biologists can use to understand single-molecule features in live cells.

Dry powder inhaler formulations-effect of polymer carrier size on the drug dispersion

Background The size of the carrier influences the aerosolization of drug from a dry powder inhaler (DPI) formulation. Currently, lactose monohydrate particles in a variety of sizes are preferably used in carrier based DPI formulations of various drugs; however, contradictory reports exist regarding the effect of the size of the carrier on the dispersion of drug. In this study we examined the influence of the intrinsic particle size of the polymeric carrier on the aerosolization of a model drug salbutamol sulphate (SS). Methods Four different sizes (20–150 lm) of polymer carriers were fabricated using solvent evaporation technique and the dispersion of SS particles from these carriers was measured by a Twin Stage Impinger (TSI). The size and morphological properties of polymer carriers were by laser diffraction and SEM, respectively. Results The FPF from these carriers was found to be increasing from 5.6% to 21.3% with increasing the carrier size. The FPF was found to be greater (21%) with the highest particle size of the carrier (150 lm). Conclusions The aerosolization of drug was dependent on the size of polymer carriers. The smaller size of the carrier resulted in lower FPF which was increased with increasing the carrier size. For a fixed mass of drug particles in a formulation, the mass of drug particles per unit area of carriers is higher in formulations containing the larger carriers, which leads to an increase in the dispersion of drug due to the increased mechanical forces occurred between the carriers and the device walls.

A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

Characterisation of the micro-architecture of direct writing melt electrospun tissue engineering scaffolds using diffusion tensor and computed tomography microimaging

This article describes the first steps toward comprehensive characterization of molecular transport within scaffolds for tissue engineering. The scaffolds were fabricated using a novel melt electrospinning technique capable of constructing 3D lattices of layered polymer fibers with well - defined internal microarchitectures. The general morphology and structure order was then determined using T 2 - weighted magnetic resonance imaging and X - ray microcomputed tomography. Diffusion tensor microimaging was used to measure the time - dependent diffusivity and diffusion anisotropy within the scaffolds. The measured diffusion tensors were anisotropic and consistent with the cross - hatched geometry of the scaffolds: diffusion was least restricted in the direction perpendicular to the fiber layers. The results demonstrate that the cross - hatched scaffold structure preferentially promotes molecular transport vertically through the layers ( z - axis), with more restricted diffusion in the directions of the fiber layers ( x – y plane). Diffusivity in the x – y plane was observed to be invariant to the fiber thickness. The characteristic pore size of the fiber scaffolds can be probed by sampling the diffusion tensor at multiple diffusion times. Prospective application of diffusion tensor imaging for the real - time monitoring of tissue maturation and nutrient transport pathways within tissue engineering scaffolds is discussed.