This study extends a recently-developed [1] cellular automata (CA) elastodynamic modeling approach to arbitrary two-dimensional geometries through development of a rule set appropriate for triangular cells. The approach is fully object-oriented (OO) and exploits OO conventions to produce compact, general, and easily-extended CA classes. Meshes composed of triangular cells allow the elastodynamic response of arbitrary two-dimensional geometries to be computed accurately and efficiently. As in the previous rectangular CA method, each cell represents a state machine which updates in a stepped-manner using a local "bottom-up" rule set and state input from neighboring cells. The approach avoids the need to develop partial differential equations and the complexity therein. Several advantages result from the method's discrete, local and object-oriented nature, including the ability to compute on a massively-parallel basis and to easily add or subtract cells in a multi-resolution manner. The extended approach is used to generate the elastodynamic responses of a variety of general geometries and loading cases (Dirichlet and Nuemann), which are compared to previous results and/or comparison results generated using the commercial finite element code, COMSOL. These include harmonic interior domain loading, uniform boundary traction, and ramped boundary displacement. Favorable results are reported in all cases, with the CA approach requiring fewer degrees of freedom to achieve similar or better accuracy, and considerably less code development.

This thesis consists of three independent essays, unified by the common theme of the distributional impacts of government. The first paper estimates the price elasticity of demand for pharmaceuticals amongst high-income older people in Australia. It exploits a natural experiment by which some people gained entitlement to a price reduction through the Commonwealth Seniors Health Card (CSHC). The preferred model is a nonlinear Instrumental Variable (IV) difference-in-difference regression, estimated on repeated cross sectional survey data using the Generalised Method of Moments. No significant evidence is found for endogenous card take-up, and so cross-sectional estimates are also considered. Taking all of the results and possible sources of bias into account, the ??headline?? estimate is -0.1, implying that quantity demanded is not highly responsive to price. The elasticity estimate is a key input into the second paper which analyses the distributional impact of the CSHC. I consider the trade-off between moral hazard and risk pooling. There have been few previous attempts internationally to address this trade-off empirically for any health insurance scheme. The utility gain through risk-pooling is found to be negligible. However, the deadweight loss through moral hazard may be considerable. I also use an illustrative model to demonstrate the possible effects of the CSHC on inter-temporal savings behaviour. While the CSHC may induce some people to save, it may have the opposite effect on others. The net impact was not determined. The third paper estimates the Australian public sector wage premium. It includes a detailed critical review of the methods available to address this issue. The chosen approach is a quasi-differenced panel data model, estimated by nonlinear IV, which has many advantages over other methods and has not been used before for this topic. I find a positive average public sector wage premium for both sexes. The best estimates are 10.0% for men and 7.1% for women. The estimate for men is statistically significant (p < 0.04) and borders on significance for women (p < 0.07). No evidence is found to suggest that the public sector has an equalising effect on the wages of its workers.

This thesis presents research that was conducted to develop anatomically realistic finite element models of breast deformation under a variety of gravity loading conditions to assist clinicians in tracking suspicious tissues across multiple imaging modalities. Firstly, the accuracy of the modelling framework in predicting deformations of a homogeneous body was measured using custom designed silicon gel phantoms. The model predicted surface deformations with an average RMS error of 1.5 mm +/- 0.2 mm and tracked internal marker locations with an average RMS error of 1.4 mm +/- 0.7 mm. A novel method was then developed to determine the reference configuration of a body, when given its mechanical properties, boundary conditions and a deformed configuration. The theoretical validity of the technique was confirmed with an analytic solution. The accuracy of the method was also measured using silicon gel experiments, predicting the reference configuration surface with an average RMS error of 1.3 mm +/- 0.1 mm, and tracking internal marker locations with an average error of 1.5 mm +/- 0.8 mm. Silicon gel composites were then created to measure the accuracy of standard techniques to model heterogeneity. The models did not match the experimentally recorded deformations. This highlighted the need for further validation exercises on modelling heterogeneity before modelling them in the breast. A semi-automated algorithm was developed to fit finite element models to the skin and muscle surfaces of each individual, which were segmented from breast MR images. The code represented the skin with an average RMS error of 1.46 mm +/- 0.32 mm and the muscle with an average RMS error of 1.52 mm +/- 0.3 mm. The framework was then tested using images of the breast obtained under different gravity loading conditions and neutral buoyancy. A homogeneous model was first developed using the neutral buoyancy images as a representation of the reference configuration. The model did not accurately capture the regional deformations of the breast under gravity loading. However, the gross shape of the breast was reproduced, indicating that a biomechanical model of the breast could be useful to reliably track tissues across multiple images for cancer diagnosis. / This research was sponsored by the Top Achiever Doctoral Scholarship and the University of Auckland Doctoral Scholarship. Extra funding for travel was provided by the Graduate Research Fund and the John Logan Campbell Trust Fund.

This thesis presents research that was conducted to develop anatomically realistic finite element models of breast deformation under a variety of gravity loading conditions to assist clinicians in tracking suspicious tissues across multiple imaging modalities. Firstly, the accuracy of the modelling framework in predicting deformations of a homogeneous body was measured using custom designed silicon gel phantoms. The model predicted surface deformations with an average RMS error of 1.5 mm +/- 0.2 mm and tracked internal marker locations with an average RMS error of 1.4 mm +/- 0.7 mm. A novel method was then developed to determine the reference configuration of a body, when given its mechanical properties, boundary conditions and a deformed configuration. The theoretical validity of the technique was confirmed with an analytic solution. The accuracy of the method was also measured using silicon gel experiments, predicting the reference configuration surface with an average RMS error of 1.3 mm +/- 0.1 mm, and tracking internal marker locations with an average error of 1.5 mm +/- 0.8 mm. Silicon gel composites were then created to measure the accuracy of standard techniques to model heterogeneity. The models did not match the experimentally recorded deformations. This highlighted the need for further validation exercises on modelling heterogeneity before modelling them in the breast. A semi-automated algorithm was developed to fit finite element models to the skin and muscle surfaces of each individual, which were segmented from breast MR images. The code represented the skin with an average RMS error of 1.46 mm +/- 0.32 mm and the muscle with an average RMS error of 1.52 mm +/- 0.3 mm. The framework was then tested using images of the breast obtained under different gravity loading conditions and neutral buoyancy. A homogeneous model was first developed using the neutral buoyancy images as a representation of the reference configuration. The model did not accurately capture the regional deformations of the breast under gravity loading. However, the gross shape of the breast was reproduced, indicating that a biomechanical model of the breast could be useful to reliably track tissues across multiple images for cancer diagnosis. / This research was sponsored by the Top Achiever Doctoral Scholarship and the University of Auckland Doctoral Scholarship. Extra funding for travel was provided by the Graduate Research Fund and the John Logan Campbell Trust Fund.

This thesis presents research that was conducted to develop anatomically realistic finite element models of breast deformation under a variety of gravity loading conditions to assist clinicians in tracking suspicious tissues across multiple imaging modalities. Firstly, the accuracy of the modelling framework in predicting deformations of a homogeneous body was measured using custom designed silicon gel phantoms. The model predicted surface deformations with an average RMS error of 1.5 mm +/- 0.2 mm and tracked internal marker locations with an average RMS error of 1.4 mm +/- 0.7 mm. A novel method was then developed to determine the reference configuration of a body, when given its mechanical properties, boundary conditions and a deformed configuration. The theoretical validity of the technique was confirmed with an analytic solution. The accuracy of the method was also measured using silicon gel experiments, predicting the reference configuration surface with an average RMS error of 1.3 mm +/- 0.1 mm, and tracking internal marker locations with an average error of 1.5 mm +/- 0.8 mm. Silicon gel composites were then created to measure the accuracy of standard techniques to model heterogeneity. The models did not match the experimentally recorded deformations. This highlighted the need for further validation exercises on modelling heterogeneity before modelling them in the breast. A semi-automated algorithm was developed to fit finite element models to the skin and muscle surfaces of each individual, which were segmented from breast MR images. The code represented the skin with an average RMS error of 1.46 mm +/- 0.32 mm and the muscle with an average RMS error of 1.52 mm +/- 0.3 mm. The framework was then tested using images of the breast obtained under different gravity loading conditions and neutral buoyancy. A homogeneous model was first developed using the neutral buoyancy images as a representation of the reference configuration. The model did not accurately capture the regional deformations of the breast under gravity loading. However, the gross shape of the breast was reproduced, indicating that a biomechanical model of the breast could be useful to reliably track tissues across multiple images for cancer diagnosis. / This research was sponsored by the Top Achiever Doctoral Scholarship and the University of Auckland Doctoral Scholarship. Extra funding for travel was provided by the Graduate Research Fund and the John Logan Campbell Trust Fund.

Biot's theory when applied to homogeneous media (involving the macroscopic flow mechanism) cannot explain the high level of attenuation observed in natural porous media over the seismic frequency range. However, several successful mesocopic inhomogeneity models have been developed to account for P wave attenuation. In this thesis I further develop the approaches to tackle S wave velocity and attenuation, to simulate transient wave propagation in poroelastic media, and to construct new models for determining the effective parameters of porous media containing mesoscopic inhomogeneities. As an important application of the double-porosity dual-permeability (DPDP) model, I have reformulated the effective Biot model using the total-field variables. This gives rise to new and more general governing equations than the previous approach based on the host phase field variables (which become a special case of the more general treatment). The analytical transient solution and dispersion characteristics for the double-porosity model and also for a poro-viscoacoustic model are derived over the entire frequency range for a homogeneous medium. The comparison between the results of the two models shows that dissipation by local mesoscopic flow of the double porosity model is very hard to fit by a single Zener element over a broad band. I chose the relaxation function to approximate the dispersion behaviour of the double porosity model just around the source centre frequency. It is shown that for most water-filled sandstones having a double porosity structure, wave propagation can be well described by the poro-viscoaoustic model with a single Zener element in the seismic frequency range. The transient solution for heterogeneous double porosity media is obtained by a numerical pseudospectral time splitting technique. This method is extended to 2.5-D poro-viscoelastic media to capture both P and S wave behaviour. I also demonstrate that if the frequency is below several Hz, then a single Kelvin-Voigt element gives an even better result than a single Zener element. I propose a two-phase permeability spherical inclusion model and obtain the dispersion curves of phase velocity and dissipation factor for the composite. I then determine the effective dynamic permeability of porous media with mesoscopic heterogeneities over the whole frequency range. This result is used to check the validity of other measures of effective dynamic permeability, deduced from the effective hydraulic permeability by replacing the permeability of the components with their dynamic values as determined from the Johnson, Koplik and Dashen (JKD) model. I also investigate the scattering of plane transverse waves by a spherical porous inclusion embedded in an infinite poroelastic medium. The vector displacement wave equations of Biot’s theory are solved as an infinite series of vector spherical harmonics for the case of a plane S-wave incidence. Then, the non-self-consistent theory is used to derive the dispersion characteristics of shear wave velocity and attenuation for a porous rock having mesoscopic spherical inclusions which are designed to represent either the patchy saturation model or the double porosity model with dilute concentrations of identical inclusions. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1457632 / Thesis (Ph.D.) -- University of Adelaide, School of Chemistry and Physics, 2009

This thesis presents research that was conducted to develop anatomically realistic finite element models of breast deformation under a variety of gravity loading conditions to assist clinicians in tracking suspicious tissues across multiple imaging modalities. Firstly, the accuracy of the modelling framework in predicting deformations of a homogeneous body was measured using custom designed silicon gel phantoms. The model predicted surface deformations with an average RMS error of 1.5 mm +/- 0.2 mm and tracked internal marker locations with an average RMS error of 1.4 mm +/- 0.7 mm. A novel method was then developed to determine the reference configuration of a body, when given its mechanical properties, boundary conditions and a deformed configuration. The theoretical validity of the technique was confirmed with an analytic solution. The accuracy of the method was also measured using silicon gel experiments, predicting the reference configuration surface with an average RMS error of 1.3 mm +/- 0.1 mm, and tracking internal marker locations with an average error of 1.5 mm +/- 0.8 mm. Silicon gel composites were then created to measure the accuracy of standard techniques to model heterogeneity. The models did not match the experimentally recorded deformations. This highlighted the need for further validation exercises on modelling heterogeneity before modelling them in the breast. A semi-automated algorithm was developed to fit finite element models to the skin and muscle surfaces of each individual, which were segmented from breast MR images. The code represented the skin with an average RMS error of 1.46 mm +/- 0.32 mm and the muscle with an average RMS error of 1.52 mm +/- 0.3 mm. The framework was then tested using images of the breast obtained under different gravity loading conditions and neutral buoyancy. A homogeneous model was first developed using the neutral buoyancy images as a representation of the reference configuration. The model did not accurately capture the regional deformations of the breast under gravity loading. However, the gross shape of the breast was reproduced, indicating that a biomechanical model of the breast could be useful to reliably track tissues across multiple images for cancer diagnosis. / This research was sponsored by the Top Achiever Doctoral Scholarship and the University of Auckland Doctoral Scholarship. Extra funding for travel was provided by the Graduate Research Fund and the John Logan Campbell Trust Fund.

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Loukas F. Kallivokas. Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

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