This thesis describes the design and application of a virtual reality simulator for orthopaedic surgeryof the proximal femur. The aim of the research was to create a simulator with the followingattributes; could be used within the current public hospital setting, reflected the perceived needs ofthe local orthopaedic community, provided surgically relevant feedback about aspects of technicalability to orthopaedic surgical trainees and the training committee, allowed practice of operativetasks which for reasons of radiation exposure could otherwise not occur, was validated, and couldbe developed further for other operations. The ultimate aim of the simulator is to allow trainees topractice aspects of surgical treatment such that their care of real patients is improved. The novel aspect of this work has been the development of a simulator which allows the trainee toperform all the steps required for two surgical procedures; namely hip fracture fixation and pinningof slipped femoral capital epiphyses. The simulator runs on the computers found within the publichospital as it does not require expensive hardware such as haptic (force feedback) devices. Resultsfrom the simulator mimic real world measurements which are seldom available to trainees asfeedback to enable them to practice their craft. A survey of the New Zealand orthopaedic surgeons and advanced trainees showed this communitywas generally supportive of simulation, though only 4 respondents had previous experience with asurgical simulator. The task of practicing angulation/spatial orientation was thought most suitablefor simulation, which is the task which the simulator specifically allows trainees to practice. Morerecently qualified surgeons were more likely to agree that simulation was an effective way topractice surgical procedures. Validation of the simulator was tested in two experiments. The simulator was shown to have facevalidity; i.e. a realistic representation of the operating room. This result was obtained by surveyingusers who had completed a number of virtual operations. Construct validity was assessed by thesimulator’s ability to identify between groups of users with differing levels of real surgicalexperience. The simulator was able to discriminate medical students from orthopaedic trainees,despite the medical students’ greater ability in computer-gaming. Advanced trainees generallyperformed better than basic trainees, though in the limited number of trainees available significancewas not reached. Finally the simulator was developed further to allow all advanced trainees within New Zealand tocomplete virtual pin placement of a slipped capital femoral epiphysis. This demonstrated thefeasibility of using the simulator for assessment of trainees within their normal training weekend. Italso revealed different operating styles, and showed how these differing styles do not correlate withthe accuracy with which the final screw is placed.

This thesis presents the results of developing road pavement deterioration models for the State Highway network in New Zealand pavement deterioration models are an integral part of pavement management systems, which are used to forecast long-term maintenance needs and funding requirements on a road network. As part of this research, a Long-term Pavement Performance (LTPP) programme has been established on 63 sections of the State Highways. These sections are representative of typical road sections and climatic conditions on New Zealand roads. Data collection on these sections is undertaken on an annual basis and consists of high accuracy manual measurements. These measurements include road roughness, rutting, visual defect identification and strength testing with a Falling Weight Deflectometer. Based on the LTPP data, new model formats for New Zealand conditions were developed including a crack initiation model and a three-stage rut progression model. The rut progression model consists of three stages, initial densification, stable rut growth and a probabilistic model to predict accelerated rut progression. The continuous probabilistic model developed predicts the initiation of pavement failure events such as crack initiation and accelerated rutting. It has been found that this model type has a strong agreement with actual pavement behaviour as it recognises a distribution of failure on roads rather than failure occurring at an particular point in time, namely, a year. The modelling of rut progression in the three stages including, initial densification, stable rut progression and accelerated rutting has resulted in a significant increased understanding of this defect, especially for thin flexible chip seal pavements. It has been established that the in-service performance of these pavements is relatively predictable. However, incorporating both the in-service performance and the failure of pavements into one model was unrealistic. Therefore, by having the different stages of rutting, resulted into a more accurate forecasting of this defect. Although this research has covered the two priority pavement models including cracking and rutting prediction, it has established the model framework for other pavement models to be developed. As more data become available, further work can be undertaken to refine the models and to extend the research into the performance of alternative construction materials.

An efficient finite element method is developed to model the spreading of excitation in ventricular myocardium by treating the thin region of rapidly depolarizing tissue as a propagating wavefront. The model is used to investigate the excitation sequence in the full canine ventricular myocardium. The solution to an eikonal–curvature equation for excitation time is shown to satisfy a reaction–diffusion equation for the bidomain myocardial model at the wavefront, while the solution to an eikonal–diffusion equation approximately satisfies the reaction–diffusion equation in the vicinity of the wavefront. The features of these two eikonal equations are discussed. A Petrov–Galerkin finite element method with cubic Hermite elements is developed to solve the eikonal–diffusion equation. The oscillatory errors seen when using the Galerkin weighted residual method with high mesh Péclet numbers are avoided by supplementing the Galerkin weights with C⁰ continuous functions based on derivatives of the interpolation functions. The ratio of the Galerkin and supplementary weights is a function of the Péclet number such that, for one-dimensional propagation, the error in the solution is within a small constant factor of the optimal error achievable in the trial space. An additional noinflow boundary term is developed to prevent spurious excitation initiating on the boundary. The need for discretization in time is avoided by using a continuation method to gradually introduce the non-linear term of the governing equation. A small amount of artificial diffusion is sometimes necessary. Simulations of excitation are performed using a model of the anisotropic canine ventricular myocardium with 23.55 degrees of freedom for the dependent variable, and results are compared with reported experimental observations. When it was assumed that Purkinje fibres influence propagation only on the endocardial surface, excitation of the entire myocardium was completed in 56 ms. Altering material parameters to represent penetration of the Purkinje fibres beneath the left endocardial surface reduced the completion time to 48 ms. Modelling the effects of the laminar structure of myocardium by reducing the propagation speed by 40% in the direction normal to the layers delayed completion of excitation by only 4%.

The deployment of third generation (3G) cellular systems is resulting in a transition from cellular systems that predominantly carry constant-bit-rate (CBR) voice traffic to multi-service packet based systems that predominantly carry variable-bit-rate (VBR) traffic. With 3G DS-CDMA cellular systems there is a direct relationship between user traffic and propagation dependent performance as additional traffic causes increased system interference. This thesis investigates the impact of VBR traffic on the propagation dependent performance of DS-CDMA cellular systems that utilise frame-by-frame dynamic resource allocation on the radio channel. A DS-CDMA cellular system model is developed and the downlink performance of both outdoor macro-cellular and indoor pico-cellular systems is evaluated with a variety of traffic types. Both traffic scheduling performance and propagation dependent performance are evaluated as the two are inter-linked. Scenarios are identified where propagation dependent performance is sensitive to the statistical properties of the user traffic streams and it is shown that a significant performance difference potentially exists between different traffic types when the number of users per cell is low. When a significant performance difference does exist, burstier more variable traffic generally results in superior propagation dependent performance. The base transceiver station (BTS) transmitter power mean and variance provides a good indication of the level of propagation dependent performance regardless of the specific traffic type. Traffic scheduling policies that deliberately reduce the variability of user traffic streams are considered and in terms of propagation dependent performance these are shown to have a minimal impact on the performance difference between different traffic types. The implications of VBR traffic on DS-CDMA cellular system design are outlined and it is shown that VBR traffic can be approximated as CBR traffic in many scenarios and this is a convenient approximation as it simplifies system design and detailed traffic models do not need to be developed.

In this thesis, the forward problem of electrocardiography is investigated from a cellular level through to potentials on the surface of the torso. This integrated modelling framework is based on three spatial scales. At the smallest spatial resolution, several cardiac cellular models are implemented that are used to represent the underlying cellular electrophysiology. A bidomain framework is used to couple multiple individual cells together and this provides a mathematical model of the myocardial tissue. The cardiac geometry is described using finite elements with high order cubic Hermite basis function interpolation. An anatomically based description of the fibrous laminar cardiac microstructure is then defined relative to the geometric mesh. Within the local element space of the cardiac finite elements, a fine collocation mesh is created on which the bidomain equations are solved. Each collocation point represents a continuum cell and contains a cellular model to describe the local active processes. This bidomain implementation works in multiple coordinate systems and over deforming domains, in addition to having the ability to spatially vary any parameter throughout the myocardium. On the largest spatial scale the passive torso regions surrounding the myocardium are modelled using a generalised Laplace equation to describe the potential field and current flows. The torso regions are discretised using either finite elements or boundary elements depending on the electrical properties of each region. The cardiac region is coupled to the surrounding torso through several methods. A traditional dipole source approach is implemented that creates equivalent cardiac sources through the summation of cellular dipoles. These dipoles are then placed within a homogeneous cardiac region and the resulting potential field is calculated throughout the torso. Two new coupling techniques are developed that provide a more direct path from cellular activation to body surface potentials. One approach assembles all of the equations from the passive torso regions and the equations from the extracellular bidomain region into a single matrix system. Coupling conditions based on the continuity of potential and current flow across the myocardial surfaces are used to couple the regions and therefore solving the matrix system yields a solution that is continuous across all of the solution points within the torso. The second approach breaks the large system into smaller subproblems and the continuity conditions are iii iv imposed through an iterative approach. Across each of the myocardial surfaces, a fixed point iteration is set up with the goal of converging towards zero potential and current flow differences between adjacent regions. All of the numerical methods used within the integrated modelling framework are rigorously tested individually before extensive tests are performed on the coupling techniques. Large scale simulations are run to test the dipole source approach against the new coupling techniques. Several sets of simulations are run to investigate the effects of using different ionic current models, using different bidomain model simplifications, and the role that the torso inhomogeneities play in generating body surface potentials. The main question to be answered by this study is whether or not the traditional approach of combining a monodomain heart with an equivalent cardiac source in a two step approach is adequate when generating body surface potentials. Comparisons between the fully coupled framework developed here and several dipole based approaches demonstrate that the resulting sets of signals have different magnitudes and different waveform shapes on both the torso and epicardial surface, clearly illustrating the inadequacy of the equivalent cardiac source models. It has been found that altering the modelling assumptions on each spatial scale produces noticeable effects. At the smallest scale, the use of different cell models leads to significantly different body surface potential traces. At the next scale the monodomain approach is unable to accurately reproduce the results from a full bidomain framework, and at the largest level the inclusion of different torso inhomogeneities has a large effect on the magnitude of the torso and epicardial potentials. Adding a pair of lungs to the torso model changes the epicardial potentials by an average of 16% which is consistent with the experimental range of between 8 and 20%. This provides evidence that only a complex, coupled, biophysically based model will be able to properly reproduce clinical ECGs.

In the 1950's and early 1960's a considerable amount of effort was devoted by Dr. H.A. Whale and others at the Seagrove Radio Research Station (now the Radio Research Centre, University of Auckland), to the examination of some of the problems involved in HF radio propagation. Among these were the evaluation of the effects of large-scale ionospheric tilts, the scattering which occurs at the earth and ionosphere, and the measurement and prediction of incoming bearing and elevation angles of signals from distant stations. In the latter stages of this work it became obvious that little was known about effects occurring at antipodal distances, so attempts were made to examine these and to postulate a propagation model consistent with the effects observed. The results presented in this thesis are a logical extension of this early work, and comprise investigations in three main areas: (1) The shape and size of the antipodal focussing area, (2) The development of a more general and less idealised propagation model, (3) The shape of the incoming angular power spectrum at antipodal distances. A summary of the theory and experimental results contained in chapters 4, 5, 6 and 7 has been published (Bold, 1969), and that contained in chapters 8 and 9 will be submitted for publication shortly.

This investigation presents research on the characteristic properties of Nylon66 and poly(ethylene naphthalate) (Ny66/PEN), and poly(butylene terephthalate) and poly(ethylene naphthalate) (PBT/PEN) blends with several weight compositions made by melt blending, by the use of 13C and 1H Nuclear magnetic resonance (NMR), Fourier transform infrared spectroscopy (FTIR), Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), Scanning electron microscopy (SEM), Differential scanning calorimetry (DSC) and Dynamic mechanical thermal analysis (DMTA), X-ray diffraction (X-RD), tensile, impact and stress relaxation tests. Ny66/PEN blends including several additives do not improve the miscibility of the constituent polymers and show lower tensile strength than those of homopolymers. However, PBT/PEN blends reveal improved tensile strengths of the blends between the ROM and MROM predictions lines with more than 50 % volume fraction of PEN. On the other hand, NMR spectra show no evidence of interchange reaction in both Ny66/PEN and PBT/PEN blends. SEM micrographs of fracture surfaces in PBT/PEN blends reveal a very small (sub-micron) domain size in contrast to large domains in Ny66/PEN blends, which indicates partial miscibility of PBT and PEN. DSC and DMTA demonstrate partial miscibility of PBT/PEN blends by the change of Tgs of each component according to the weight proportions of the constituent polymers. Stress relaxation tests for the specimens of PBT/PEN blends and the homopolymers, using the Taguchi method of experimental design, determine that the most significant factor is the temperature, followed by PEN content and then the initial stress, and interaction effects between factors are insignificant. To fit the relaxation curves of the PBT/PEN blends and the homopolymers at different temperatures, PEN contents and initial stresses, four different equations have been used. The coefficients of the equation that fit best are used to predict the relaxation behaviour of PBT/PEN blends at a temperature between 30C and 60C, and at the initial stresses of 7 MPa.

Medical imaging is an essential tool for improving the diagnoses, understanding and treatment of a large variety of diseases. Over the last century technology has advanced from the discovery of x-rays to a variety of 3D imaging tools such as magnetic resonance imaging, computed tomography, positron emission tomography and ultrasonography. As a consequence the size and complexity of medical data sets has increased tremendously making it ever more difficult to understand, analyze, compare and communicate this data. Visualization is an attempt to simplify these tasks according to the motto "An image says more than a thousand words". This thesis introduces a toolkit for visualizing biomedical data sets with a particular emphasis on second-order tensors, which are mathematically described by matrices and can be used to express complex tissue properties such as material de-formation and water diffusion. The toolkit has a modular design which facilitates the comparison and exploration of multiple data sets. A novel field data structure allows the interactive creation of new measures and boolean filters are introduced as a universal visualization tool. Various new visualization methods are presented including new colour mapping techniques, ellipsoid-based textures and a line integral convolution texture for visualizing tensor fields. To motivate the design and to assist in the use of the toolkit, guidelines for creating effective visualizations are derived by using perceptual concepts from cognitive science. A new classification for visual attributes according to representational accuracy, perceptual dimension and spatial requirements is presented and the results are used to derive values for the information content and information density of each attribute. A review and a classification of visualization icons completes the theoretical background. The thesis concludes with two case studies. In the first case study the toolkit is used to visualize the strain tensor field in a healthy and a diseased human left ventricle. New insight into the cardiac mechanics is obtained by applying and modifying techniques traditionally used in solid mechanics and computational fluid dynamics. The second case study explores ways to obtain in vivo information of the brain anatomy by visualizing and systematically exploring Diffusion Tensor Imaging (DTI) data. Three new techniques for the visualization of DTI data are presented: Barycentric colour maps allow an integrated view of different types of diffusion anisotropy. Ellipsoid-based textures and Anisotropy Modulated Line Integral Convolution create images segmented by tissue type and incorporating a texture representing the 3D orientation of nerve fibers. The effectiveness of the exploration approach and the new visualization techniques are demonstrated by identifying various anatomical structures and features from a diffusion tensor data set of a healthy brain.

It is crucial to understand the fundamental mechanisms of cleaning milk protein fouling to optimise Cleaning-in-place (CIP) process. Using Whey Protein Concentrate (WPC) gel as a model material and a rapid ultraviolet (UV) spectrophotometry, a comprehensive laboratory study on the cleaning of the WPC gel deposits from hard surface with alkaline cleaning solutions has been conducted. The kinetics of the cleaning process has been established and mathematical models have been developed in order to elucidate the influences of various parameters on cleaning process. This study has provided sound evidence that whey protein concentrate gel is a reliable simulation of the whey protein fouling deposits used in most milk protein fouling and cleaning studies. Based on treating denatured whey protein gels as biopolymers, a chemical reaction controlled polymer dissolution cleaning mechanism has been proposed. The polymer dissolution plays a major role of removing proteinaceous deposits when treated with alkaline solutions under the flow conditions tested. Similar to the diffusion of cleaning chemicals and chemical reactions, the reptation (induction) is also one of essential steps for the dissolution of WPC gels in alkaline solutions. The disengagement of intermediate reaction products (altered protein molecules) from a gel-solution interface and subsequent mass transfer of these reaction products to the bulk cleaning solutions are the rate-limiting steps for the cleaning process. The typical dissolution cleaning rate curve of WPC gels in alkaline solutions includes swelling, uniform and decay cleaning stages. This study on cleaning kinetics shows that increasing the cleaning temperature can improve the cleaning efficiency. The apparent activation energy for these three stages is 32.6, 40.5, and 38.3 kJ/mol, respectively, which is in agreement with previous research works. Increasing flow velocity enhances the cleaning process. However, this effect could be reduced when and the cleaning process gradually changes from a mass transfer-controlled process to a disengagement-controlled process, where the flow velocity is very high. The introduction of the hydrolysis, β-elimination reactions and some competing chemical reactions have highlighted the complex of chemical reactions involved in cleaning of proteinaceous fouling using alkaline solutions. The changes in molecular mass distribution and SH content of WPC gel dissolved at various temperatures observed has confirmed the assumption that all these chemical reactions are temperature dependent. The investigation on the swelling, microstructural and mechanical properties of WPC gels treated with alkaline solutions also illustrates the concentration dependency of these chemical reactions. The mechanical property studies demonstrate that the chemical treatment could make WPC gel weaker and easier to be destroyed. However, the relationship between the mechanical properties and the cleaning process needs to be further studied. Based on the polymer dissolution and mass transfer theory, a mathematical model of chemical cleaning has been proposed. Various parameters, such as tr (reptation time), Rm, (constant cleaning rate), mc, (the critical mass), ξ (rate constant in swelling stage), kA (rate constant in decay stage) and Ψ (a dimensionless parameter) have been used to characterise the whole cleaning process. Among the parameters used in the cleaning model, the constant cleaning rate (Rm) is the most important one and determines the overall efficiency of a cleaning process, which has been further predicted and expressed as a product of mass transfer coefficient and solubility of disengaged protein molecules. The successful model formulations for the cleaning rate and cleaning time under various operation conditions are a good outcome of the rational mechanisms proposed for the removal of proteinaceous fouling. This research has provided a good foundation for further fundamental research in this area and for optimising the cleaning processes.

Coronary blood flow through the ventricular contraction cycle has been investigated in this thesis using an anatomically accurate computational model. Using Strahler ordered morphological data and an avoidance algorithm a three dimensional finite element model has been constructed of the largest six generations of the coronary arterial network within an anatomically accurate finite element model of the left and right ventricles. Segment radii, lengths and connectivity are consistent with the literature, local network branch angles are consistent with the principle of minimum shear stress at bifurcations, and an even spatial distribution of vessel segments throughout the myocardium has been achieved. A finite difference collocation grid has been generated on the coronary finite element mesh. The Navier Stokes equations governing blood flow through elastic vessels have been reduced to one dimension and are solved on this finite difference grid using the two step Lax Wendroff method. Blood flows at bifurcations are calculated using an iterative method ensuring conservation of mass and momentum. The microcirculation networks are modelled using a lumped parameter model incorporating the nonlinear variation of resistance and compliance with pressure by fitting results from published anatomical data. The venous network is assumed to parallel the generated arterial model. The calculated blood flow through the network model demonstrates physiological pressure drops, flow rates and a regional distribution within the ventricular geometry consistent with experimental data. The intramyocardial pressure (IMP) exerted on the coronary vasculature during contraction is calculated from quasi-static solutions of the equations of finite deformation applied to the ventricular model with a nonlinear anisotropic constitutive law. IMP is found to vary approximately linearly between ventricular pressure at the endocardium and atmospheric pressure at the epicardium. IMP and vessel stretch are included in the transmural pressure radius relationship to model the effect of myocardial deformation on coronary flow. The calculated coronary blood flow through the contraction cycle shows that arterial flow is predominantly diastolic while venous flow is significantly increased during systole. Calculated time varying velocity profiles in the large epicardial vessels compare well with published experimental results. Regionally averaged velocities in small vessels show that arterial inflow is most significantly impeded at the left ventricular endocardium. Furthermore, the large time constant associated with the capillary and venule networks limits the filling of these vessels during diastole particularly at the endocardium. An increase in heart rate, modelled by reducing the time for diastole causes an increase in small vessel epicardial blood flow and a decrease in blood flow through small vessels within the myocardium. The decrease in flow is most pronounced at the left ventricular endocardium.