This thesis describes extensions to 2D and 3D model-based segmentation algorithms for the analysis of ultrasound images and sequences. Starting from a common 2D+t "track-to-last" algorithm, it is shown that the typical method of searching for boundary candidates perpendicular to the model contour is unnecessary if, for each boundary candidate, its corresponding position on the model contour is optimised jointly with the model contour geometry. With this observation, two 2D+t segmentation algorithms, which accurately recover boundary displacements and are capable of segmenting arbitrarily long sequences, are formulated and validated. Generalising to 3D, subdivision surfaces are shown to be natural choices for continuous model surfaces, and the algorithms necessary for joint optimisation of the correspondences and model surface geometry are described. Three applications of 3D model-based segmentation for ultrasound image analysis are subsequently presented and assessed: skull segmentation for fetal brain image analysis; face segmentation for shape analysis, and single-frame left ventricle (LV) segmentation from echocardiography images for volume measurement. A framework to perform model-based segmentation of multiple 3D sequences - while jointly optimising an underlying linear basis shape model - is subsequently presented for the challenging application of right ventricle (RV) segmentation from 3D+t echocardiography sequences. Finally, an algorithm to automatically select boundary candidates independent of a model surface estimate is described and presented for the task of LV segmentation. Although motivated by challenges in ultrasound image analysis, the conceptual contributions of this thesis are general and applicable to model-based segmentation problems in many domains. Moreover, the components are modular, enabling straightforward construction of application-specific formulations for new clinical problems as they arise in the future.

This thesis focuses on studying the interaction and evolution of the needle domains in barium titanate single crystal through the simulation and experimental methods. The results are expected to assist in the interpretation of the arrangement and evolution of the needle domains and improve the design of future material. The existence of a needle domain gives rise to an internal stress field and electric field around the needle tip, which influences the polarization switching process and crack propagation in a single crystal. A model is established to study the interaction and evolution of the needle domains in barium titanate single crystals using the theory of dislocations. Considering the electrical and mechanical incompatibility at the needle tip, the fields produced by a needle domain are represented using the fields due to the equivalent edge dislocations and line charges distributed over the needle tip. Accordingly, the dislocation fields derived by Barnett and Lothe for anisotropic piezoelectric media are used to analyse the stress and electric fields around the needle domains. The calculation of the modified Peach-Koehler force and the total energy due to the needle domains is used to study the interaction among the needle domains and the stability of the needle pattern. Through experimental observation, we further know about the microstructure and common pattern of needle domains. X-ray diffraction is used to map the shape of needle tip and detect the strain field around the needle tip. The interaction of pairs of needle domains in an infinite piezoelectric body is studied. It is found that the needle tip interactions tend to be dominated by the electrostatic terms. Additionally, the stability of groups of needle domains is investigated. Stable configurations of needle domains in a herringbone pattern are identified, consistent with experimental evidence. However, comb-like arrays of needles are found to be unstable. This is contrary to experimental observations, where needle domains are observed in aligned arrays. This contradictory result leads to an analysis of the effect of charge produced by the polarization jump at a needle tip on domain interaction. The existence and position of stable equilibrium states are found to be sensitive to a change in the quantity of polarization charge. When the polarization charge is reduced to about 48% of its theoretical value, the modified model works well to interpret the stability of comb-like needle pattern and herringbone needle pattern. A viscous model is proposed to further analyse the evolution of the needle domains under the external perturbation. Based on the superposition theory proposed by Van der Giessen, boundary value problems are discussed. Single needles and pairs of needle domains are selected to analyse the effect of boundary condition on the distribution and arrangement of the needle domains. After that, the evolution of the comb-like needle domains under the applied external loads is studied. During the process of analysis, a lattice friction model, and the viscous model are compared.

With a continuing and rising demand for hydrocarbons, the energy companies are installing infrastructure ever further offshore, where such infrastructure is often exposed to extreme waves. This thesis explores some aspects of wave-structure interaction, particularly the maximum water surface elevation increase in severe storms due to these local interactions. The effects on wave-structure interactions of column cross-sectional shape are investigated using linear and second-order wave diffraction theory. For multi-column structures, the excitation of locally resonant wave modes (near-trapping) is studied for several column cross-sectional shapes, and a simple method for estimating the surface elevation mode shape is given. The structure of the quadratic transfer functions for second-order sum wave elevation is investigated and an approximation assuming these QTFs are flat perpendicular to the leading diagonal is shown to be adequate for the first few lowest frequency modes. NewWave-type focused wave groups can be used as a more realistic model of extreme ocean waves. A Net Amplification Factor based on the NewWave model is given as an efficient tool for finding the incident frequencies most likely to cause a violent wave-structure interaction and where these violent responses are likely to occur. Statistics are collected from Monte Carlo type simulations of random waves to verify the use of the Net Amplification Factor. Going beyond linear calculations, surface elevation statistics are collected to second-order and a `designer' wave is found to model the most extreme surface elevation responses. A `designer' wave can be identified at required levels of return period to help to understand the relative size of harmonic components in extreme waves. The methods developed with a fixed body are then applied to an identical hull which is freely floating, and the responses between the fixed and moving cases are compared. The vertical heave motion of a semi-submersible in-phase with the incident wave crests is shown to lead to a much lower probability of water-deck impact for the same hull shape restrained vertically. The signal processing methods developed are also applied to a single column to allow comparison with experimental results. Individual harmonic components of the hydrodynamic force are identified up to at least the fifth harmonic. Stokes scaling is shown to hold even for the most violent interactions. It is also shown that the higher harmonic components of the hydrodynamic force can be reconstructed from just the fundamental force time history, and a transfer function in the form of a single phase and an amplitude for each harmonic. The force is also reconstructed well to second-order from the surface elevation time history using diffraction transfer functions. Finally, possible causes of damage to a platform high above mean water level in the North Sea are investigated.

This DPhil project is set in the context of single crystal elasticity-plasticity finite element modelling. Its core objective was to develop and implement a methodology for predicting the evolution of texture in single and dual-phase material systems. This core objective has been successfully achieved. Modelling texture evolution entails essentially modelling large deformations (as accurately as possible) and taking account of the deformation mechanisms that cause texture to change. The most important deformation mechanisms are slip and twinning. Slip has been modelled in this project and care has been taken to explore conditions where it is the dominant deformation mechanism for the materials studied. Modelling slip demands that one also models dislocations since slip is assumed to occur by the movement of dislocations. In this project a model for geometrically necessary dislocations has been developed and validated against experimental measurements. A texture homogenisation technique which relies on interpretation of EBSD data in order to allocate orientation frequencies based on representative area fractions has been developed. This has been coupled with a polycrystal plasticity RVE framework allowing for arbitrarily sized RVEs and corresponding allocation of crystallographic orientation. This has enabled input of experimentally measured initial textures into the CPFE model allowing for comparison of predictions against measured post-deformation textures, with good agreement obtained. The effect of texture on polycrystal physical properties has also been studied. It has been confirmed that texture indeed has a significant role in determining the average physical properties of a polycrystal. The thesis contributes to the following areas of micro-mechanics materials research: (i) 3D small deformation crystal plasticity finite element (CPFE) modelling, (ii) geometrically necessary dislocation modelling, (iii) 3D large deformation CPFE modelling, (iv) texture homogenisation methods, (v) single and dual phase texture evolution modelling, (vi) prediction of polycrystal physical properties, (vii) systematic calibration of the power law for slip based on experimental data, and (viii) texture analysis software development (pole figures and Kearns factors).

Bayesian learning methods are the basis of many powerful analysis techniques in neuroimaging, permitting probabilistic inference on hierarchical, generative models of data. This thesis primarily develops Bayesian analysis techniques for magnetic resonance imaging (MRI), which is a noninvasive neuroimaging tool for probing function, perfusion, and structure in the human brain. The first part of this work fits nonlinear biophysical models to multimodal functional MRI data within a variational Bayes framework. Simultaneously-acquired multimodal data contains mixtures of different signals and therefore may have common noise sources, and a method for automatically modelling this correlation is developed. A Gaussian process prior is also used to allow spatial regularization while simultaneously applying informative priors on model parameters, restricting biophysically-interpretable parameters to reasonable values. The second part introduces a novel data fusion framework for multivariate data analysis which finds a joint decomposition of data across several modalities using a shared loading matrix. Each modality has its own generative model, including separate spatial maps, noise models and sparsity priors. This flexible approach can perform supervised learning by using target variables as a modality. By inferring the data decomposition and multivariate decoding simultaneously, the decoding targets indirectly influence the component shapes and help to preserve useful components. The same framework is used for unsupervised learning by placing independent component analysis (ICA) priors on the spatial maps. Linked ICA is a novel approach developed to jointly decompose multimodal data, and is applied to combined structural and diffusion images across groups of subjects. This allows some of the benefits of tensor ICA and spatially-concatenated ICA to be combined, and allows model comparison between different configurations. This joint decomposition framework is particularly flexible because of its separate generative models for each modality and could potentially improve modelling of functional MRI, magnetoencephalography, and other functional neuroimaging modalities.

Computational modelling and simulation, in close interaction with experiments, has provided invaluable insight into the biochemical, mechanical and electrophysiological function and dysfunction of the heart. However, limitations in imaging techniques and computing resources have precluded the analysis of tissue architecture near the cellular scale and the effect of this architecture on cardiac function. It is the wider aim of this thesis to develop a framework to characterise cardiac microstructure and to investigate the role of microstructure in cardiac propagation dynamics and arrhythmogenesis. An initial modelling study elucidates the effect of blood vessels in sustaining arrhythmic episodes, and how the accurate modelling of fibre direction in the vicinity of the vessels mitigates this detrimental mechanism. A mathematical model of fibre orientation in a simple geometry around blood vessels has been developed, based on information obtained from highly detailed histological and MRI datasets. A simulation regime was chosen, guided by the vasculature extracted from whole heart MRI images, to analyse ventricular wavefront propagation for different orientations and positions of blood vessels. Our results demonstrate not only that the presence of the blood vessels encourages curvature in the activation wavefront around the blood vessels, but further that vessels act to restrict and prolong phase singularities. When compared to a more simplistic implementation of fibre orientation, the model is shown to weaken wavefront curvature and reduce phase singularity anchoring. Having established the importance of microstructural detail in computational models, it seems expedient to generate accurate data in this regard. An automated registration toolchain is developed to reconstruct histological slices based on coherent block face volumes, in order to present the first 3-D sub-cellular resolution images of cardiac tissue. Although mesoscopic geometry is faithfully reproduced throughout much of the dataset, low levels of transformational noise obfuscate tissue microstructure. These distortions are all but eradicated by a novel transformational diffusion algorithm, with characteristics that outperform any previous method in the literature in this domain, with respect to robustness, conservation of geometry and extent of information transfer. Progress is made towards extracting microstructural models from the resultant histological volumes, with a view to incorporating this detail into simulations and yielding a deeper understanding of the role of microstructure in arrhythmia.

Although the tensile mechanical properties of tendon have been well characterised, the viscoelastic and anisotropic properties remain uncertain. This thesis addresses the anisotropic and viscoelastic material properties of tendon. A method to characterise the three-dimensional shape of tendon is reported and experiments to characterise the fibre-aligned and fibre-transverse viscoelastic properties of tendon are presented. The cross-sectional profiles of bovine digital extensor tendons were determined by a laser-slice method. Linear dimensions were measured within 0.15 mm and cross-sectional areas within 1.7 mm². Tendons were compressed between two glass plates in creep loading at multiple loads. Compression was then modelled in a finite element environment. Tendon was found to be nearly incompressible and reproduction of its isochronal load-displacement curve was achieved with a neo-Hookean material model (E ≃ 0.3 MPa). The fibre-aligned tensile mechanical properties were described using a Quasi-Linear Viscoelastic model. The model was effective at reproducing cyclic loading; however, it was ineffective at predicting stress relaxation outside the scope of data used to fit the model. When all experimental results are considered together, two significant conclusions are made: (1) tendon is much stiffer in fibre-aligned tension than in fibre-transverse compression and (2) the fibre-aligned tensile response is strain dependant, while the transverse response is not.

An estimated 85% of haemorrhagic strokes are secondary to the rupture of an intracranial aneurysm (IA), a localised, blood-filled dilation of the artery wall. The clinically observed rupture of occluded IAs has led to hypothesise that the presence of thrombus may restrict the transport of nutrients, most notably oxygen, to the aneurysmal wall, thus heightening the risk of rupture through the deleterious effects of hypoxia on cellular functionality. The limited research into O2 transport within IAs demonstrate the need for further exploration into the possible detrimental hypoxic conditions as a result of intrasaccular haemodynamics and thrombusformation in untreated, treated and evolving IAs, with the ultimate goal of further understanding disease evolution and developing prognostic decision support models for clinical intervention. Preliminary computational fluid dynamic simulations conducted on a 2Daxisymmetric model of a thrombosed artery highlighted the relative importance of wall-side versus the fluid-side mass transport of oxygen. A sensitivity analysis demonstrated that variations in thrombus thickness, and arterial wall cellular respiration rates have the greatest influence on the oxygen distribution to the portion of wall in direct contact with the thrombus. The results of the coupled flow-mass transport computational fluid dynamic simulations within patient-specific IA show that a reduction in intrasaccular flow as a consequence of stent deployment affects the rate at which oxygenated blood reaches the entirety of the dome. Nonetheless, the distribution ofO2 to the aneurysmal wall itself does not differ from the observed oxygen distribution across the wall when the same IA is left untreated. Conversely, the low velocity recirculations observed in an IA presenting with a very high aspect ratio (i.e a narrow neck and high sack height) limited the transport of oxygen to such an extent as to completely deprive the delivery of oxygen to the fundus. The presence of thrombus within the IA dome results in a dramatic reduction in oxygen delivery to the wall, the extent of which is dependent on the local thrombus thickness. Finally, a novel fluid-solid-growth-mass transport (FSGT) mathematical model is conceived to explore the biochemical role of thrombus on the evolution of an IA. The shear-regulate propagation of a thrombus layer during membrane expansion leads to the gradual decrease in oxygen tension within the wall. Moreover, as a consequence of coupling this oxygen deficiency to fibroblast functionality, the collagen fibre mass density was shown to increase at an insufficient rate to compensate for the transfer in load from the degrading elastinous consitituents to the collagenous constituents, thus resulting in the increased stretch of collagen fibres in order to maintain mechanical equilibrium. Moreover this over-expansion results in the gradual unstable evolution of the IA. The observed obstruction to oxygen delivery as a result of intrasaccular haemodynamics and thrombosis compounds the need for further development of more comprehensive chemo-mechano-biological models of IAs so as to better ascertain the level of rupture risk posed by a hypoxic environment. Refinement to the models proposed within this work would prove invaluable to creating a fully integrated multi-physics, multi-scale in silico framework in aid to patient diagnostics and individual treatment planning of IAs.

Using some form of dynamical model in a visual tracking system is a well-known method for increasing robustness and indeed performance in general. Often, quite simple models are used and can be effective, but prior knowledge of the likely motion of the tracking target can often be exploited by using a specially-tailored model. Specifying such a model by hand, while possible, is a time-consuming and error-prone process. Much more desirable is for an automated system to learn a model from training data. A dynamical model learnt in this manner can also be a source of useful information in its own right, and a set of dynamical models can provide discriminatory power for use in classification problems. Methods exist to perform such learning, but are limited in that they assume the availability of 'ground truth' data. In a visual tracking system, this is rarely the case. A learning system must work from visual data alone, and this thesis develops methods for learning dynamical models while explicitly taking account of the nature of the training data --- they are noisy measurements. The algorithms are developed within two tracking frameworks. The Kalman filter is a simple and fast approach, applicable where the visual clutter is limited. The recently-developed Condensation algorithm is capable of tracking in more demanding situations, and can also employ a wider range of dynamical models than the Kalman filter, for instance multi-mode models. The success of the learning algorithms is demonstrated experimentally. When using a Kalman filter, the dynamical models learnt using the algorithms presented here produce better tracking when compared with those learnt using current methods. Learning directly from training data gathered using Condensation is an entirely new technique, and experiments show that many aspects of a multi-mode system can be successfully identified using very little prior information. Significant computational effort is required by the implementation of the methods, and there is scope for improvement in this regard. Other possibilities for future work include investigation of the strong links this work has with learning problems in other areas. Most notable is the study of the 'graphical models' commonly used in expert systems, where the ideas presented here promise to give insight and perhaps lead to new techniques.

An intracranial aneurysm (IA) is a balloon-like focal lesion on the cerebral arterial wall. IAs are poorly understood, but are commonly considered to be a disease caused by multiple factors. Current interventional treatments are accompanied with risks. Given the low incidence of rupture, it would be ideal to only treat aneurysms identified with rupture risk. Numerical models of aneurysm development may provide insight into the disease mechanisms, and contribute to the prediction of disease progression. Better understanding of the disease aetiology will also guide clinical decision making. Different hypotheses have been proposed on the influence of haemodynamic stimuli on IA inception. We investigate this influence by examining the haemodynamic stimuli of the 'pre-aneurysmal' vasculature in the locations of IA formation in 22 clinical cases. The 'pre aneurysmal' geometries are obtained by applying a novel numerical vessel reconstruction method on the aneurysmal geometries. This automated reconstruction method propagates a closed curve along the vessel skeleton using the local Frenet frames to smoothly morph the upstream boundary into the downstream boundary. We observe that locally elevated wall shear stress (WSS) and gradient oscillatory number (GON) are highly correlated with regions susceptible to sidewall IA formation, whilst haemodynamic indices associated with the oscillation of the WSS vectors have much lower correlations. A common assumption made in the literature on arterial growth and remodelling (G&R) is that the 'state of stretch' (denoted as the attachment stretch) at which collagen fibres are configured in the extracellular matrix (ECM) is assumed to be constant. This will lead to an unrealistically thickened arterial wall in modelling aneurysm evolution. We propose a novel 1D mathematical model of collagen microstructural adaption during IA evolution. We assume new collagen fibres are configured into the ECM in a state of attachment stretch distribution which can be temporally adaptive. We explicitly define the functional form of this distribution and model its temporal adaption during IA evolution. This model is then implemented into two 3D models of IA evolution: a solid structural model and Fluid-Solid-Growth (FSG) model. In the solid structural model, the artery is modelled as a two-layer, nonlinear elastic cylindrical membrane using a physiologically realistic constitutive model. The development of the aneurysm is considered as a consequence of the growth and remodelling of its material constituents: elastinous constituents are prescribed to degrade in a localised circular patch; collagen concentration and recruitment variables enable the growth and remodelling of collagen fabric to be simulated; adaption of the attachment stretch distribution is confined locally within the region of aneurysm evolution. The sophisticated solid model predicts stabilised saccular IAs with realistic sizes and wall thicknesses. The FSG model simulates the IA development on patient-specific vasculature: the updated 3D solid structural model is integrated into a patient-specific geometry of the vasculature and the growth and remodelling of the constituents is now linked to the local haemodynamic stimuli obtained from a rigid-wall computational fluid dynamics analysis. Adaption of the attachment stretch distribution is also confined locally in the region where the constituents degrade. An illustrative case of IA development on patient specific geometry is provided. Based on our study, we conclude that incorporating the adaption of attachment stretch distribution is necessary to simulate IA evolution with physiological evolving wall thicknesses. However, how vascular cells confine this adaption heterogeneously needs further investigation. Improved understanding and modelling of the biology of the arterial wall is needed for more sophisticated models of aneurysm evolution. It will in turn assist in understanding the aetiology of IA formation. Ultimately we hope to have a patient-specific growth model that could have the potential be used to assist diagnostic decisions.