An increasingly important research area within the field of cardiac modelling is the development and study of methods of model-based parameter estimation from clinical measurements of cardiac function. This provides a powerful approach for the quantification of cardiac function, with the potential to ultimately lead to the improved stratification and treatment of individuals with pathological myocardial mechanics. In particular, the diastolic function (i.e., blood filling) of left ventricle (LV) is affected by its capacity for relaxation, or the decay in residual active tension (AT) whose inhibition limits the relaxation of the LV chamber, which in turn affects its compliance (or its reciprocal, stiffness). The clinical determination of these two factors, corresponding to the diastolic residual AT and passive constitutive parameters (stiffness) in the cardiac mechanical model, is thus essential for assessing LV diastolic function. However these parameters are difficult to be assessed in vivo, and the traditional criterion to diagnose diastolic dysfunction is subject to many limitations and controversies. In this context, the objective of this study is to develop model-based applicable methodologies to estimate in vivo, from 4D imaging measurements and LV cavity pressure recordings, these clinically relevant parameters (passive stiffness and active diastolic residual tension) in computational cardiac mechanical models, which enable the quantification of key clinical indices characterising cardiac diastolic dysfunction. Firstly, a sequential data assimilation framework has been developed, covering various types of existing Kalman filters, outlined in chapter 3. Based on these developments, chapter 4 demonstrates that the novel reduced-order unscented Kalman filter can accurately retrieve the homogeneous and regionally varying constitutive parameters from the synthetic noisy motion measurements. This work has been published in Xi et al. 2011a. Secondly, this thesis has investigated the development of methods that can be applied to clinical practise, which has, in turn, introduced additional difficulties and opportunities. This thesis has presented the first study, to our best knowledge, in literature estimating human constitutive parameters using clinical data, and demonstrated, for the first time, that while an end-diastolic MR measurement does not constrain the mechanical parameters uniquely, it does provide a potentially robust indicator of myocardial stiffness. This work has been published in Xi et al. 2011b. However, an unresolved issue in patients with diastolic dysfunction is that the estimation of myocardial stiffness cannot be decoupled from diastolic residual AT because of the impaired ventricular relaxation during diastole. To further address this problem, chapter 6 presents the first study to estimate diastolic parameters of the left ventricle (LV) from cine and tagged MRI measurements and LV cavity pressure recordings, separating the passive myocardial constitutive properties and diastolic residual AT. We apply this framework to three clinical cases, and the results show that the estimated constitutive parameters and residual active tension appear to be a promising candidate to delineate healthy and pathological cases. This work has been published in Xi et al. 2012a. Nevertheless, the need to invasively acquire LV pressure measurement limits the wide application of this approach. Chapter 7 addresses this issue by analysing the feasibility of using two kinds of non-invasively available pressure measurements for the purpose of inverse parameter estimation. The work has been submitted for publication in Xi et al. 2012b.

Stroke is one of the leading causes of death and adult disability worldwide. The major therapeutic intervention for acute ischemic stroke is the administration of recombinant tissue plasminogen activator (rtPA) to help to restore blood flow to the brain. This has been shown to increase the survival rate and to reduce the disability of ischemic stroke patients. However, rtPA is associated with intracranial haemorrhage and thus its administration is currently limited to only about 5% of ischemic stroke patients. More advanced imaging techniques can be used to better stratify patients for rtPA treatment. One new imaging technique, chemical exchange saturation transfer (CEST) magnetic resonance imaging, can potentially image intracellular pH and since tissue acidification happens prior to cerebral infarction, CEST has the potential to predict ischemic injury and hence to improve patient selection. Despite this potential, most studies have generated pH-weighted rather than quantitative pH maps; the most widely used metric to quantify the CEST effect is only able to generate qualitative contrast measurements and suffers from many confounds. The greatest clinical benefit of CEST imaging lies in its ability to non-invasively measure quantitative pH values which may be useful to identify salvageable tissue. The quantitative techniques and work presented in this thesis thus provide the necessary analysis to determine whether a threshold for the quantified CEST effect or for pH exists to help to define tissue outcome following stroke; to investigate the potential of CEST for clinical stroke imaging; and subsequently to facilitate clinical translation of CEST for acute stroke management.

The erosion and transport of fertile topsoil is a serious problem in the U.S., Australia, China and throughout Europe. It results in extensive environmental damage, reduces soil fertility and productivity, and causes significant environmental loss. It is as big a threat to the future sustainability of global populations as climate change, but receives far less attention. With both chemicals (fertilizers, pesticides, herbicides) and biological pathogens (bacteria, viruses) preferentially sorbing to silt and clay sized soil particles, estimating contaminant fluxes in eroded soil also requires predicting the transported soils particle size distribution. The Hairsine-Rose (HR) erosion model is considered in this thesis as it is one of the very few that is specifically designed to incorporate the effect of particle size distribution, and differentiates between non-cohesive previously eroded soil compared with cohesive un-eroded soil. This thesis develops a new extended erosion model that couples the HR approach with the one-dimensional St Venant equations, and an Exner bed evolution equation to allow for feedback effects from changes in the local bed slope on surface hydraulics and erosion rates to be included. The resulting system of 2I +3 (where I = number of particle size classes) nonlinear hyperbolic partial differential equations is then solved numerically using a Liska-Wendroff predictor corrector finite difference scheme. Approximate analytical solutions and series expansions are derived to overcome singularities in the numerical solutions arising from either boundary or initial conditions corresponding to a zero flow depth. Three separate practical applications of the extended HR model are then considered in this thesis, (i) flow through vegetative buffer strips, (ii) modelling discharge hysteresis loops and (iii) the growth of antidunes, transportational cyclic steps and travelling wave solutions. It is shown by comparison against published experimental flume data that predictions from the extended model are able to closely match measurements of deposited sediment distribution both upstream and within the vegetative buffer strip. The experiments were conducted with supercritical inflow to the flume which due to the increased drag from the vegetative strip, resulted in a hydraulic jump just upstream of the vegetation. As suspended sediment deposited at the jump, this resulted in the jump slowly migrating upstream. The numerical solutions were also able to predict the position and hydraulic jump and the flow depth throughout the flume, including within the vegetative strip, very well. In the second application, it is found that the extended HR model is the first one that can produce all known types of measured hysteresis loops in sediment discharge outlet data. Five main loop types occur (a) clockwise, (b) counter-clockwise, (c,d) figure 8 of both flow orientations and (e) single curve. It is clearly shown that complicated temporal rainfall patterns or bed geometry are not required to developed complicated hysteresis loops, but it is the spatial distribution of previously eroded sediment that remains for the start of a new erosion event, which primarily governs the form of the hysteresis loop. The role of the evolution of the sediment distribution in the deposited layer therefore controls loop shape and behavior. Erosion models that are based solely on suspended sediment are therefore unable to reproduce these hysteretic loops without a priori imposing a hysteretic relationship on the parameterisations of the erosion source terms. The rather surprising result that the loop shape is also dominated by the suspended concentration of the smallest particle size is shown and discussed. In the third application, a linear stability analysis shows that instabilities, antidunes, will grow and propagate upstream under supercritical flow conditions. Numerical simulations are carried out that confirm the stability analysis and show the development and movement of antidunes. For various initial parameter configurations a series of travelling antidunes, or transportational cyclic steps, separated by hydraulic jumps are shown to develop and evolve to a steady form and wave speed. Two different forms arise whereby (a) the deposited layer completely shields the underlying original cohesive soil so that the cohesive layer plays no role in the speed or shape of the wave profile or (b) the cohesive soil is exposed along the back of the wave such that both the non-cohesive and cohesive layers affect the wave profile. Under (a) the solutions are obtained up to an additive constant as the actual location of the boundary of the cohesive soil is not required, whereas for (b) this constant must be determined in order to find the location on the antidune from where the cohesive soil becomes accessible. For single size class soils the leading order travelling wave equations are fairly straightforward to obtain for both cases (a) and (b). However for multi-size class soils, this becomes much more demanding as up to 2I + 3 parameters must be found iteratively to define the solution as each size class has its own wave profile in suspension and in the antidune.

Cerebral ischemia is a vascular disorder that is characterized by the reduction of blood supply to the brain, resulting in impaired metabolism and finally death of brain cells. Cerebral ischemia is a major clinical problem associated with global morbidity and mortality rates of about 30%. Clinical management of cerebral ischemia relies heavily on perfusion analysis using dynamic susceptibility contrast MRI (DSC-MRI). DSC-MRI analysis is performed using mathematical models that simulate the underlying vascular physiology of brain. Cerebral perfusion is calculated using perfusion imaging and is used as a marker of tissue health status; low perfusion being an indicator of impaired tissue metabolism. In addition to measurement of cerebral perfusion, it is possible to quantify the blood flow variation within the capillary network referred to as cerebral microvascular hemodynamics. It has been hypothesized that microvascular hemodynamics are closely associated with tissue oxygenation and that hemodynamics might undergo a considerable amount of variation to maintain normal tissue metabolism under conditions of ischemic stress. However with DSC-MRI perfusion imaging, quantification of cerebral hemodynamics still remains a big challenge. Singular Value Decomposition (SVD) is currently a standard methodology for estimation of cerebral perfusion with DSC-MRI in both research and clinical settings. It is a robust technique for quantification of cerebral perfusion, however, the quantification of hemodynamic information cannot be achieved with SVD methods because of the non-physiological behaviour of SVD in microvascular hemodynamic estimation. SVD is sensitive to the noise in the MR signal which appears in the calculated microvascular hemodynamics, thus making it difficult to interpret for pathophysiological significance. Other methods, including model-based approaches or methods based on likelihood estimation, stochastic modeling and Gaussian processes, have been proposed. However, none of these have become established as a means to study tissue hemodynamics in perfusion imaging. Possibly because of the associated constrains in these methodologies that limited their sensitivity to hemodynamic variation in vivo. The objective of the research presented in this thesis is to develop and to evaluate a method to perform a quantitative estimation of cerebral hemodynamics using DSC-MRI. A new Control Point Interpolation (CPI) method has been developed to perform a non-parametric analysis for DSC-MRI. The CPI method was found to be more accurate in estimation of cerebral perfusion than the alternative methods. Capillary hemodynamics were calculated by estimating the transit time distribution of the tissue capillary network using the CPI method. The variations in transit time distribution showed quantitative differences between normal tissue and tissue under ischemic stress. The method has been corrected for the effects of macrovascular bolus dispersion and tested over a larger clinical cohort of patients with atherosclerosis. CPI method is thus a promising method for quantifying cerebral hemodynamics using perfusion imaging. CPI method is an attempt to evaluate the use of quantitative hemodynamic information in diagnostic and prognostic monitoring of patients with ischemia and vascular diseases.

Incremental Sheet Forming (ISF) is a progressive metal forming process, where the deformation occurs locally around the point of contact between a tool and the metal sheet. The final work-piece is formed cumulatively by the movements of the tool, which is usually attached to a CNC milling machine. The ISF process is dieless in nature and capable of producing different parts of geometries with a universal tool. The tooling cost of ISF can be as low as 5–10% compared to the conventional sheet metal forming processes. On the laboratory scale, the accuracy of the parts created by ISF is between ±1.5 mm and ±3mm. However, in order for ISF to be competitive with a stamping process, an accuracy of below ±1.0 mm and more realistically below ±0.2 mm would be needed. In this work, we first studied the ISF deformation process by a simplified phenomenal linear model and employed a predictive controller to obtain an optimised tool trajectory in the sense of minimising the geometrical deviations between the targeted shape and the shape made by the ISF process. The algorithm is implemented at a rig in Cambridge University and the experimental results demonstrate the ability of the model predictive controller (MPC) strategy. We can achieve the deviation errors around ±0.2 mm for a number of simple geometrical shapes with our controller. The limitations of the underlying linear model for a highly nonlinear problem lead us to study the ISF process by a physics based model. We use the elastoplastic constitutive relation to model the material law and the contact mechanics with Signorini’s type of boundary conditions to model the process, resulting in an infinite dimensional system described by a partial differential equation. We further developed the computational method to solve the proposed mathematical model by using an augmented Lagrangian method in function space and discretising by finite element method. The preliminary results demonstrate the possibility of using this model for optimal controller design.

Flood inundation is a major natural hazard that can have very severe socio-economic consequences. This thesis presents an enhanced numerical model for flood simulation. After setting the context by examining recent large-scale flood events, a literature review is provided on shallow flow numerical models. A new version of the hyperbolic horizontal variable density shallow water equations with source terms in balanced form is used, designed for flows over complicated terrains, suitable for wetting and drying fronts and erodible bed problems. Bed morphodynamics are included in the model by solving a conservation of bed mass equation in conjunction with the variable density shallow water equations. The resulting numerical scheme is based on a Godunov-type finite volume HLLC approximate Riemann solver combined with MUSCL-Hancock time integration and a non-linear slope limiter and is shock-capturing. The model can simulate trans-critical, steep-fronted flows, connecting bodies of water at different elevations. The model is validated for constant density shallow flows using idealised benchmark tests, such as unidirectional and circular dam breaks, damped sloshing in a parabolic tank, dam break flow over a triangular obstacle, and dam break flow over three islands. The simulation results are in excellent agreement with available analytical solutions, alternative numerical predictions, and experimental data. The model is also validated for variable density shallow flows, and a parameter study is undertaken to examine the effects of different density ratios of two adjacent liquids and different hydraulic thrust ratios of species and liquid in mixed flows. The results confirm the ability of the model to simulate shallow water-sediment flows that are of horizontally variable density, while being intensely mixed in the vertical direction. Further validation is undertaken for certain erodible bed cases, including deposition and entrainment of dilute suspended sediment in a flat-bottomed tank with intense mixing, and the results compared against semi-analytical solutions derived by the author. To demonstrate the effectiveness of the model in simulating a complicated variable density shallow flow, the validated numerical model is used to simulate a partial dam-breach flow in an erodible channel. The calibrated model predictions are very similar to experimental data from tests carried out at Tsinghua University. It is believed that the present numerical solver could be useful at describing local horizontal density gradients in sediment laden and debris flows that characterise certain extreme flood events, where sediment deposition is important.

A significant proportion of the world's population and physical assets are located in low lying coastal zones. Accurate prediction of wave induced run-up and overtopping of sea defences are important in defining the extent and severity of wave action, and in assessing risk to people and property from severe storms and tsunamis. This thesis describes a one-dimensional numerical model based on the Boussinesq equations of Madsen and Sorensen (1992) and the non-linear shallow water equations. The model is suitable for simulating propagation of weakly non-linear and weakly dispersive waves from intermediate to zero depth, such that any inundation and/or overtopping caused by the incoming waves is also calculated as part of the simulation. Wave breaking is approximated by locally switching to the non-linear shallow water equations, which can model broken waves as bores. A piston paddle wavemaker is incorporated into the model for complete reproduction of laboratory experiments. A domain mapping technique is used in the vicinity of the paddle to transform a time-varying domain into a fixed domain, so that the governing equations can be more readily solved. First, various aspects of the numerical model are verified against known analytical and newly derived semi-analytical solutions. The complete model is then validated with laboratory measurements of run-up and overtopping involving solitary waves. NewWave focused wave groups, which give the expected shape of extreme wave events in a linear random sea, are used for further validation. Simulations of experiments of wave group run-up on a plane beach yield very good agreement with the measured run-up distances and free surface time series. Wave-by-wave overtopping induced by focused wave groups is also successfully simulated with the model, with satisfactory agreement between the experimental and the predicted overtopping volumes. Repeated simulations, now driven by second order paddle displacement signals, give insight into second order error waves spuriously generated by using paddle signals derived from linear theory. Separation of harmonics reveals that the long error wave is significantly affecting the wave group shape and leading to enhanced runu-up distances and overtopping volumes. An extensive parameter study is carried out using the numerical model investigating the influence on wave group run-up of linear wave amplitude at focus, linear focus location, and wave group phase at focus. For a given amplitude, both the phase and the focus location significantly affect the wave group run-up. It is also found that the peak optimised run-up increases with the wave amplitude, but wave breaking becomes an inhibiting factor for larger waves. This methodology is proposed for extreme storm wave induced run-up analysis.

Logarithmic sensors are capable of capturing the wide dynamic range of intensities available in nature with minimum number of bits and post-processing required. A simple circuit able to perform logarithmic capture is one utilising a MOS device in weak inversion. However, the output of this pixel is crippled due to fixed pattern noise. Technique proposed to reduce this noise fail to produce high quality images on account of unaccounted high gain variations in the pixel. An electronic calibration technique is proposed which is capable of reducing both multiplicative as well as additive FPN. Contrast properties matching that of human eye are reported from these sensors. With reduced FPN, the pixel performance at low intensities becomes concerning. In these regions, the high leakage current of the CMOS process affects the logarithmic pixel. To reduce this current, two different techniques using a modified circuit and another with modified layout are tested. The layout technique is observed to reduce the leakage current. In addition, this layout can be used to linearise the output of logarithmic pixel in low light regions. The unique linear response at low light and logarithmic pixel at high light is further investigated. A new model based on the device physics is derived to represent this response. The fixed pattern noise profile is also investigated. An intelligent iterative scheme is proposed and verified to extract the photocurrent flowing in the pixel and correct the fixed pattern noise utilising the new model. Future research ideas leading to better designs of logarithmic pixels and post-processing of these signals are proposed at the end of the thesis.

Abnormal vascular structure has been identified as one of the major characteristics of tumours. In this thesis, we carry out quantitative analysis on different tumour vascular structures and research the relationship between vascular structure and its transportation efficiency. We first study segmentation methods to extract the binary vessel representations from microscope images. We found that local phase-hysteresis thresholding is able to segment vessel objects from noisy microscope images. We also study methods to extract the centre lines of segmented vessel objects, a process termed as skeletonization. We modified the conventional thinning method to regularize the extremely asymmetrical structure found in the segmented vessel objects. We found this method is capable to produce vessel skeletons with satisfactory accuracy. We have developed a software for 3D vessel structural analysis. This software is consisted of four major parts: image segmentation, vessel skeletonization, skeleton modification and structure quantification. This software has implemented local phase-hysteresis thresholding and structure regularization-thinning methods. A GUI was introduced to enable users to alter the skeleton structures based on their subjective judgements. Radius and inter branch length quantification can be conducted based on the segmentation and skeletonization results. The accuracy of segmentation, skeletonization and quantification methods have been tested on several synthesized data sets. The change of tumour vascular structure after drug treatment was then investigated. We proposed metrics to quantify tumour vascular geometry and statistically analysed the effect of tested drugs on normalizing tumour vascular structure. finally, we developed a spatio-temporal model to simulate the delivery of oxygen and 3-18 F-fluoro-1-(2-nitro-1-imidazolyl)-2-propanol (Fmiso), which is the hypoxia tracer that gives out PET signal in an Fmiso PET scanning. This model is based on compartmental models, but also considers the spatial diffusion of oxygen and Fmiso. We validated our model on in vitro spheroid data and simulated the oxygen and Fmiso distribution on the segmented vessel images. We contend that the tumour Fmiso distribution (as observed in Fmiso PET imaging) is caused by the abnormal tumour vascular structure which is further aroused from tumour angiogenesis process. We depicted a modelling framework to research the relationships between tumour angiogenesis, vessel structure and Fmiso distribution, which is going to be the focus of our future work.

Despite the association between hippocampal atrophy and a vast array of highly debilitating neurological diseases, such as Alzheimer’s disease and frontotemporal lobar degeneration, tools to accurately and robustly quantify the degeneration of this structure still largely elude us. In this thesis, we firstly evaluate previously-developed hippocampal segmentation methods (FMRIB’s Integrated Registration and Segmentation Tool (FIRST), Freesurfer (FS), and three versions of a Classifier Fusion (CF) technique) on two clinical MR datasets, to gain a better understanding of the modes of success and failure of these techniques, and to use this acquired knowledge for subsequent method improvement (e.g., FIRSTv3). Secondly, a fully automated, novel hippocampal segmentation method is developed, termed Fast Marching for Automated Segmentation of the Hippocampus (FMASH). This combined region-growing and atlas-based approach uses a 3D Sethian Fast Marching (FM) technique to propagate a hippocampal region from an automatically-defined seed point in the MR image. Region growth is dictated by both subject-specific intensity features and a probabilistic shape prior (or atlas). Following method development, FMASH is thoroughly validated on an independent clinical dataset from the Alzheimer’s Disease Neuroimaging Initiative (ADNI), with an investigation of the dependency of such atlas-based approaches on their prior information. In response to our findings, we subsequently present a novel label-warping approach to effectively account for the detrimental effects of using cross-dataset priors in atlas-based segmentation. Finally, a clinical application of MR hippocampal segmentation is presented, with a combined MR-PET analysis of wholefield and subfield hippocampal changes in Alzheimer’s disease and frontotemporal lobar degeneration. This thesis therefore contributes both novel computational tools and valuable knowledge for further neurological investigations in both the academic and the clinical field.