Background: Research in heart disease can be aided by modelling myocardial hemodynamics with knowledge of coronary pressure and vascular resistance measured from the geometry and morphometry of coronary vasculature. This study presents methods to automatically reconstruct accurate detailed coronary vascular anatomical models from high-resolution three-dimensional optical fluorescence cryomicrotomography image volumes for simulating blood flow in coronary arterial trees. Methods: Images of fluorescent cast and bead particles perfused into the same heart comprise the vasculature and microsphere datasets, employed in a novel combined approach to measure vasculature and simulate a flow model on the extracted coronary vascular tree for estimating regional myocardial perfusion. The microspheres are used in two capacities - as fiducial biomarker point sources for measuring the image formation in order to accurately measure the vasculature dataset and as flowing particles for measuring regional myocardial perfusion through the reconstructed vasculature. A new model-based template-matching method of vascular radius estimation is proposed that incorporates a model of the optical fluorescent image formation measured from the microspheres and a template of the vessels’ tubular geometry. Results: The new method reduced the error in vessel radius estimation from 42.9% to 0.6% in a 170 micrometer vessel as compared to the Full-Width Half Maximum method. Whole-organ porcine coronary vascular trees, automatically reconstructed with the proposed method, contained on the order of 92,000+ vessel segments in the range 0.03 – 1.9 mm radius. Discrepancy between the microsphere perfusion measurements and regional flow estimated with a 1-D steady state linear static blood flow simulation on the reconstructed vasculature was modelled with daughter-to-parent area ratio and branching angle as the parameters. Correcting the flow simulation by incorporating this model of disproportionate distribution of microspheres reduced the error from 24% to 7.4% in the estimation of fractional microsphere distribution in oblique branches with angles of 100°-120°.

This thesis addresses orchestration of servers amongst multiple co-hosted internet services such as e-Banking, e-Auction and e-Retail in hosting centres. The hosting paradigm entails levying fees for hosting third party internet services on servers at guaranteed levels of service performance. The orchestration of server ensemble in hosting centres is considered in the context of maximising the hosting centre's revenue over a lengthy time horizon. The inspiration for the server orchestration approach proposed in this thesis is drawn from nature and generally classed as swarm intelligence, specifically, sophisticated collective behaviour of social insects borne out of primitive interactions amongst members of the group to solve problems beyond the capability of individual members. Consequently, the approach is self-organising, adaptive and robust. A new scheme for server ensemble orchestration is introduced in this thesis. This scheme exploits the many similarities between server orchestration in an internet hosting centre and forager allocation in a honeybee (Apis mellifera) colony. The scheme mimics the way a honeybee colony distributes foragers amongst flower patches to maximise nectar influx, to orchestrate servers amongst hosted internet services to maximise revenue. The scheme is extended by further exploiting inherent feedback loops within the colony to introduce self-tuning and energy-aware server ensemble orchestration. In order to evaluate the new server ensemble orchestration scheme, a collection of server ensemble orchestration methods is developed, including a classical technique that relies on past history to make time varying orchestration decisions and two theoretical techniques that omnisciently make optimal time varying orchestration decisions or an optimal static orchestration decision based on complete knowledge of the future. The efficacy of the new biomimetic scheme is assessed in terms of adaptiveness and versatility. The performance study uses representative classes of internet traffic stream behaviour, service user's behaviour, demand intensity, multiple services co-hosting as well as differentiated hosting fee schedule. The biomimetic orchestration scheme is compared with the classical and the theoretical optimal orchestration techniques in terms of revenue stream. This study reveals that the new server ensemble orchestration approach is adaptive in a widely varying external internet environments. The study also highlights the versatility of the biomimetic approach over the classical technique. The self-tuning scheme improves on the original performance. The energy-aware scheme is able to conserve significant energy with minimal revenue performance degradation. The simulation results also indicate that the new scheme is competitive or better than classical and static methods.

The self-assembly of structured particles into monodisperse clusters is a challenge on the nano-, micro- and even macro-scale. While biological systems are able to self-assemble with comparative ease, many aspects of this self-assembly are not fully understood. In this thesis, we look at the strategies and rules that can be applied to encourage the formation of monodisperse clusters. Though much of the inspiration is biological in nature, the simulations use a simple minimal patchy particle model and are thus applicable to a wide range of systems. The topics that this thesis addresses include: Encapsulation: We show how clusters can be used to encapsulate objects and demonstrate that such `templates' can be used to control the assembly mechanisms and enhance the formation of more complex objects. Hierarchical self-assembly: We investigate the use of hierarchical mechanisms in enhancing the formation of clusters. We find that, while we are able to extend the ranges where we see successful assembly by using a hierarchical assembly pathway, it does not straightforwardly provide a route to enhance the complexity of structures that can be formed. Pore formation: We use our simple model to investigate a particular biological example, namely the self-assembly and formation of heptameric alpha-haemolysin pores, and show that pore insertion is key to rationalising experimental results on this system. Phase re-entrance: We look at the computation of equilibrium phase diagrams for self-assembling systems, particularly focusing on the possible presence of an unusual liquid-vapour phase re-entrance that has been suggested by dynamical simulations, using a variety of techniques.

During human immunodeficiency virus 1 (HIV-1) infection, the viral population is in constant battle with the host immune system. The cytotoxic T-lymphocyte (CTL) response, a branch of the adaptive immune response, is implicated in viral control and can drive viral evolution in the infected host population. Endogenous viral peptides, or ‘epitopes’, are presented to CTLs by human leukocyte antigen (HLA) class I molecules on the surface of infected cells where they may be identified as non-self. Mutations in or proximal to a viral epitope can result in ‘escape’ from CTLs targeting that epitope. The repertoire of epitopes which may be presented is dependent upon host class I HLA types. As such, reversion may occur after transmission due to changes in viral fitness and selection in the context of a new HLA background. Thus, parameters describing the dynamics of CTL escape and reversion are key to understanding how CTL responses within individuals relate to HIV-1 sequence evolution in the infected host population. Escape and reversion can be studied directly using biological assays and longitudinal viral sequence data, or indirectly by considering viral sequences across multiple hosts. Indirect approaches include tree based methods which detect associations between host HLA and viral sequence but do not estimate rates of escape and reversion, and ordinary differential equation (ODE) models which estimate these rates but do not consider the dependency structure inherent in viral sequence data. We introduce two models which estimate escape and reversion rates whilst accounting for the shared ancestry of viral sequence data. For our first model, we lay out an integrated Bayesian approach which combines genealogical inference and an existing epidemiological model to inform escape and reversion rate estimates. Using this model, we find evidence for correlation between escape rate estimates across widely separated geographical regions. We also observe a non-linear negative correlation between in vitro replicative capacity and escape rate. Both findings suggest that epistasis does not play a strong role in the escape process. Although our first model worked well, it had some key limitations which we address in our second method. Notably, by making a series of approximations, we are able account for recombination and analyse very large datasets which would be computationally infeasible under the first model. We verify our second approach through extensive simulations, and use the method to estimate both drug and HLA associated selection along portions of the HIV-1 genome. We test the results of the model using existing knowledge, and determine a collection of putative selected sites which warrant further investigation. Finally, we find evidence to support the notion that the CTL response played a role in HIV-1 subtype diversification.

Harmonia axyridis is a ladybird native to Asia, but introduced widely as a biocontrol agent. It is invasive and detrimental to native species in North America, which meant its arrival in Britain was met with concern. Establishment was seen as an opportunity to track the spread of an invasive alien species (IAS) whilst also monitoring impacts on native species. The aims of this thesis were to examine the responses of native British ladybirds to the arrival of H. axyridis, to establish the effect of the IAS on native ladybirds when compared to other drivers, and to investigate the possible facilitation of the H. axyridis invasion by natural enemy release. Modelling ladybird distributions with life-history and resource-use traits found that species predatory on a wide range of prey families had larger range sizes than those which ate fewer prey types. This suggests that the wide diet breadth of the IAS is likely to have played a critical role in the species’ rapid spread. Dietary niche overlap between H. axyridis and native ladybirds showed positive correlation with declines of native ladybirds. This indicates that the IAS is playing an important role, but the significance of urbanisation suggests habitat destruction is also significant. Abundance of H. axyridis was influenced by habitat type and aphid abundance, but not by the native ladybird community, suggesting the spread of the IAS will not be slowed by biotic resistance. Harmonia axyridis is attacked by native parasitoids, but at a much lower rate than is the native Coccinella septempunctata, in line with natural-enemy release theory. There was no evidence of attack rate increasing with time since arrival in an area. Overall, H. axyridis is an extremely successful IAS, with detrimental effects on native ladybirds which are likely to continue.

The astonishing progress of molecular biology, engineering and computer science has resulted in mature technologies capable of examining multiple cellular components at a genome-wide scale. Protein-protein interactions are one example of such growing data. These data are often organised as networks with proteins as nodes and interactions as edges. Albeit still incomplete, there is now a substantial amount of data available and there is a need for biologically meaningful methods to analyse and interpret these interactions. In this thesis we focus on how to compare protein interaction networks (PINs) and on the rela- tionship between network architecture and the biological characteristics of proteins. The underlying theme throughout the dissertation is the use of small subgraphs – small interaction patterns between 2-5 proteins. We start by examining two popular scores that are used to compare PINs and network models. When comparing networks of the same model type we find that the typical scores are highly unstable and depend on the number of nodes and edges in the networks. This is unsatisfactory and we propose a method based on non-parametric statistics to make more meaningful comparisons. We also employ principal component analysis to judge model fit according to subgraph counts. From these analyses we show that no current model fits to the PINs; this may well reflect our lack of knowledge on the evolution of protein interactions. Thus, we use explanatory variables such as protein age and protein structural class to find patterns in the interactions and subgraphs we observe. We discover that the yeast PIN is highly heterogeneous and therefore no single model is likely to fit the network. Instead, we focus on ego-networks containing an initial protein plus its interacting partners and their interaction partners. In the final chapter we propose a new, alignment-free method for network comparison based on such ego-networks. The method compares subgraph counts in neighbourhoods within PINs in an averaging, many-to-many fashion. It clusters networks of the same model type and is able to successfully reconstruct species phylogenies solely based on PIN data providing exciting new directions for future research.

Modelling and simulation are essential to modern research in cell biology. This thesis follows a journey starting from the construction of new stochastic methods for discrete biochemical systems to using them to simulate a population of interacting haematopoietic stem cell lineages. The first part of this thesis is on discrete stochastic methods. We develop two new methods, the stochastic extrapolation framework and the Stochastic Bulirsch-Stoer methods. These are based on the Richardson extrapolation technique, which is widely used in ordinary differential equation solvers. We believed that it would also be useful in the stochastic regime, and this turned out to be true. The stochastic extrapolation framework is a scheme that admits any stochastic method with a fixed stepsize and known global error expansion. It can improve the weak order of the moments of these methods by cancelling the leading terms in the global error. Using numerical simulations, we demonstrate that this is the case up to second order, and postulate that this also follows for higher order. Our simulations show that extrapolation can greatly improve the accuracy of a numerical method. The Stochastic Bulirsch-Stoer method is another highly accurate stochastic solver. Furthermore, using numerical simulations we find that it is able to better retain its high accuracy for larger timesteps than competing methods, meaning it remains accurate even when simulation time is speeded up. This is a useful property for simulating the complex systems that researchers are often interested in today. The second part of the thesis is concerned with modelling a haematopoietic stem cell system, which consists of many interacting niche lineages. We use a vectorised tau-leap method to examine the differences between a deterministic and a stochastic model of the system, and investigate how coupling niche lineages affects the dynamics of the system at the homeostatic state as well as after a perturbation. We find that larger coupling allows the system to find the optimal steady state blood cell levels. In addition, when the perturbation is applied randomly to the entire system, larger coupling also results in smaller post-perturbation cell fluctuations compared to non-coupled cells. In brief, this thesis contains four main sets of contributions: two new high-accuracy discrete stochastic methods that have been numerically tested, an improvement that can be used with any leaping method that introduces vectorisation as well as how to use a common stepsize adapting scheme, and an investigation of the effects of coupling lineages in a heterogeneous population of haematopoietic stem cell niche lineages.

We investigate the biological constraints determined by the complex relationships between ecological and immunological processes of host-pathogen interactions, with emphasis on influenza viruses in human, which are responsible for a number of pandemics in the last 150 years. We begin by discussing prolegomenous reviews of historical perspectives on the use of theoretical modelling as a complementary tool in public health and epidemiology, current biological background motivating the objective of the thesis, and derivations of mathematical models of multi-locus-allele systems for infectious diseases with co-circulating serotypes. We provide detailed analysis of the multi-locus-allele model and its age-specific extension. In particular, we establish the necessary conditions for the local asymptotic stability of the steady states and the existence of oscillatory behaviours. For the age-structured model, results on the existence of a mild solution and stability conditions are presented. Numerical studies of various strain spaces show that the dynamic features are preserved. Specifically, we demonstrate that discrete antigenic forms of pathogens can exhibit three distinct dynamic features, where antigenic variants (i) fully self-organize and co-exist with no strain structure (NSS), (ii) sort themselves into discrete strain structure (DSS) with non-overlapping or minimally overlapping clusters under the principle of competitive exclusion, or (iii) exhibit cyclical strain structure (CSS) where dominant antigenic types are cyclically replaced with sharp epidemics dominated by (1) a single strain dominance with irregular emergence and re-emergence of certain pathogenic forms, (2) ordered alternating appearance of a single antigenic type in periodic or quasi-periodic form similar to periodic travelling waves, (3) erratic appearance and disappearance of synchrony between discrete antigenic types, and (4) phase-synchronization with uncorrelated amplitudes. These analyses allow us to gain insight into the age-specific immunological profile in order to untangle the effects of strain structures as captured by the clustering behaviours, and to provide public health implications. The age-structured model can be used to investigate the effect of age-specific targeting for public health purposes.

This biomedical engineering thesis explores the opportunities and challenges of 2D+t contrast echocardiography for left ventricle functional analysis, both clinically and within a computer vision atlas-based deformable template model framework. A database was created for the experiments in this thesis, with 21 studies of contrast Dobutamine Stress Echo, in all 4 principal planes. The database includes clinical variables, human expert hand-traced myocardial contours and visual scoring. First the problem is studied from a clinical perspective. Quantification of endocardial global and local function using standard measures shows expected values and agreement with human expert visual scoring, but the results are less reliable for myocardial thickening. Next, the problem of segmenting the endocardium with a computer is posed in a standard landmark and atlas-based deformable template model framework. The underlying assumption is that these models can emulate human experts in terms of integrating previous knowledge about the anatomy and physiology with three sources of information from the image: texture, geometry and kinetics. Probabilistic atlases of contrast echocardiography are computed, while noting from histograms at selected anatomical locations that modelling texture with just mean intensity values may be too naive. Intensity analysis together with the clinical results above suggest that lack of external boundary definition may preclude this imaging technique for appropriate measuring of myocardial thickening, while endocardial boundary definition is appropriate for evaluation of wall motion. Geometry is presented in a Principal Component Analysis (PCA) context, highlighting issues about Gaussianity, the correlation and covariance matrices with respect to physiology, and analysing different measures of dimensionality. A popular extension of deformable models ---Active Appearance Models (AAMs)--- is then studied in depth. Contrary to common wisdom, it is contended that using a PCA texture space instead of a fixed atlas is detrimental to segmentation, and that PCA models are not convenient for texture modelling. To integrate kinetics, a novel spatio-temporal model of cardiac contours is proposed. The new explicit model does not require frame interpolation, and it is compared to previous implicit models in terms of approximation error when the shape vector changes from frame to frame or remains constant throughout the cardiac cycle. Finally, the 2D+t atlas-based deformable model segmentation problem is formulated and solved with a gradient descent approach. Experiments using the similarity transformation suggest that segmentation of the whole cardiac volume outperforms segmentation of individual frames. A relatively new approach ---the inverse compositional algorithm--- is shown to decrease running times of the classic Lucas-Kanade algorithm by a factor of 20 to 25, to values that are within real-time processing reach.

Ankylosing spondylitis (AS) is a common inflammatory arthritis of the spine and other affected joints, which is highly heritable, being strongly influenced by the HLA-B27 status, as well as hundreds of mostly unknown genetic variants of smaller effect. The aim of my research was to confirm some of the previously observed genetic associations and to identify new associations, many of which are in biological pathways relevant to AS pathogenesis, most notably the IL-23/T_H17 axis (IL23R) and antigen presentation (ERAP1 and ERAP2). Studies presented in this thesis include replication and refinement of several potential associations initially identified by earlier GWAS (WTCCC-TASC, 2007 and TASC, 2010). I conducted an extended study of IL23R association with AS and undertook a meta-analysis, confirming the association between AS and IL23R (non-synonymous SNP rs11209026, p=1.5 x 10-9, OR=0.61). An extensive re-sequencing and fine mapping project, including a meta-analysis, to replicate and refine the association of TNFRSF1A with AS was also undertaken; a novel variant in intron 6 was identified and a weak association with a low frequency variant, rs4149584 (p=0.01, OR=1.58), was detected. Somewhat stronger associations were seen with rs4149577 (p=0.002, OR=0.91) and rs4149578 (p=0.015, OR=1.14) in the meta-analysis. Associations at several additional loci had been identified by a more recent GWAS (WTCCC2-TASC, 2011). I used in silico techniques, including imputation using a denser panel of variants from the 1000 Genomes Project, conditional analysis and rare/low frequency variant analysis, to refine these associations. Imputation analysis (1782 cases/5167 controls) revealed novel associations with ERAP2 (rs4869313, p=7.3 x 10-8, OR=0.79) and several additional candidate loci including IL6R, UBE2L3 and 2p16.3. Ten SNPs were then directly typed in an independent sample (1804 cases/1848 controls) to replicate selected associations and to determine the imputation accuracy. I established that imputation using the 1000 Genomes Project pilot data was largely reliable, specifically for common variants (genotype concordence~97%). However, more accurate imputation of low frequency variants may require larger reference populations, like the most recent 1000 Genomes reference panels. The results of my research provide a better understanding of the complex genetics of AS, and help identify future targets for genetic and functional studies.