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The exact relationship between changes in myocardial microstructure as a result of heart disease and the signal measured using diffusion tensor cardiovascular magnetic resonance (DT-CMR) is currently not well understood. Computational modelling of diffusion in combination with realistic numerical phantoms offers the unique opportunity to study effects of pathologies or the efficacy of improvements to acquisition protocols in a controlled in-silico environment. In this work, Monte Carlo random walk (MCRW) methods are used to simulate diffusion in a histology-based 3D model of the myocardium. Sensitivity of typical DT-CMR sequences to changes in tissue properties is assessed. First, myocardial tissue is analysed to identify important geometric features and diffusion parameters. A two-compartment model is considered where intra-cellular compartments with a reduced bulk diffusion coefficient are separated from extra-cellular space by permeable membranes. Secondary structures like groups of cardiomyocyte (sheetlets) must also be included, and different methods are developed to automatically generate realistic histology-based substrates. Next, in-silico simulation of DT-CMR is reviewed and a tool to generate idealised versions of common pulse sequences is discussed. An efficient GPU-based numerical scheme for obtaining a continuum solution to the Bloch--Torrey equations is presented and applied to domains directly extracted from histology images. In order to verify the numerical methods used throughout this work, an analytical solution to the diffusion equation in 1D is described. It relies on spectral analysis of the diffusion operator and requires that all roots of a complex transcendental equation are found. To facilitate a fast and reliable solution, a novel root finding algorithm based on Chebyshev polynomial interpolation is proposed. To simulate realistic 3D geometries MCRW methods are employed. A parallel simulator for both grid-based and surface mesh--based geometries is presented. The presence of permeable membranes requires special treatment. For this, a commonly used transit model is analysed. Finally, the methods above are applied to study the effect of various model and sequence parameters on DT-CMR results. Simulations with impermeable membranes reveal sequence-specific sensitivity to extra-cellular volume fraction and diffusion coefficients. By including membrane permeability, DT-CMR results further approach values expected in vivo.

This work comprises of an investigation into the application of virtual geometric reconstruction and computational fluid dynamics to the upper respiratory tract, to investigate how their anatomical form affects airflow and to examine the potential of 3D modelling of the airway as a potential surgical adjunct. For the latter purpose, the technology would need to have the ability to produce clinically relevant flow information in a timely, cost-effective fashion. Furthermore, it would need to ensure accurate model reproducibility, with specified limits to inter-user variability; thereby reducing costly post-processing in order for computational simulations to be performed. In this work, computational analysis of airway flow is subjected to critical assessment, examining each stage in the process of model building, testing and validation. The first stage is that of translating clinical scan data (usually CT or MRI) into a virtual 3D model for geometric analysis and flow simulation. In defining the airway geometry, key issues are variations in the quality of scan data, together with variations in the procedures used for image analysis and segmentation. Either may compromise the accuracy and the reproducibility of results and some of the results to be presented will indicate that there is a need for systematic research into threshold choices used for image segmentation of both normal and pathological geometries. A further issue is dynamic airway movement: most current scan data does not capture such data, but examples are shown to indicate the scale of such neglected effects. Having obtained a virtual anatomy, in the following stage computational fluid dynamics simulations can be performed to assess flow dynamics. Even though 3D virtual modelling is already used clinically by cardiothoracic and maxillofacial surgeons, knowledge of specificity and sensitivity of measures applied to geometries as complex as the nasal airway as indicators of physiological performance or markers of pathology is still unknown (Rao and Menon, 2015, Saad et al., 2013). In particular, uncertainties in determining the original geometry affect the predictions of flow, which is an issue as yet scarcely addressed. Here, results of a pilot study detailing a methodology to investigate the scale of such effects in computational prediction of nasal airway flows will be described. Whilst completing the two stages, namely model building and computational simulation provide the required output of air flow prediction, a third stage necessary for developing the technology is validation. In this work, an experimental procedure based on rapid prototype manufacture of replica airways, introduced as part of an investigation of the effects of glottis aperture on pressure loss in the trachea, provides a means for validating the computational methodology. Indeed, such replica models may offer an alternative to computational methodologies for more complex problems. Finally, the processes by which models are created and simulations performed are discussed in the context of requirements for validation and streamlining of the process for clinical acceptability.

This thesis comprises an investigation of the dynamics of airflow in the upper respiratory tract from the nose to the carina using computational modelling. The work primarily considers inspiratory flow and comprises separate detailed studies of airflow in three distinct regions: the nose, the larynx and the trachea. In the nose, both airflow dynamics and the associated processes of heat and water exchange are studied. The geometry of the nasal cavity is highly variable both inter- and intra-subjectively. The consequences of inter- and intra-subject variability for both airflow and exchange processes during inspiration is investigated using 10 subject geometries obtained by MRI scans in the decongested and congested states. Non-dimensional scalings are applied to quantify the effects of flowrate and geometry on wall shear stress, heat and water transport. It is found that the anterior nasal cavity contributes most to the exchange process and that decongestion generally affects the distribution of inspiratory flow, promoting a switch towards more inferior pathways. Flow in the larynx is controlled by the position of the vocal folds, which determine the glottis aperture. Even with the vocal folds fully abducted, inspiratory airflow experiences a degree of constriction and exits the glottis as a jet which dissipates in the trachea. The effect of glottis aperture on pressure loss and flow structure is examined, and the results compared with those from a separate experimental investigation. In pathological tracheal geometries, characterized by severe constriction and deviation as caused by compressive retrosternal goitre, far more severe pressure losses may occur than in the normal trachea. The third investigation performed in this work describes a computational approach to assess pathological tracheal resistance. Direct and large eddy simulation results are applied to determine the profile of energy dissipation in the case of a progressive tracheal compression. The study examines the effects of inflow disturbances on the breakup of the jet downstream of the constriction and the consequent loss characteristics. The effect of domain truncation, associated with the typical field of view of clinical imaging, is an important consideration and is investigated.

The mechanics of airflow in the large airways during inspiration affects important physiological functions such as ventilation, olfaction, heat exchange and mass transfer. The behaviour of the airflow is important not only for healthcare applications including diagnosis, intervention planning and assessment, but for inhalation toxicology. This research aims to further the understanding of human nasal physiology through computational modelling. Specifically, the effects of transient inhalation conditions on flow dynamics and transport were characterised and the changes in flow behaviour in response to certain pathologies quantified. The key findings can be summarised as follows: Firstly, the time scales for airflow in the large airways have been identified and the initial flow patterns revealed. Three phases in the temporal behaviour of the flow were identified (flow initiation, quasi-equilibrium and decay). The duration of each phase differs depending on the quantity of interest. Flow in the nose was characterised as transitional, whilst in parts of the descending airways it is turbulent, particularly in the faster moving regions around the jets which may occur in the pharynx, larynx and at the superior end of the trachea. The bulk of the flow is biased to fill only certain regions of the airways, whilst other regions carry little flow, due to features upstream. Analysis of cross-sectional images provided by medical imaging does not necessarily provide a representative view of the area available to the flow. Various scalar species were employed to represent the fate of nanoparticles and gaseous species within the airways. Only species with high diffusion rates exhibited significant absorption at the airway walls. Airway pathologies often cause changes to the geometry of the airway. One such pathology, the goitre, was found to curve the trachea and in some cases cause constriction. Both these geometric changes were found to increase the pressure loss and energy required to drive flow through the trachea. Furthermore, the flow in pathological cases was more disturbed. High resolution simulations have been used to address these topics and the scales simulated have been analysed in terms of the smallest features possible in the flow to determine their fidelity.

This work comprises an investigation of airflow and transport in the human upper airways, which not only perform essential air conditioning physiological functions (heat and water exchange and primary filtration) but also house the olfactory receptors. The conflicting requirements posed by efficient air transit on the one hand and sampling for olfaction on the other renders the geometry of the upper airways complex. Knowledge of the geometry and flow conditions are primary requirements for understanding the physiological mechanics of the airways. This work describes the application of imaging and experimental measurement techniques to determine the variations in nasal airway geometry and the characteristics of nasal inspiratory flow. Whilst the results are relevant to a host of applications, the particular case of sinonasal ventilation well illustrates the interrelation between form, flow and function as well as motivating the development of improved techniques for clinical management. Specifically 3T MR imaging has been investigated as a means to define the anatomy in congested and decongested states. Results show very large changes in nasal airway calibre and moreover allow the variation in mucosal engorgement throughout the nasal cavity to be mapped. Highly time resolved hot wire measurements of inspiratory flow profiles revealed for the first time the rapid temporal development of inspiratory flow during normal inspiration and dramatically so during sniffing. Variations in flow profile were recorded across a cohort of subjects for conditions of normal inspiration, sniffing and smelling. Sinonasal gas exchange is of particular interest given the common occurrence of sinus pathologies. Here short half-life Krypton imaging has been used to investigate gas exchange between the maxillary sinus and the nasal cavity. It has been shown that the technique can provide quantitative assessment of volume flow rate in a model, demonstrating the rapid venting associated with an accessory ostium.

This work comprises an investigation of the fluid mechanics of nasal airflow, primarily using computational fluid dynamics simulations, though with some flow visualisation experiments. The objective of the work is to provide a basic understanding of the flow phenomena that in turn govern transport and exchange processes in the nasal airways. In keeping with the goal of elucidating the basic fluid mechanics, simplified models of the nasal cavity airway were considered together with two representative realistic models. Computations were performed using a commercially available 3D laminar finite-volume solver (Fluent 6.3.26, ANSYS), for steady and unsteady flow conditions. The reduced models replicate the steady pressure loss vs. flow curve found in realistic geometries, and in the unsteady case, confirm the validity of simple inertance modelling to deduce the form of the pressure-flow loop. By selective inclusion/ exclusion of a simplified middle turbinate, the simulations reveal how the turbinate redirects and controls inspired air. In the absence of the middle turbinate, large scale instabilities were observed in the cavity flow and their strength and distribution were seen to increase concomitant with increasing flow rate. It was further identified that the inclusion of this turbinate reduced large scale flow instability and that flow partitioning was predominantly determined by the impingement of the inspiratory jet on its surface. The consequence of the narrow mean passage width characteristic of the nasal airways is explored by comparing an idealised 2D model with 3D geometries of increasing calibre. A strong interrelationship was found to exist between geometric and flow characteristics. In particular, the narrow width of the normal nasal airways is shown to exert a strongly stabilising effect on the mean flow during inspiration. In 3D, whereas increasing calibre width is associated with a progressive destabilisation of the flow, for the same inspiratory flow rate, there would be a concomitant drop in maximum velocity. The computational results moreover detail the evolution of the time-dependent flow within the simplified anatomies and the instability at the margins of the inspiratory jet are shown to compare well with those found in flow visualisation experiments. In the last part of the thesis, steady modelling of the flow in the anatomically realistic geometries is used to investigate their heat and water exchange capacity as well as the characteristics of particle transport and deposition. These results are related to those found in the idealised models.

Recent research on small amplitude helical pipes for use as bypass grafts and arterio- venous shunts suggest that in-plane mixing induced by the geometry may help prevent occlusion by thrombosis. In this thesis, a coordinate transformation of the Navier-Stokes equations is solved within a spectral/hp element framework to study the flow field and mixing behaviour of small-amplitude helical pipes. An apparent discrepancy between the flow field and particle trajectories is observed, whereby particle paths display a pattern characteristic of a double vortex, though the flow field reveals only a single dominant vortex. It is shown that a combination of trans- lational and rotational reference frames changes resolves this discrepancy. It is then proposed that joining together two helical geometries, of differing helical radii, will enhance mixing, through the phenomenon of 'streamline crossing'. An idealised prediction of the mixing is obtained by concatenating the velocity field solutions from the respective single helical geometries. The mixing is examined using Poincar ́e sections, residence time data and information entropy. The flow is then solved for those combined geometries showing the most improvement in mixing, with a 70% increase in mixing efficiency achieved, with only a small increase in pressure loss. It is found that although the true velocity fields vary significantly from the prediction, the overall mixing behaviour is captured, allowing the use of the idealised prediction for guiding future designs of combined geometries.

The spectral/hp element numerical technique is applied to the direct numerical simulation (DNS) and linearised stability analysis of fluid flow in two geometries of fundamental fluid mechanical interest, each with relevance to biomechanical flow. The fluid model is that of incompressible. Newtonian, viscous flow in rigid geometries. The first model, that of a three dimensional tube with a reflex double 45° bend is subject to a fully three-dimensional DNS analysis. This model serves as an idealised artery model, relevant to curved arteries and as an extremely simplified peripheral artery graft model. The persistence of the first Dean vortex pair at higher Reynolds number, as observed by Hoogstraten et al., is again observed, and qualitative explanation is offered by examination of the generation and annihilation of axial vorticity. In addition, results are presented of an unsteady analysis subject to Womersley inflow. Higher frequency results display the shedding of new horseshoe vortical structures. The second model is that of a two dimensional simplified constricted artery model, subjected to a BiGlobal linearised stability analysis. Two new three-dimensional saturated steady states are located for steady flows in a symmetric geometry, and one for an asymmetric geometry. In addition, the Floquet analysis of pulsatile flow is performed upon both symmetric and asymmetric geometries, with primary instabilities located, neutral stability curves presented and Floquet modes and saturated three-dimensional flow cycles obtained.

This thesis presents a non-invasive procedure, based on magnetic resonance imaging (MRI) and computational fluid dynamics (CFD), to characterise the geometry and the flow environment of the distal anastomosis of peripheral by-pass grafts in vivo. A technique to reconstruct three-dimensional models from medical images is described. This technique exploits implicit functions to interpolate the lumen of blood vessels. Algorithms to smooth the reconstructions are discussed together with procedures to represent the reconstructions by parametric surfaces. Reconstructions obtained by the proposed method are accurate and reproducible within the resolution of the images. The technique is automatic and does not rely on topological information known a priori. Hence, its application is not limited to the modelling of vascular structures only. The reconstructions of the anastomoses of 24 patients are classified according to their planarity and to the angles between blood vessels. These parameters are computed with minimum user intervention from the medial lines of the vessels obtained by a three-dimensional thinning algorithm. The results show that the anastomotic geometry depends on the surgical procedure followed to construct the graft. Anastomoses of superficial grafts show a wider angle between graft and proximal host vessel and are less planar. The steady blood flowfield is computed at the patient-specific Reynolds number in four anastomoses using a spectral/hp element method. The distribution of wall shear stress and the transport of fluid particles are influenced by the anastomotic geometry. Larger vortical structures are observed in anastomoses whose angle between graft and proximal host vessel is wider, or whose configuration is less planar; wall shear stresses are higher in anastomoses whose vessels are partially stenosed. Coupling MRI and CFD allows to assess the effects of the in vivo geometry on blood flow and to investigate which anastomotic configurations induce a haemodynamic environment that may delay the progression of disease.