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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.