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Objective: This study aimed to comprehensively examine the roles of size, location, and number of tears in the progression of surgically repaired type A aortic dissection (TAAD) by assessing haemodynamic changes through patient-specific computational fluid dynamic (CFD) simulations. Methods: Two patient-specific TAAD geometries with replaced ascending aorta were reconstructed based upon computed 15 tomography (CT) scans, after which 10 hypothetical models (5 per patient) with different tear configurations were artificially created. CFD simulations were performed on all the models under physiologically realistic boundary conditions. Results: Our simulation results showed that increasing either the size or number of the re-entry tears reduced the luminal pressure difference (LPD) and maximum time-averaged wall shear stress (TAWSS), as well as areas exposed to abnormally high or low TAWSS values. Models with a large re-entry tear outperformed the others by reducing the maximum LPD by 1.88 mmHg and 7.39 mmHg, for patients 1 and 2, respectively. Moreover, proximally located re-entry tears in the descending aorta were more effective at reducing LPD than distal re-entry tears. Discussion: These computational results indicate that the presence of a relatively large re-entry tear in the proximal descending aorta might help stabilize post-surgery aortic growth. This finding has important implications for the management and risk stratification of surgically repaired TAAD patients. Nevertheless, further validation in a large patient cohort is needed.

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Fractals are fascinating structures, not only for their aesthetic appeal, but also because they allow for the investigation of physical properties in non-integer dimensions. In these unconventional systems, a myriad of intrinsic features might come into play, such as the fractal dimension, the spectral dimension, or the fractal geometry. Despite abundant theoretical and numerical studies, experiments in fractal networks remain elusive. Here, we experimentally investigate quantum transport in fractal networks by performing continuous-time quantum walks in fractal photonic lattices with incremental propagation lengths. Photons act as the walkers and evolve in the lattices after being injected into one initial site. We unveil the transport properties through the photon evolution pattern at different propagation lengths and the analysis of the variance and the P'olya number, which are calculated based on the probability distribution of the patterns. Contrarily to classical fractals, we observe anomalous transport governed solely by the fractal dimension. In addition, the critical point at which there is a transition from normal to anomalous transport is highly dependent on the fractal geometry. Our experiment allows the verification of physical laws in a quantitative manner and reveals the transport dynamics with unprecedented detail, thus opening a path to the understanding of more complex quantum phenomena governed by fractality., Comment: 45 pages, 21 figures, comments welcome!

Higher-order topological insulator, as a newly found non-trivial material and structure, possesses a topological phase beyond the bulk-boundary correspondence. Here, we present an experimental observation of photonic higher-order topological crystalline insulator and its topological protection to quantum superposition and entanglement in a two-dimensional lattice. By freely writing the insulator structure with femtosecond laser and directly measuring evolution dynamics with single-photon imaging techniques, we are able to observe the distinct features of the topological corner states in C_4 and C_2 photonic lattice symmetry. Especially, we propose and experimentally identify the topological corner states by exciting the photonic lattice with single-photon superposition state, and we examine the protection impact of topology on quantum entanglement for entangled photon states. The single-photon dynamics and the protected entanglement reveal an intrinsic topological protection mechanism isolating multi-partite quantum states from diffusion-induced decoherence. The higher-order topological crystalline insulator, built-in superposition state generation, heralded single-photon imaging and quantum entanglement demonstrated here link topology, material, and quantum physics, opening the door to wide investigations of higher-order topology and applications of topological enhancement in genuine quantum regime., Comment: 46 pages, 6 figures in main text, 16 figures in Supplementary Materials

Quantum computation, aiming at tackling hard problems beyond classical approaches, has been flourishing with each passing day. Unfortunately, a fully scalable and fault-tolerant universal quantum computer remains challenging based on the current technology. Boson sampling, first proposed by Aaronson and Arkhipov, is commonly believed as the most promising candidate to reach the intermediate quantum computational milestone, namely, quantum supremacy. Following this leading proposal, many experimental implementations as well as variants of boson sampling have been shown. However, most of these works are limited to small scale and cannot fulfill the permanent-of-Gaussians conjecture. Here, we experimentally demonstrate the largest scale boson sampling in the collision-free dominant regime using multi-port interferometer in a 3D photonic chip. We measure all 6,545 no-collision output combinations and validate the experimental results. Our work shows the potential of 3D photonic chip platform and represents a solid step toward large scale boson sampling., Comment: 18 pages, 5 figures, comments welcome!

Quantum entanglement and coherence are two fundamental features of nature, arising from the superposition principle of quantum mechanics. While considered as puzzling phenomena in the early days of quantum theory, it is only very recently that entanglement and coherence have been recognized as resources for the emerging quantum technologies, including quantum metrology, quantum communication, and quantum computing. In this work we study the limitations for the interconversion between coherence and entanglement. We prove a fundamental no-go theorem, stating that a general resource theory of superposition does not allow for entanglement activation. By constructing a CNOT gate as a free operation, we experimentally show that such activation is possible within the more constrained framework of quantum coherence. Our results provide new insights into the interplay between coherence and entanglement, representing a substantial step forward for solving longstanding open questions in quantum information science., Comment: 11 pages, 5 figures, Submitted

The chemical and physicochemical properties of mung bean starch oxidized by sodium hypochlorite and esterified with succinic anhydride were studied. Mung bean starch was modified by oxidation with sodium hypochlorite and esterified with succinic anhydride. The native mung bean starch (NMBS) granules were shown to have an irregular shape, which varied from oval to round to bean shape with a smooth surface. Succinylation led to partial rupture of the granule integrity while oxidation converted the smooth surface of the native granules to a surface with fissures. Swelling capacity improved through succinylation but was reduced after oxidation. Oxidation enhanced solubility; however, succinylation showed no uniform effect throughout the temperature range studied. Both modifications increased hydrophilic tendency and demonstrated decreased gelatinization temperature compared to the NMBS. Oil absorption capacity and syneresis of native starch was enhanced after oxidation but was reduced after succinylation. Both starch types, native and modified, exhibited non-Newtonian behavior, but to a different extent. The gel formation of oxidized starch revealed the highest storage modulus followed by native starch and then succinated starch.

Type B aortic dissection is a potentially devastating disease of the aorta initiated by a tear in the inner lining of the aortic wall. Blood flow through this tear causes the aortic wall layers to separate and a secondary channel of blood flow know as the ‘false lumen’ forms. Complete thrombosis (clotting) of the false lumen, is the desired outcome of either medical or endovascular (TEVAR) treatment. However, it is currently unclear at the time of diagnosis how a specific dissection will progress with either treatment option. Anatomical studies have identified a range of morphological factors that may be influential in disease progression, though no single parameter has been found to be independently predictive of patient prognosis. Computational fluid dynamics (CFD) studies have aimed to assess the hemodynamic state of dissection, however, studies have generally been limited due to simplified geometries and unphysiological boundary conditions due to the lack of patient-specific in vivo flow data. Thanks to recent developments in imaging technologies, in vivo flow data can now be acquired through 4D-flow magnetic resonance imaging (MRI), though detailed evaluation of dissection flow fields is limited due to poor image quality. CFD has the potential to be a useful tool in clinical practice for predicting disease progression, as long as the results are physiological to specific patients. 4D-flow MRI data could provide the patient-specific details required to build detailed and accurate CFD models. The primary objective of this thesis is to develop clinically applicable computational models to accurately simulate hemodynamics and thrombus formation in type B dissection patients. A 4D-flow MRI based CFD workflow was developed and key model inputs were assessed in detail. The use of a patient-specific 3D inlet velocity profile was compared to commonly used idealised profiles, with the 3D profile producing results which agreed best with in vivo data. The importance of major and minor aortic branches in geometry segmentation was assessed, and results showed that exclusion of such branches can significantly impact predicted hemodynamics and thrombus formation. The finalised CFD workflow was evaluated against in vivo data and was shown to be able to faithfully reproduce dissection hemodynamics in a study of 5 patients. A hemodynamics-based thrombus predicting model was evaluated and simplified in order to improve computational efficiency for clinical application. Finally, the CFD workflow and thrombus model were utilised in studies on the influence of re-entry tears both pre- and post-TEVAR. Open Access

Novel branched stent-grafts (BSG) have been developed for endovascular repair of complex thoracic aortic aneurysms (TAA) involving the aortic arch or thoracoabdominal aorta, but their haemodynamic performance has not been adequately studied. In addition, surgical replacement of the ascending aorta with a Dacron graft remains the gold standard for type A aortic dissection (TAAD), although 12% of patients are at risk of aortic rupture due to further dilatation of the residual dissected aorta. The underlying mechanisms for progressive aortic dilatation following TAAD repair are poorly understood, but haemodynamic and biomechanical factors are believed to play an important role. Therefore, the present study aims to provide more insights into the haemodynamics in novel BSGs developed for treating complex aortic diseases, and a comprehensive evaluation of flow and biomechanical conditions in post-surgery TAADs by means of state-of-the-art computational methods. The first part of this thesis focuses on evaluating the haemodynamic performance of novel BSG designs, including thoracoabdominal branch endoprosthesis (TAMBE) and dual-branched thoracic endograft. Haemodynamics in idealised and patient-specific BSG models has been analysed by examining side branch outflow waveforms, wall shear stress related indices, and displacement forces, in order to assess their long-term durability. The numerical results show that all the stent-graft models examined in this study are capable of providing normal blood perfusion to side vessels, and are at low risk of in-stent thrombosis and device migration. Furthermore, it has been shown that geometric variations in TAMBE do not affect the key haemodynamic results, indicating its potential suitability for a variety of visceral artery anatomies. Comparisons of dual-branched thoracic endograft models with different inner tunnel diameters suggest that BSGs with larger inner tunnel diameters than the respective vessels would be preferred. Comparisons between the pre- and post-intervention models show that insertion of a dual-branched stent-graft significantly alters the flow pattern in the aortic arch, some of which may have a detrimental effect in the long term, thus requiring follow-up studies. The second part of the thesis provides a comprehensive analysis of the haemodynamic and biomechanical conditions in surgically repaired TAAD. Geometric and haemodynamic parameters have been analyzed and compared between the group of patients with stable aortic diameter and another group with progressive aortic dilatation. The number of re-entry tears (6±5 vs 2±1;P= 0.02) and luminal pressure difference (1.3 ±1 vs 11.7 ±14.6 mmHg;P= 0.001) have been identified as potential predictors of progressive aortic dilatation in TAAD patients following surgical repair. This is an important finding and can potentially assist clinicians to make the most appropriate choice or surgical plan for individual patients. Based on the finite element analysis of four patient-specific cases, there are no clear differences in biomechanical parameters between the stable and unstable groups. Furthermore, a preliminary fluid-solid interaction (FSI) simulation performed on a single TAAD model has demonstrated the important influence of wall compliance on pressures in the true and false lumen. Compared to a rigid wall model, the FSI simulation results show a reduction in systolic pressure by up to 10 mmHg and a slight increase in diastolic pressure. However, pressures in the true and false lumen are affected in the same way, so that the luminal pressure difference remains the same between the rigid and FSI models. Open Access

Aortic valve (AV) diseases are life-threatening conditions which affect millions of people worldwide and, if left untreated, can lead to death a few years after symptom onset. Patients affected by AV diseases are commonly referred to surgical AV replacement (SAVR). However, more than 30% of patients are not suitable for SAVR. For this reason, transcatheter aortic valve implantation (TAVI) has been attracting growing interest. Several clinical studies compared the outcomes of these techniques, showing that TAVI could be a valid alternative to SAVR. However, there is a lack of detailed knowledge about changes in the aortic hemodynamic conditions following these procedures. The main aim of this thesis is to develop efficient and robust methodologies to study and compare the influences of different AV replacement procedures on aortic hemodynamics. An image-based patient-specific computational model has been developed, which uses magnetic resonance images (MRI) acquired from patients to obtain realistic geometry and boundary conditions (BCs) for computational fluid dynamics (CFD) analysis. The implemented physiological BCs were compared with the most commonly used inlet and outlet BCs, and showed the best agreement with in vivo data. The model was then applied to study and compare SAVR, TAVI and aortic root replacement using a variety of prostheses. In addition, an experimental set-up was designed to further study TAVI hemodynamics by combining 3D-printing, 4D flow MRI and CFD. Finally, a preliminary analysis of valve leaflet thrombosis was conducted. It has been shown that both TAVI and SAVR are able to greatly improve the aortic hemodynamics, but this often deviates from conditions in healthy volunteers, with the extent of abnormalities strongly dependent on the type of prostheses or valve disease. The work also demonstrated the feasibility of predicting valve leaflet thrombosis using a shear-driven model for thrombus formation and growth. Open Access

Thermosensitive liposome (TSL)-mediated drug delivery in combination with focused ultrasound (FUS) induced hyperthermia has been considered as a promising alternative to conventional chemotherapy. Tumour cells residing in tumour interstitial space can only be killed when they are exposed to therapeutic levels of drug concentration. Interstitial transport, as an essential step to carry drug molecules to tumour cells, must be examined in detail to gain mechanistic understandings of TSL delivery in combination with hyperthermia exposure. The process starting from the infusion of drug-loaded TSL to the uptake of chemotherapy drug by tumour cells involves multiple physical and biochemical steps; these include acoustic wave propagation in tissue upon the application of FUS, heat transfer in response to FUS heating, diffusive and convective transport of TSL and released drug from the blood stream and across the vessel wall into the interstitial space, as well as the transfer of bioavailable drug across the cell membrane and its eventual uptake by tumour cells. To understand the transport mechanism and the interactions among the different steps, mathematical models have been developed to simulate the TSL drug delivery system. First, a multi-compartmental model is developed and applied to idealised tumour cord geometry with an aim to identify the key transport parameters that affect the predicted therapeutic outcome. Results suggest that hyperthermia duration and drug release rates are the most influential parameters. Based on this finding, multivariable optimisation is carried out in searching for the optimal conditions that would maximise tumour cell killing while minimising the risk of side effect. This is followed by the development of a multiphysics continuum-based model for detailed examination of spatial and temporal distributions of key variables (e.g. temperature and drug concentration) in realistic tumour geometry reconstructed from magnetic resonance images. The results provide more insights into the spatial profiles of temperature upon the application of FUS and hyperthermia-induced drug release. Comparisons are made between two TSL delivery systems, a conventional TSL loaded with doxorubicin (DOX) and a novel imageable TSL (iTSL) loaded with topotecan (TOP). Results show that the iTSL-TOP system achieves much higher cancer cell killing fraction than the conventional TSL-DOX system. Since non-uniform temperature profile and heterogeneous drug distribution at the tumour site are identified as limiting factors, initial attempts are made to determine the influences of the number and location of ultrasound focal points on temperature distribution. Although the computational models employed in the present study have a number of limitations, they are capable of providing detailed spatiotemporal information that cannot be obtained in vivo. The modelling framework can serve as a useful tool for evaluation and optimisation of therapeutic efficacy of FUS-TSL drug delivery systems. Open Access

The aberrance of the vasculature in tumours has been linked to increased aggressiveness and poor drug delivery in tumours. Complexities in the microarchitecture of tumour vasculature occurring on microscopic scales can affect fluid flow and drug transport making it difficult to predict tumour response to treatment. Given this, mathematical models can play an important role in understanding the various aspects of the tumour vasculature that can promote invasiveness and limit drug delivery. In this work, computational models are developed to investigate the effect of tumour vasculature on fluid flow and drug distribution and novel imaging methods are assessed for their ability to characterise the tumour vasculature in whole human tumours. A mathematical angiogenesis model is used to generate microscopic details including individual vessel properties on a whole vascular network scale which are coupled with a fluid flow and drug transport model. The interstitial fluid pressure (IFP) in the tumour model was found to be elevated with increased heterogeneity caused by the presence of a necrotic core and heterogenous vessel permeability. Subtle changes to the network on a microscopic scale significantly influenced fluid flow in the tumour vessels and tissue. Delivery of doxorubicin to tumours was found to be highly dependent on the properties of tumour vasculature and blood flow, where regions with excessive branching and vessel tortuosity had reduced drug concentrations due to poor blood flow. Hence, the vascular density was not found to be the main factor in the accumulation of the drug within the tissue space and it’s uptake by cancer cells. An interplay between treatment strategy including dose and administration mode and properties of the vasculature was found by evaluating the spatial intracellular concentration. The fluid flow and drug transport models showed the significant effect of incorporating the microscopic properties of the tumour vasculature which can influence fluid flow and drug distribution on a macroscopic scale. The imaging methods assessed in this work shows that Optical projection tomography combined with fluorescent Immunohistochemistry labelling methods can be used to extract angiogenesis related parameters in whole human tumours. Additionally, the method was able to extract clean network topologies that show promise in application to understanding fluid flow and drug transport in real tumours. Open Access

Carotid stenosis is a local narrowing of the carotid artery, and is usually found in the internal carotid artery. The presence of a high-degree stenosis in a carotid artery may provoke transition from laminar to turbulent flow during part of the cardiac cycle. Turbulence in blood flow can influence haemodynamic parameters such as velocity profiles, shear stress and pressure, which are important in wall remodelling. Patients with severe stenosis could be treated with a minimally invasive clinical procedure, carotid artery stenting (CAS). Although CAS has been widely adopted in clinical practice, the complication of in-stent restenosis (ISR) has been reported after CAS. The incidence of ISR is influenced by stent characteristics and vessel geometry, and correlates strongly with regions of neointimal hyperplasia (NH). Therefore, the main purpose of this study is to provide more insights into the haemodynamics in stenosed carotid artery and in post-CAS geometries via computational simulation. The first part of the thesis presents a computational study on flow features in a stenotic carotid artery bifurcation using two computational approaches, large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) incorporating the Shear Stress Transport model with the γ-Reθ transition (SST-Tran) models. The computed flow patterns are compared with those measured with particle image velocimetry (PIV). The results show that both SST-Tran and LES can predict the PIV results reasonably well, but LES is more accurate especially at locations distal to the stenosis where flow is highly disturbed. The second part of the thesis is to determine how stent strut design may influence the development of ISR at the carotid artery bifurcation following CAS. Key parameters that can be indicative of ISR are obtained for different stent designs and compared; these include low and oscillating wall shear stress (WSS), high residence time, and wall stress. A computationally efficient methodology is employed to reproduce stent strut geometry. This method facilitates the accurate reconstruction of actual stent geometry and details of strut configuration and its inclusion in the fluid domain. Computational simulations for flow patterns and low-density lipoprotein (LDL) transport are carried out in order to investigate spatial and temporal variations of WSS and LDL accumulation in the stented carotid geometries. Furthermore, finite element (FE) analysis is performed to evaluate the wall stress distribution with different stent designs. The results reveal that the closed-cell stent design is more likely to create atheroprone and procoagulant flow conditions, causing larger area to be exposed to low wall shear stress (WSS), elevated oscillatory shear index, as well as to induce higher wall stress compared to the open-cell stent design. This study also demonstrates the suitability of SST-Tran and LES models in capturing the presence of complex flow patterns in post-stenotic region. Open Access

Type B aortic dissection is a critical clinical emergency caused by the rupture of the inner wall of the aorta. The formation of a tear allows blood to flow into the aortic wall layers, leading to the formation of a second blood-filled region known as the "false lumen". This disease compromises blood supplies to organs in the abdomen and can lead to complications such as aortic aneurysm, rupture or malperfusion syndromes, resulting in a high mortality risk. Although Type B aortic dissections are generally associated with high in-hospital survival, post-discharge prognosis is poor and highly variable. Significant predictors for long term outcomes include the formation and extent of thrombosis in the false lumen. Partial false lumen thrombosis has been identified as a significant predictor for late complications due to increased false lumen pressure and hence a high risk for aneurysm growth and rupture. On the other hand, improved outcomes are associated with complete false lumen thrombosis, which can be achieved through endovascular repair. If it was possible to predict which patients would develop false lumen thrombosis and to what extent and how to improve the chances for complete thrombosis, treatments could be significantly improved. The main purpose of this thesis is to develop a computationally efficient approach to predict thrombus formation in patients affected by Type B aortic dissection. A hemodynamics-based computational model has been developed, which employs shear rates, fluid residence time, and platelet distribution to evaluate the likelihood for thrombosis and to simulate the growth of thrombus and its effects on blood flow over time. The computational approach has been applied to idealised and patient-specific geometries to (i) assess the accuracy of model predictions, and (ii) identify geometric features that favour false lumen thrombosis. Finally, data acquired as part of the ADSORB trial have been used to further validate the model and to identify potential predictors of true and false lumen volume changes. It has been demonstrated that the model is capable of predicting which patients are most likely to develop thrombosis of the false lumen and to what extent, for both medically treated patients and those following TEVAR. This information can potentially help clinicians to select the most appropriate treatment or surgical strategy for individual patients. Open Access

Aortic dissection (AD) is a multifactorial disease that affects the aorta. The trigger of AD is the formation of a tear in the wall of the aorta which splits the wall layers allowing blood flows inside it. The propagation of dissection along the wall creates two separate cavities, a true lumen (TL) and a false lumen (FL) divided by a septum. AD is associated with complicated haemodynamics which in turn affects the progression of the disease. The aim of this project was to analyse flow characteristics and wall shear stress in hypothetical and realistic models with different tear sizes, branch vessel distributions and outlet boundary conditions. First, an idealised model without branches was created to examine the influence of entry and re-entry tear sizes. Four combinations of tear sizes were examined for this purpose. This was followed by an idealised model with branches, for which 30 simulations, with different branch vessel distribution, were performed to evaluate the importance of inflow and outflow capacities of the TL and FL. Finally, a patient-specific model was built based on medical images, and the effects of outlet boundary conditions were investigated. It was found that pressure difference between the TL and FL, velocities and wall shear stress (WSS) distributions were sensitive to the size of all the tears and their ratio. A balance between the inflow and outflow capacities of the FL reduced the risk of collapse and could help stabilise the dissection. However, increasing the inflow capacity of the TL increased the pressure in the already pressurized lumen, while increasing the outflow capacity reduced the pressure in the TL and may induce TL collapse. Results from the patient-specific model confirmed that the Windkesel outflow boundary condition appeared to be the most promising as it correctly predicted a reduction of flow into the TL branches and a significant increase of flow into the FL branch, in accordance with the in vivo observation. However, the predicted flow patterns, WSS distributions and pressure differences were not particularly sensitive to the type of outflow boundary conditions employed. Open Access

Thromboembolic diseases such as myocardial infarction and ischemic stroke are one of the main causes of death in the world. These pathologies occur when an abnormal blood clot develops in the human body and travels throughout the circulatory system as an embolus. If the occlusion takes place in the cerebral arteries, it can lead to acute ischemic stroke which, if not treated rapidly, will cause morbidity and death. One of the forms of treatment for ischemic stroke is thrombolytic therapy whereby a drug known as alteplase is provided intravenously to the patient so as to dissolve the occluding thrombus. This treatment, however, can provoke life-threatening side-effects such as intracerebral haemorrhage (ICH) and therefore is limited to only a subset of patients that are free of contraindications. Furthermore, thrombolytic therapy can sometimes be ineffective in treating certain types of occlusions. As such, there is considerable interest in the medical community in determining the scenarios where thrombolytic therapy can be ineffective and how existing treatment can be optimised. To this end, a multi-physics and multi-scale computational model has been developed in an attempt to simulate the treatment of ischemic stroke with thrombolytic therapy. Blood flow and drug transport are described by partial differential equations that are solved with the aid of computational fluid dynamics (CFD) software. Fibrinolysis is described using a microscale model whereby changes in the clot microstructure give rise to changes in macroscopic properties of the clot such as clot resistance and composition. Arterial geometries include idealised models using CAD software and patient-specific models extracted from computed tomography angiography (CTA) images. Physiological flow boundary conditions are implemented by using 3 element Windkessel models while drug transport boundary conditions are determined with the aid of a compartmental model. Clots of different shapes, lengths and locations are studied and their dissolution patterns are examined under different thrombolysis regimens. Predicted changes in the intra-arterial flowrate and pressure are consistent with data in the literature. The results show that under the assumption of homogeneous clot properties, clot lysis patterns are strongly dependent on clot position, whereas clot dissolution time is merely determined by clot length. Numerical simulations of different thrombolysis regimens indicate that treatment dose and duration can be personalised according to clot length and clot composition in order to lower the risk of ICH (intracerebral haemorrhage) and ensure successful vessel recanalization. It is demonstrated that the computational model developed in this study can be used to investigate clot dissolution in patient-specific geometries. Future work will attempt to test the use of this computational model in clinical settings and as an aid in the development of new therapies. Open Access

Personalised external aortic root support (PEARS) was designed to prevent progressive aortic dilatation, and the associated risk of aortic dissection, in patients with Marfan syndrome by providing an additional support to the aorta. The objective of this thesis was to understand the biomechanical implications of PEARS surgery as well as to investigate the altered haemodynamics associated with the disease and its treatment. Finite element (FE) models were developed using patient-specific aortic geometries reconstructed from pre and post-PEARS magnetic resonance (MR) images of three Marfan patients. The wall and PEARS materials were assumed to be isotropic, incompressible and linearly elastic. A static load on the inner wall corresponding to the patients’ pulse pressure was applied with a zero-displacement constraint at all boundaries. Results showed that peak aortic stresses and displacements before PEARS were located at the sinuses of Valsalva but following PEARS surgery, they were shifted to the aortic arch, at the intersection between the supported and unsupported aorta. The zero-displacement constraint at the aortic root was subsequently removed and replaced with downward motion measured from in vivo images. This revealed significant increases in the longitudinal wall stress, especially in the pre-PEARS models. Computational fluid dynamics (CFD) models were developed to evaluate flow characteristics. The correlation-based transitional Shear Stress Transport (SST-Tran) model was adopted to simulate potential transitional and turbulence flow during part of the cardiac cycle and flow waveforms derived from phase-contrast MR images were imposed at the inlets. Qualitative patterns of the haemodynamics were similar pre- and post-PEARS with variations in mean helicity flow index (HFI) of -10%, 35% and 20% in the post-PEARS aortas of the three patients. A fluid-structure interaction (FSI) model was developed for one patient, pre- and post-PEARS in order to examine the effect of wall compliance on aortic flow as well as the effect of pulsatile flow on wall stress. This model excluded the sinuses and was based on the laminar flow assumption. The results were similar to those obtained using the rigid wall and static structural models, with minor quantitative differences. Considering the higher computational cost of FSI simulations and the relatively small differences observed in peak wall stress, it is reasonable to suggest that static structural models would be sufficient for wall stress prediction. Additionally, aortic root motion had a more profound effect on wall stress than wall compliance. Further studies are required to assess the statistical significance of the findings outlined in this thesis. Recommendations for future work were also highlighted, with emphasis on model assumptions including material properties, residual stress and boundary conditions. Open Access

Stroke is the third biggest killer and the leading cause of severe disability in the UK. The most common type of stroke is known as an ischaemic stroke in which blood vessels in the brain become blocked, most often as a result of rupture of atherosclerotic plaques formed in the carotid arteries, especially at the bifurcation and in the entrance to the internal carotid artery which feeds the cerebral circulation. The carotid arteries can be examined through ultrasound scans, which provide images of the vessel allowing assessment of the severity of carotid disease. In this project, ultrasound images of carotid arteries acquired from patients with varying degrees of carotid disease are analysed and computational models are built to predict the mechanical stresses within carotid arteries with or without atherosclerosis. Ultrasound imaging was chosen owing to its non-invasive nature and wide availability. Work presented in this thesis follows a logical progression. First, image analysis tools are developed and presented in Chapter 3. Based on the processed ultrasound images, finite element models of carotid arteries are constructed and biomechanical analyses of varying degrees of complexity are carried out. In Chapter 4, the carotid artery is assumed as an elastic material, and comparisons are made between 2-D and 3-D models based on idealised geometry. In an attempt to improve the predictive ability of the model and achieve better understanding of disease progression, the viscoelastic behaviour of the carotid vessel wall is taken into account, and detailed analyses of the effect of vessel wall viscosity and hysteresis are presented in Chapter 5. Methods used to derive subject-specific viscoelastic material properties from in vivo pressure-diameter data are also described. Finally, in order to understand the effect of interaction between the viscoelastic vessel wall and blood flow in carotid arteries, fully coupled fluid-structure interaction (FSI) models are developed, and the FSI model as well as its validation are presented in Chapter 6. Work reported in this thesis has shown that by combining ultrasound measurement with computational analysis, it is possible to provide additional information that will aid clinicians in their diagnosis and decision making. Carotid biomechanical analysis can be carried out with subject-specific information, such as viscoelastic wall properties and geometry, derived from in vivo data acquired non-invasively. The ultrasound-image based modelling approach developed in this thesis will also help improve our understanding of the role of vessel wall motion in the development and progression of carotid diseases. Open Access

The presence of disease in the cardiovascular system results in changes in flow and pressure patterns. Increased resistance to the flow observed in cases of aortic valve and coronary artery disease can have as a consequence abnormally high pressure gradients, which may lead to overexertion of the heart muscle, limited tissue perfusion and tissue damage. In the past, computational fluid dynamics (CFD) methods have been used coupled with medical imaging data to study haemodynamics, and it has been shown that CFD has great potential as a way to study patient-specific cases of cardiovascular disease in vivo, non-invasively, in great detail and at low cost. CFD can be particularly useful in evaluating the effectiveness of new diagnostic and treatment techniques, especially at early ‘concept’ stages. The main aim of this thesis is to use CFD to investigate the relationship between pressure and flow in cases of disease in the coronary arteries and the aortic valve, with the purpose of helping improve diagnosis and treatment, respectively. A transitional flow CFD model is used to investigate the phenomenon of pressure recovery in idealised models of aortic valve stenosis. Energy lost as turbulence in the wake of a diseased valve hinders pressure recovery, which occurs naturally when no energy losses are observed. A “concept” study testing the potential of a device that could maximise pressure recovery to reduce the pressure load on the heart muscle was conducted. The results indicate that, under certain conditions, such a device could prove useful. Fully patient-specific CFD studies of the coronary arteries are fewer than studies in larger vessels, mostly due to past limitations in the imaging and velocity data quality. A new method to reconstruct coronary anatomy from optical coherence tomography (OCT) data is presented in the thesis. The resulting models were combined with invasively acquired pressure and flow velocity data in transient CFD simulations, in order to test the ability of CFD to match the invasively measured pressure drop. A positive correlation and no bias were found between the calculated and measured results. The use of lower resolution reconstruction methods resulted in no correlation between the calculated and measured results, highlighting the importance of anatomical accuracy in the effectiveness of the CFD model. However, it was considered imperative that the limitations of CFD in predicting pressure gradients be further explored. It was found that the CFD-derived pressure drop is sensitive to changes in the volumetric flow rate, while bench-top experiments showed that the estimation of volumetric flow rate from invasively measured velocity data is subject to errors and uncertainties that may have a random effect on the CFD pressure result. This study demonstrated that the relationship between geometry, pressure and flow can be used to evaluate new diagnostic and treatment methods. In the case of aortic stenosis, further experimental work is required to turn the concept of a pressure recovery device into a potential clinical tool. In the coronary study it was shown that, though CFD has great power as a study tool, its limitations, especially those pertaining to the volumetric flow rate boundary condition, must be further studied and become fully understood before CFD can be reliably used to aid diagnosis in clinical practice. Open Access

One of the clinical challenges in the treatment of diseases with a discrete distribution is the local delivery of active drugs without causing systemic side effects. Doxorubicin, an anti-cancer drug, is an example that may cause damage to patients due to its interaction with normal cells. Tissue plasminogen activator (tPA) is another active agent whose effectiveness is compromised due to its unselective effect on both healthy and pathological blood clots. Thermal sensitive liposome is a drug carrier that is not only able to entrap drug into it hydrophilic interior but can also release encapsulated agents upon mild hyperthermia. Currently, lysolipid-containing thermal sensitive liposome (LTSL) is a standard formulation due to its rapid release behaviour. However, concerns have been raised regarding the negative effect of lysolipid on LTSL stability that results in undesirable leakage of encapsulated drug in vivo at physiological temperature. Therefore, the first aim of the project was to develop a lysolipid-free thermal sensitive liposome (TSL) formulation. For this purpose, doxorubicin was adopted as a model drug. The amount of doxorubicin molecules encapsulated in TSL (0.0123 mg of doxorubicin per 1 mg of lipid) was 2 times the amount in the existing publications (0.05 mg of doxorubicin per 1 mg of lipid ). This was done by optimizing the incubation temperature (36oC for 1 hour) during preparation of TSL. When heated from room temperature to 42 oC, doxorubicin-encapsulated-TSLs release encapsulated doxorubicin molecules faster than their LTSL counterpart. This may result from a higher membrane-bound doxorubicin concentration in dox-TSLs. The second objective of the project was to develop a tPA-encapsulated TSL (tPA-TSL) formulation that can release encapsulated tPA molecules under hyperthermia condition. It has been demonstrated that the developed tPA-TSL was able to release encapsulated tPA upon 7 minute heating at 45oC. The release of tPA molecules was expected to result from irreversible destruction of liposome upon heating, as was demonstrated by reduction of particle size. Open Access

Effective delivery of therapeutic agents to tumour cells is essential to the success of most cancer treatment therapies except for surgery. The transport of drug in solid tumour involves multiple biophysical and biochemical processes which are strongly dependent on the physicochemical properties of the drug and biological properties of the tumour. Owing to the complexities involved, mathematical models are playing an increasingly important role in identifying the factors leading to inadequate drug delivery to tumours. In this study, a computational model is developed which incorporates real tumour geometry reconstructed from magnetic resonance images, drug transport through the tumour vasculature and interstitial space, as well as drug uptake by tumour cells. The effectiveness of anticancer therapy is evaluated based on the percentage of survival tumour cells by directly solving the corresponding pharmacodynamics equation using predicted intracellular drug concentration. Computational simulations have been performed for the delivery of doxorubicin through various delivery modes, including bolus injection and continuous infusion of doxorubicin in free form, and thermo-sensitive liposome mediated doxorubicin delivery activated by high intensity focused ultrasound. Predicted results show that continuous infusion is far more effective than bolus injection in maintaining high levels of intracellular drug concentration, thereby increasing drug uptake by tumour cells. Moreover, multiple-administration is found to be more effective in improving the cytotoxic effect of drug compared to a single administration. The effect of heterogeneous distribution of microvasculature on drug transport in a realistic model of liver tumour is investigated, and the results indicate that although tumour interstitial fluid pressure is almost uniform, drug concentration is sensitive to the heterogeneous distribution of microvasculature within a tumour. Results from three prostate tumours of different sizes suggest a nonlinear relationship between transvascular transport of anticancer drugs and tumour size. Numerical simulations of thermo-sensitive liposome-mediated drug delivery coupled with high intensity focused ultrasound heating demonstrate the potential advantage of this novel drug delivery system for localised treatment while minimising drug concentration in normal tissue. Open Access

Slug flow is one of the most common flow patterns in multiphase oil/gas transport in pipelines. Due to its complexity, it poses numerous challenges to model development. Industrial slug flow models are one-dimensional and can give poor predictions in situations where the associated closures and simplifications are no longer valid. Computational Fluid Dynamics (CFD) facilitates high-resolution studies of slug flow dynamics by implementing multi-dimensional models. Understanding the physics of slug flow would help identify the main flow mechanisms to be modelled and enable the development of mechanistic slug flow models for commercial software. In this thesis, a computational approach is developed. The front tracking method (FTM) (Tryggvason et al. 2001) and the phase field method (PFM) (Ding et al. 2007) are used to model long bubbles in slug flows. Results of the validation study show good agreement with DeBisschop et al. (2002), who performed simulations of long bubbles in two-dimensional channels in the creeping-flow limit. Their work is extended here to moderate Archimedes numbers (10 < Ar < 200). The effects of inertia, surface tension, viscosity and inclination angle on the terminal velocity and the shape of a long bubble in different flow conditions are investigated. Furthermore, the FTM is coupled with a discrete bubble tracking method (DBTM), which has resulted in a robust hybrid method to model small and large bubbles simultaneously in an Eulerian-Lagrangian fashion. The method allows the study of the interaction of the small bubbles with a long bubble. The work is extended further to three dimensions using the PFM. The validation study shows good agreement with the present two-dimensional numerical work. The geometry is converted from a square channel to a pipe to facilitate a more realistic simulation of slug flow in pipelines. This work will provide a rigorous basis for developing simplified models. Open Access

A conventional 2D (two-dimensional) culture, in T-flasks or multi-well plates, is commonly perfo med for the stem cell development; however, it is time and labour consuming process. Moreover, it is impractical to scale-up to high cell number production. Growing stem cells inside bioreactor might be a solution. 3D bioreactor is not only a solution for scalable production but also a mimic environment for in vivo system. Herein, sparged-type bioreactors (e.g. airlift bioreactor) were chosen as bioreactors to differentiate murine embryonic stem cells (mESCs) into type II pneumocytes in the lung. There are two main sections in this thesis: the design of airlift bioreactor using computational fluid dynamics (CFD) and the differentiation of mESCs into the alveolar progenitor cells in a sparged bioreactor. The airlift bioreactors provide a better environment, which theoretically has been known to simulate the gas-exchange interface encountered in the lung alveoli. They require a low power input and provide a low shear environment with good mixing. The hydrodynamics (gas holdup, superficial liquid velocity, and shear rate) and mass transfer (kLa, the volumetric mass transfer coefficient) features of different airlift designs were determined by CFD. The simulations were based on a 3D transient model, Eulerian-Eulerian approach, and two-phase liquid/gas model with all phases being treated as laminar flow. The superficial gas velocity was varied from 0.001 m/s to 0.02 m/s. The simulation results indicated that the hydrodynamics were corresponded to the data found in literatures and the gas holdup were agreed with an experiment validation. The CFD results also suggested that in which range of superficial gas velocity (ug) that the system can be operated without any fluctuation in terms of the hydrodynamics. In addition, the airlift bioreactor is suitable for shear sensitive cells with high mass transfer rate, e.g. kLa, = 180 hr-1 at ug= 0.01 m/s and normoxia (20% O2) condition. Hence, the results from these simulations have been initially utilised as a promising hypothesis to design an airlift bioreactor for the scalable and automatable culture in multiphase bioreactors. For the second part, mESCs were encapsulated in a calcium-alginate hydrogel to create a 3D environment then the encapsulated cells weregrown in both 3D static culture, in a T-flasks, and the sparged bioreactor. The gas, 5% CO2 and 20% O2, was directly sparged into the bioreactor. The A549 conditioned medium was used to induced the mESCs to the endodermal lineages, targeting for the alveolar type II cells, type II pneumocytes. The differentiated cells expressed lung cell markers: SPC (pneumocyte type II), and FoxA2 (endoderm marker). In experiments, the relative expression of SPC markers reached the maximum level, 10-fold increase, at day 14 and day 20 for 3D static culture and the sparged bioreactor, respectively. After day 20 of the differentiation process, the pneumocyte-like cells in static culture trend to lose their SPC expression whereas the cells in sparged bioreactor maintain relatively high SPC markers. At the end of a differentiation protocol, day 30, it was observed that both systems highly expressed the endodermal makers, FoxA2, i.e. approximately 2000-fold increase for static culture and 5000-fold increase for the sparged bioreactor. In conclusion, the direct gassing in the sparged bioreactor not only enhanced the differentiation of embryonic stem cells into type II pneumocytes but also mimicked the in vivo environment in the lung therefore the differentiated cells can maintain the lung phenotype for a long term culture, up to 5 weeks in vitro culture. This in vitro system would be beneficial for drug screening and regenerative medicine applications. Open Access

Deep Vein Thrombosis is a common complication in bed-ridden patients, described as the main cause of preventable hospital deaths in the UK (NICE 2010). Mechanical prophylaxis aims to promote venous flow, either statically with compression stockings, or dynamically with intermittent pneumatic compression or electrical muscle stimulation. Previous studies used ultrasound for venous flow measurements, limited to a single deep vein at a time, and some anatomical MRI for investigating the mechanisms behind these prophylaxes. MRI velocity mapping is used clinically in the arterial system where gating enables data accumulation over multiple cardiac cycles. This thesis describes the development of two real-time MRI spiral velocity mapping sequences for imaging venous blood flow in the leg, where venous flow variability is largely unrelated to the cardiac cycle. Real-time imaging with spiral gradient readouts minimised image duration. A phase-image fitting technique requiring only a velocity-encoded phase image was implemented for acceleration. For in vivo comparison, conventional flow imaging required metronome-guided breathing for a regular venous flow waveform. The long spiral readouts were sensitive to off-resonance and flow artefacts, where some unpublished effects were investigated. The off-resonance associated with deoxygenation of venous blood did not cause notable spiral artefacts, but disrupted the phase-image fitting technique and required correction with a pre-scan. The spiral flow methods demonstrated increased venous blood velocity and flow during application of mechanical compression. Metronome-guided breathing was also applied to vein wall imaging, where it detected wall thickening in patients with Behçet’s disease compared with normal subjects. For the first time, this thesis evaluated real-time MRI spiral velocity mapping of venous blood velocity and flow. The high resolution (1mm) and short image time required caused challenging off-resonance and flow artefacts. With some limitations, real-time spiral flow MRI during operation of compression devices may assist in their optimisation.

Atherosclerosis is a major cause of morbidity and mortality in the western world. The focal depletion of oxygen and accumulation of macromolecules are believed to initiate, accelerate and complicate the development of atherosclerosis. However, species concentrations in vessel walls are difficult to measure in vivo non-invasively. Therefore, it is essential to obtain detailed concentration profiles of atherogenic molecules to gain further understanding of the mass transfer mechanisms within arterial walls. In the present study, comprehensive mathematical models describing species transport in large arteries are developed and presented. Existing mathematical models are reviewed and reconciled. A fluid phase model, a single-layered and a multilayered fluid-wall models are employed to simulate the mass transfer processes in proatherosclerotic arteries. Since trans-endothelial transport is considered to be an important sub-process in the system and is dependent on wall shear stress (WSS) imposed on the endothelial surface, shear-dependent transport properties are derived from relevant experimental data in the literature. A novel approach, which exploits the optimisation theory, is proposed and used to determine model parameters based on the experimental data. Furthermore, numerical schemes to accommodate the effects of pulsatile flow on lipid transport in the arterial wall are presented in the thesis. Mathematical models and numerical schemes are tested and compared using idealised computational geometries. Then the models are applied to realistic geometries to investigate: 1) oxygen transport in a normal human abdominal aorta and an abdominal aortic aneurysm (AAA) with intralumenal thrombus (ILT); 2) macromolecular transport in a mildly stenosed human right coronary artery (RCA). Based on the model predictions, mechanisms inducing hypoxia and macromolecular accumulation are discussed in depth.