Severe stenosis may cause critical flow conditions related to artery collapse, plaque cap rupture which leads directly to stroke and heart attack. In this paper, a nonlinear viscoelastic model and a numerical method are introduced to study dynamic behaviors of the tube wall and viscous flow through a viscoelastic tube with a stenosis simulating blood flow in human carotid arteries. The Mooney-Rivlin material model is used to derive a nonlinear viscoelastic thin-wall model for the stenotic viscoelastic tube wall. The mechanical parameters in the Mooney-Rivlin model are calculated from experimental measurements. Incompressible Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation are used as the governing equation for the fluid flow. Interactions between fluid flow and the viscoelastic axisymmetric tube wall are handled by an incremental boundary iteration method. A Generalized Finite Differences Method (GFD) is used to solve the fluid model. The Fourth-Order Runge-Kutta method is used to deal with the viscoelastic wall model where the viscoelastic parameter is adjusted to match experimental measurements. Our result shows that viscoelasticity of tube wall causes considerable phase lag between the tube radius and input pressure. Severe stenosis causes cyclic pressure changes at the throat of the stenosis, cyclic tube compression and expansions, and shear stress change directions in the region just distal to stenosis under unsteady conditions. Results from our nonlinear viscoelastic wall model are compared with results from previous elastic wall model and experimental data. Clear improvements of our viscoelastic model over previous elastic model were found in simulating the phase lag between the pressure and wall motion as observed in experiments. Numerical solutions are compared with both stationary and dynamic experimental results. Mooney-Rivlin model with proper parameters fits the non-linear experimental stress-strain relationship of wall very well. The phase lags of tube wall motion, flow rate variations with respect to the imposed pulsating pressure are simulated well by choosing the viscoelastic parameter properly. Agreement between numerical results and experimental results is improved over the previous elastic model.

Cervical stenotic myelopathy (CSM) is an important musculoskeletal and neurologic disease of the horse. Clinical disease occurs due to malformations of the vertebrae in the neck causing stenosis of the cervical vertebral canal and subsequent spinal cord compression. The disease is multifactorial in nature, therefore a clearer understanding of the etiology and pathogenesis of CSM will allow for improved management and therapeutic practices. This thesis examines issues of equine CSM diagnosis, skeletal tissue pathology, and inherited genetic determinants utilizing advances in biomedical imaging technologies and equine genomics. Magnetic resonance imaging (MRI) data provided a more complete assessment of the cervical column through image acquisition in multiple planes. First, MRI was compared to standing cervical radiographs for detection of stenosis. Using canal area or the cord canal area ratio, MRI more accurately predicted sites of compression in CSM cases. Secondly, articular process skeletal pathology localized on MRI was found to be more frequent and severe in CSM horses compared to controls. In addition, lesions were generalized throughout the cervical column and not limited to the spinal cord compression sites. A subset of lesions identified on MRI was evaluated using micro-CT and histopathology. Osteochondrosis, osseous cyst-like structures, fibrous tissue replacement of bone, and osteosclerosis were observed. These lesions support likely developmental aberrations of vertebral bone and cartilage maturation with secondary biomechanical influences. Bone cyst-like structures are a novel finding in this disease. Finally, the long-standing question of the contribution of genetic determinants to CSM was investigated using a genome wide association study (GWAS). Multiple significant loci were identified supporting the influence of a complex genetic trait in clinical disease. A simple Mendelian trait controlled by one gene is unlikely given the detection of variants across multiple chromosomes. Major contributions from this research include documentation of articular process bone and cartilage pathology in horses with CSM, support for abnormal cervical vertebrae development being an important contributing factor in the etiology and/or pathogenesis of equine CSM, and evidence that multiple genetic loci contribute to the CSM disease phenotype.

While computed tomographic angiography (CTA) has emerged as a powerful noninvasive option that allows for direct visualization of arterial stenosis(AS), it cant assess the hemodynamic abnormality caused by an AS. Alternatively, trans-stenotic pressure gradient (TSPG) and fractional flow reserve (FFR) are well-validated hemodynamic indices to assess the ischemic severity of an AS. However, they have significant restriction in practice due to invasiveness and high cost. To fill the gap, a new computational modality, called <i>InVascular</i> has been developed for non-invasive quantification TSPG and/or FFR based on patient's CTA, aiming to quantify the hemodynamic abnormality of the stenosis and help to assess the therapeutic/surgical benefits of treatment for the patient. Such a new capability gives rise to a potential of computation aided diagnostics and therapeutics in a patient-specific environment for ASs, which is expected to contribute to precision planning for cardiovascular disease treatment. <i>InVascular</i> integrates a computational modeling of diseases arteries based on CTA and Doppler ultrasonography data, with cutting-edge Graphic Processing Unit (GPU) parallel-computing technology. Revolutionary fast computing speed enables noninvasive quantification of TSPG and/or FFR for an AS within a clinic permissible time frame. In this work, we focus on the implementation of inlet and outlet boundary condition (BC) based on physiological image date and and 3-element Windkessel model as well as lumped parameter network in volumetric lattice Boltzmann method. The application study in real human coronary and renal arterial system demonstrates the reliability of the in vivo pressure quantification through the comparisons of pressure waves between noninvasive computational and invasive measurement. In addition, parametrization of worsening renal arterial stenosis (RAS) and coronary arterial stenosis (CAS) characterized by volumetric lumen reduction (S) enables establishing the correlation between TSPG/FFR and S, from which the ischemic severity of the AS (mild, moderate, or severe) can be identified. In this study, we quantify TSPG and/or FFR for five patient cases with visualized stenosis in coronary and renal arteries and compare the non-invasive computational results with invasive measurement through catheterization. The ischemic severity of each AS is predicted. The results of this study demonstrate the reliability and clinical applicability of <i>InVascular</i>.

1 Abstract: Time-dependent and three-dimensional flow of Newtonian fluid is studied in context of two biomechanical applications, flow in cerebral aneurysms and flow in stenotic valves. In the first part of the thesis, the computational meshes obtained from the medical imaging techniques are used for the computation of hemodynamic parameters associated with the rupture potency of the cerebral aneurysms. The main result is the computation within twenty geometries of aneurysms. It is shown that the aneurysm size has more important role in wall shear stress distribution than the fact whether the aneurysm is ruptured or unruptured. The second part of the thesis is addressed to the flow in stenotic valves. It is shown that the method cur- rently used in medical practice is based on assumptions which are too restrictive to be apply to blood flow in the real case. The full continuum mechanics model is presented with physiologically relevant boundary conditions and it is shown that results are consistent with measured data obtained from literature. Then we focus on the obtaining the pressure field from the velocity field. The presented method provides more accurate pressure approximation than commonly used Pressure Poisson Equation. The last chapter of the thesis is dedicated to Nitsche's method for treating slip boundary...

Comprendre, prédire et finalement retarder la transition vers la turbulence dans les écoulements sont d'importants problèmes posés aux scientifiques depuis les travaux pionniers d'Osborne Reynolds en 1883. Ces questions ont été principalement adressées à l'aide de la théorie des instabilités hydrodynamiques. A cause des ressources informatiques limitées, les analyses de stabilité linéaire reposent essentiellement sur d'importantes hypothèses simplificatrices telles que celle d'un écoulement parallèle. Dans ce cadre, connu sous le nom de stabilité locale, seule la stabilité d'écoulement ayant un fort intérêt académique mais relativement peu d'applications pratiques a pu être étudiée. Néanmoins, au cours de la décennie passée, l'hypothèse d'écoulement parallèle a été relaxée au profit de celle d'un écoulement bidimensionnel conduisant alors à ce que l'on appelle la stabilité globale. Ce nouveau cadre permet alors d'étudier les mécanismes d'instabilité et de transition ayant lieu au sein d'écoulements plus réalistes. Plus particulièrement, la stabilité d'écoulements fortement non-parallèles pouvant présenter des décollements massifs, une caractéristique fréquente dans les écoulements d'intérêt industriel, peut maintenant être étudiée. De plus, avec l'accroissement constant des moyens de calcul et le développement de nouveaux algorithmes de recherche de valeurs propres itératifs, il est aujourd'hui possible d'étudier la stabilité d'écoulements pleinement tridimensionnels pour lesquels aucune hypothèse simplificatrice n'est alors nécessaire. Dans la continuité des travaux présentés par Bagheri et al. en 2008, le but de la présente thèse est de développer les outils nécessaires à l'analyse de la stabilité d'écoulements 3D. Trois écoulements ont été choisis afin d'illustrer les nouvelles capacités de compréhension apportées par l'analyse de la stabilité globale appliquée à des écoulements tridimensionnels réels : i) l'écoulement au sein d'une cavité entraînée 3D, ii) l'écoulement se développant dans un tuyau sténosé, et enfin iii) l'écoulement de couche limite se développant au passage d'une rugosité cylindrique montée sur une plaque plane. Chacun de ces écoulements a différentes applications pratiques allant d'un intérêt purement académique à une application biomédicale et aérodynamique. Ce choix d'écoulements nous permet également d'illustrer les différents aspects des outils développés au cours de cette thèse ainsi que les limitations qui leur sont inhérentes. / Understanding, predicting and eventually delaying transition to turbulence in fluid flows have been challenging issues for scientists ever since the pioneering work of Osborne Reynolds in 1883. These problems have mostly been addressed using the hydrodynamic linear stability theory. Yet, due to limited computational resources, linear stability analyses have essentially relied until recently on strong simplification hypotheses such as the “parallel flow” assumption. In this framework, known as “local stability theory”, only the stability of flows with strong academic interest but limited practical applications can be investigated. However, over the course of the past decade, simplification hypotheses have been relaxed from the “parallel flow” assumption to a two-dimensionality assumption of the flow resulting in what is now known as the “global stability theory”. This new framework allows one to investigate the instability and transition mechanisms taking place in more realistic flows. More particularly, the stability of strongly non-parallel flows exhibiting separation, a common feature of numerous flows of practical interest, can now be studied. Moreover, with the continuous increase of computational power available and the development of new iterative eigenvalue algorithms, investigating the global stability of fully three-dimensional flows, for which no simplification hypothesis is necessary, is now feasible. Following the work presented in 2008 by Bagheri et al., the aim of the present thesis is thus to develop the tools mandatory to investigate the stability of 3D flows. Three flow configurations have been chosen to illustrate the new investigation capabilities brought by global stability theory when it is applied to realistic three-dimensional flows: i) the flow within a cuboid lid-driven cavity, ii) the flow within an asymmetric stenotic pipe and iii) the boundary layer flow developing over a cylindrical roughness element mounted on a flat plate. Each of these flows have different practical applications ranging from purely academic interests to biomedical and aerodynamical applications. They also allow us to put in the limelight different aspects and possible limitations of the various tools developed during this PhD thesis.

Die Magnetresonanztomographie (MRT), die Mehrschicht-Spiral-Computertomographie (MSCT) und die Elektronenstrahl-Computertomographie (EBCT) sind nichtinvasive diagnostische Verfahren, welche die bisherige kardiale Bildgebung zumindest in Teilbereichen ersetzen oder ergänzen können. MR-Perfusions- und MR-Funktionsuntersuchungen konnten in der vorgelegten Arbeit direkte Parameter der myokardialen Vitalität regional erfassen. Die Signalintensitäten im Blut und im Herzmuskel dienten zur quantitativen Bestimmung der Myokardperfusion. Die Ortsauflösung ermöglichte eine Differenzierung der subendo- und der subepikardialen Durchblutung. Zusätzliche Streßuntersuchungen steigerten die Sensitivität des Verfahrens. Relativ geringgradige Koronarstenosen ließen sich durch vornehmlich subendokardial lokalisierte Perfusionsdefekte nachweisen. MR-Tagging- Funktionsanalysen konnten durch ein artifizielles Markierungsgitter zwischen endokardial lokalisiertem Narbengewebe und epikardial liegendem vitalem Gewebe differenzieren. Die Dehnungen, Stauchungen und Rotationen des Myokardverbandes wurden registriert und ausgewertet. Die MSCT und die EBCT wurden als Röntgenverfahren für die nichtinvasive Koronarangiographie verglichen. Bei der Definition der Gefäßkonturschärfe über die Anstiegssteilheit der CT-Dichtewerte zeigte sich eine bessere Abbildungsqualität der MSCT gegenüber der EBCT. Die Bestimmung der Segmenterkennbarkeit zeigte, dass mit der MSCT signifikant mehr erkannt werden konnten. Die vorgestellten kardialen MR- und CT-Untersuchungen konnten aus Gründen der Reproduzierbarkeit sowie aufgrund des Strahlenschutzes nur tierexperimentell durchgeführt werden. Die Validität der unterschiedlichen Tiermodelle ist in vorausgegangenen Studien belegt worden. Die in der Literatur verfügbaren Ergebnisse am Menschen bestätigen in vieler Weise die vorgelegten Daten. / Magnetic resonance imaging (MRI), multislice spiral computed tomography (MSCT), and electron-beam computed tomography (EBCT) are noninvasive imaging modalities that may supplement or in part even replace established diagnostic procedures for assessment of the heart. MRI perfusion and functional studies were shown to enable determination of direct parameters of regional myocardial vitality. The signal intensities of blood and myocardium served to quantify myocardial perfusion. The spatial resolution allowed for differentiating subendocardial and subepicardial perfusion. Additional stress tests improved the sensitivity of the procedure. Relatively low-grade coronary artery stenoses were identified by the presence of perfusion gaps primarily in subendocardial location. Functional analysis by means of MRI tagging using an artificial grid allowed for differentiating endocardial scar tissue from epicardial vital tissue. Extension, compression, and rotation of the myocardial complex were recorded and analyzed. MSCT and EBCT were compared as radiographic procedures for noninvasive coronary angiography. MSCT was found to be superior to EBCT in terms of image quality defined as vascular contour sharpness determined as the steepness of the increase in CT densities. Assessment of segment identification showed that significantly more segments were visualized by MSCT. The cardiac MRI and CT studies presented here could only be performed in animals because of the radiation exposure involved and to ensure reproducibility of the results. The validity of the different animal models used has been demonstrated in preceding studies. The results of the present animal experiments are in agreement with many of the human data published in the literature.