Indiana University-Purdue University Indianapolis (IUPUI) / Glaucoma is a multifactorial ocular disease progressively leading to irreversible blindness. There is clear evidence of correlations between alterations in ocular hemodynamics and glaucoma; however, the mechanisms giving rise to these correlations are still elusive. The objective of this thesis is to develop mathematical models and methods to help elucidate these mechanisms. First, we develop a mathematical model that describes the deformation of ocular structures and ocular blood flow using a reduced-order fluid-structure interaction model. This model is used to investigate the relevance of mechanical and vascular factors in glaucoma. As a first step in expanding this model to higher dimensions, we propose a novel energy-based technique for coupling partial and ordinary differential equations in blood flow, using operator splitting. Next, we combine clinical data and model predictions to propose possible explanations for the increase in venous oxygen saturation in advanced glaucoma patients. We develop a computer-aided manipulation process of color Doppler images to extract novel waveform parameters to distinguish between healthy and glaucomatous individuals. The results obtained in this work suggest that: 1) the increase in resistance of the retinal microcirculation contributes to the influence of intraocular pressure on retinal hemodynamics; 2) the influence of cerebrospinal fluid pressure on retinal hemodynamics is mediated by associated changes in blood pressure; 3) the increase in venous oxygen saturation levels observed among advanced glaucoma patients depends on the value of the patients’ intraocular pressure; 4) the normalized distance between the ascending and descending limb of the ophthalmic artery velocity profile is significantly higher in glaucoma patients than in healthy individuals.

L'anévrisme de l'aorte abdominale est une pathologie devant être traitée par chirurgie quand son diamètre atteint 5.5cm, en raison d’un risque de rupture qui est souvent mortelle. La chirurgie endovasculaire consiste à déployer une endoprothèse dans l’anévrisme pour l’exclure de la circulation sanguine. Cette chirurgie souffre cependant d'un taux relativement élevé de complications post-opératoires à long terme, nécessitant des interventions coûteuses. Ces complications sont principalement d’origine mécanique et pourraient être anticipées grâce à la simulation numérique.Cette thèse a pour objectif d'élaborer une méthodologie de simulation personnalisée de déploiement d'endoprothèses dans des anévrismes, dans le but final de fournir un outil d'aide à la décision aux praticiens hospitaliers pour améliorer leur planning pré-opératoire.Une méthodologie permettant de déployer numériquement des endoprothèses bifurquées, composées de plusieurs modules, dans des anévrismes aortiques personnalisés, de géométries quelconques, a été conçue. Des simulations numériques ont été effectuées sur cinq cas cliniques réels, dont des cas fortement tortueux et complexes àplanifier pour les praticiens hospitaliers. La méthodologie a été validée par comparaison des résultats numériques avec la position des stents sur les scanners post-opératoires.La capacité de la méthodologie numérique à simuler le déploiement d’endoprothèses dans des géométries personnalisées d’anévrismes aortiques a été démontrée. Ces simulations possèdent un fort potentiel, en pouvant permettre de mieux adapter les endoprothèses aux patients et d’anticiper les complications post-opératoires dès le planning pré-opératoire. / Abdominal aortic aneurysm is a pathology which needs to be treated by surgery when its diameter reaches 5.5cm, due to high risk of rupture that is often lethal. Endovascular repair consists in deploying a stent-graft inside the aneurysmal sac to exclude it from the blood flow. However, the drawback of this surgery is the relatively important post-operative complication rate at long-term, requiring costly secondary interventions. The origin of these complications is mainly related to mechanics and therefore, they could be prevented thanks to numerical simulation.The objective of this thesis is to elaborate a simulation methodology to deploy in silico stent-grafts in patient-specific aneurysms. The ultimate goal is to provide practioners with a computer aided decision tool to improve their pre-operative planning.A methodology was developed to simulate the deployment of bifurcated stent-grafts, composed of several modules, in patient-specific aortic aneurysms, whatever their geometry. Finite-element analyses were performed on several clinical cases from real patients, some of them which were highly tortuous and complex for practioners to achieve an accurate preoperative planning. The methodology was validated by comparing numerical results with the position of the stents in the post-operative scans.The ability of finite-element analyses to simulate stent-graft deployment in patient-specific aortic aneurysm geometries was proved in this thesis. Simulations have great potential for adapting stent-grafts to each patient and for anticipating possible post-operative complications at the stage of pre-operative planning.