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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>.

L'objectif de cette thèse est la modélisation mathématique des mécanismes de contraction musculaire à l'échelle microscopique dans le but de proposer et d'intégrer ces modèles dans un environnement de simulation cardiaque multi-échelle.Ce travail est réalisé dans le contexte de la médecine numérique, qui propose d'améliorer le traitement des patients par l'utilisation d'outils numériques.La première contribution de cette thèse est une analyse bibliographique des travaux expérimentaux caractérisant l’interaction actine-myosine et ses régulations afin de compiler les informations sous une forme utilisable pour le développement de modèles.Cette étape est une condition préalable essentielle à la modélisation.Nous proposons ensuite une hiérarchie de modèles de contraction musculaire à partir d'un modèle stochastique raffiné existant, mais validé uniquement pour les muscles squelettiques, en appliquant des hypothèses de simplification successives.Les étapes de simplification transforment l'équation différentielle stochastique initiale en une équation aux dérivées partielles avec une description qui fait partie de la famille de modèles dérivée du modèle Huxley'57.Une simplification supplémentaire conduit ensuite à un modèle décrit par un ensemble d'équations différentielles ordinaires.La pertinence des modèles proposés, qui ciblent différentes échelles de temps, est démontrée en les comparant aux données expérimentales obtenues avec des muscles cardiaques, et leur domaine de validité est étudié.Pour intégrer ces descriptions dans un environnement de simulation cardiaque, nous avons étendu ces modèles afin de prendre en compte les mécanismes de régulation de la force qui se produisent in vivo.Cela conduit à de nouvelles équations aux dérivées partielles.Ensuite, nous lions les modèles de contraction microscopiques à un modèle d’organe macroscopique.Nous suivons pour cela une approche fondée sur les principes thermodynamiques pour traiter la nature multi-échelle en temps et en espace du tissu musculaire aux niveaux continu et discret.La validité de cet environnement de simulation est démontrée en présentant sa capacité à reproduire le comportement du coeur et en particulier les caractéristiques essentielles de l'effet Frank-Starling. / This PhD thesis deals with the mathematical description of the micro-scale muscle contraction mechanisms with the aim of proposing and integrating our models into a multiscale heart simulation framework.This research effort is made in the context of digital medicine, which proposes to improve the treatment of patients with the use of numerical tools.The first contribution of this thesis is a literature review of the experimental works characterizing the actin-myosin interaction and its regulations to compile information in a useable form for the development of models.This stage is an essential prerequisite to modeling.We then propose a hierarchy of muscle contraction models starting from a previously proposed refined stochastic model, which was only validated for skeletal muscles, and applying successive simplification assumptions.The simplification stages transform the initial stochastic differential equation into a partial differential equation with a model that is part of the Huxley'57 model family.A further simplification then leads to a description governed by a set of ordinary differential equations.The relevance of these models, targeting different time scales, is demonstrated by comparing them with experimental data obtained with cardiac muscles and their range of validity is investigated.To integrate these microscopic descriptions into a heart simulation framework, we extend the models to take into account the force regulation mechanisms that take place in vivo, leading to the derivation of new partial differential equations.Then, we link the microscopic contraction models to the macroscopic organ model.We follow for that an approach based on the thermodynamical principles to deal with the multi-scale nature in time and space of the muscle tissue at the continuous and at the discrete levels.The validity of this simulation framework is demonstrated by showing its ability to reproduce the heart behavior and in particular to capture the essential features of the Frank-Starling effect.