Image/Model Fusion for the Quantification of Mitral Regurgitation Severity. (Fusion Image/Modèles numériques pour la quantification de la sévérité de la Régurgitation Mitrale)

In order to ensure the proper functioning of the organs of the human body, a regular supply of nutrients and oxygen is necessary. This is ensured by the regular contraction of the heart, a major organ of the cardiovascular system. Periodically, the heart -- divided into four cavities -- fills with blood and then contracts to eject it toward the various organs of the body. The right atrium and right ventricle send the deoxygenated blood to the lungs while the left atrium and left ventricle send the oxygenated blood toward the rest of the body. Four passive valves prevent backward blood flow between the different heart cavities. As a result of certain cardiac diseases, these valves may not function properly, which can lead to a retrograde flow of blood. In the case of the mitral valve, located between the left ventricle and the left atrium, it is referred to as mitral regurgitation. The management of this disease is complex and may require extensive treatment such as valve replacement. It is therefore necessary to quantify the severity of mitral regurgitation in order to propose an appropriate treatment. A number of techniques have been developed to quantify the severity of mitral regurgitation. One example is the PISA (Proximal Isovelocity Surface Area) method; based on simplifying assumptions, this method estimates the size of the regurgitant orifice as well as the volume of regurgitated blood during a heartbeat from Color Doppler echocardiographic images. Despite its popularity, this method suffers from a number of shortcomings in terms of estimation accuracy and reproducibility. Recent developments in ultrasound imaging allow the acquisition of relevant data regarding cardiac hemodynamics and ventricular dynamics. On the other hand, the maturity of cardiac mathematical modeling makes it possible to simulate blood flow in a satisfactory way. In this context, it is assumed that combining echocardiographic images with digital models could help to improve the quantification of mitral regurgitation and therefore the quality of patient care. In the first part of this document, a 3D mathematical model of cardiac hemodynamics is developed. Particular attention is being paid to integrating a mitral regurgitation model that is both versatile and simple to use. Numerical examples are provided to assess the advantages and disadvantages of the proposed model. We will also take the opportunity to model the isovolumetric phases of the heart. A relatively accurate model of cardiac hemodynamics, but nevertheless reasonable in term of numerical complexity, is thus obtained at the end of this first part. The second part of this document describes the strategy adopted to allow the fusion of medical images with the numerical simulations. First, an automatic method allowing the personalization of the mathematical model developed in the first part of the manuscript, based on medical images, is presented. An echocardiographic image database is used to test the robustness of the method. The variability of this database is also used for the simulation of synthetic regurgitation, thus allowing a systematic evaluation of the PISA method. A second step is to evaluate how much the absence of a tangential component of wall movement, a component of movement difficult to obtain in echocardiography, can impact cardiac hemodynamics. Finally, as the methods presented are still too expensive from a numerical point of view, we conclude with the presentation of a blood flow reconstruction method combining Color Doppler images with physical constraints related to blood incompressibility. A quantitative assessment of the quality of this reconstruction is made possible by the use of the numerical simulations produced throughout this thesis.