Modelagem da perfusão cardíaca em exames de ressonância magnética com contraste

Abstract

This thesis presents two mathematical models to describe the dynamics of a contrast agent (CA) in the myocardium in a cardiac magnetic resonance imaging (MRI) perfusion exam. This exam provides important information on ischemia and infarct: the perfusion on di erent regions, the status of microvascular structures, the presence of brosis and the relative volume of extracellular space. This information is obtained by inferring the dynamics of the contrast in the myocardial tissue from the acquired images. The evaluation of these physiological parameters plays an important role in the assessment of myocardial viability. However, the nature of cardiac physiology poses great challenges in the estimation of these parameters. Brie y, these are currently estimated qualitatively via visual inspection of images and comparison of relative brightness between di erent regions of the heart. Therefore, there is a great urge for techniques that can help to quantify cardiac perfusion. In this thesis, two new mathematical models that describes the spatio-temporal dynamics of the CA are proposed. The rst is a continuum multidomain model based on ow in porous media, and the second is a coupled model, that replaces the intravascular continuum domain by a discrete domain of arterial tree. Both are based in systems of partial di erential equations. For the purpose of obtaining myocardial pro les of pressure and velocity, the continuum model uses Darcy's law, whereas the coupled model uses Poiseuille's law. CA dynamics is described by reaction-di usionadvection equations in both intravascular and interstitial spaces. The interaction of brosis and the CA is also considered. The models treat the domains as anisotropic media and also depicts the recirculation of the CA. The model parameters were adjusted based on try-and-error to reproduce clinical data. In addition, di erent scenarios were simulated: normal perfusion; endocardial ischemia due to stenosis; and myocardial infarct. Therefore, the computational model was able to correlate anatomical features, stenosis and the presence of brosis, with functional ones, cardiac perfusion. Altogether, the results obtained suggest that the models can support the process of non-invasive cardiac perfusion quanti cation.