Modeling of Cardiac Perfusion in contrast enhanced MRI exams

Описание: I reproduced on this video the talk that I gave on my P.hD defense, on 03/01/2019.

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 different regions, the status of microvascular structures, the presence of fibrosis 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. Briefly, these are currently estimated
qualitatively via visual inspection of images and comparison of relative brightness between different 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 first is a continuum multidomain model based on flow 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 differential equations. For the purpose of obtaining myocardial profiles 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-diffusion-advection equations in both intravascular and interstitial spaces. The interaction of fibrosis 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, different 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 fibrosis, with functional ones, cardiac perfusion. Altogether, the results obtained suggest that the models can support the process of non-invasive cardiac perfusion quantification.