Abstract
This work presents a new mathematical model to describe cardiac perfusion in the myocardium as acquired by cardiac magnetic resonance (CMR) perfusion exams. The combination of first pass (or contrast-enhanced CMR) and late enhancement CMR is a widely used non-invasive exam that can identify abnormal perfused regions of the heart via the use of a contrast agent (CA). The exam provides important information to the diagnosis, management, and prognosis of ischemia and infarct: 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 spatiotemporal 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 work, we propose a new mathematical model based on multidomain flow in porous media. The model is based on a system of partial differential equations. Darcy's law is used to obtain the pressure and velocity distribution. CA dynamics is described by reaction-diffusion-advection equations in the intravascular space and in the interstitial space. The interaction of fibrosis and the CA is also considered. The new model treats the domains as anisotropic media and imposes a closed loop of intravascular flow, which is necessary to reproduce the recirculation of the CA. The model parameters were adjusted to reproduce clinical data. In addition, the model was used to simulate different scenarios: normal perfusion; endocardial ischemia due to stenosis in a coronary artery in the epicardium; 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 suggest that the model can support the process of non-invasive cardiac perfusion quantification.
Highlights
Cardiovascular diseases have a close relation with high blood pressure, smoking, diabetes, lack of exercise, obesity, high blood cholesterol, poor diet, and excessive alcohol (Mendis et al, 2011; Mehta et al, 2015)
Among all the injuries related to a compromised cardiac perfusion that can evolve inside the heart, one that occurs frequently is the obstruction of a coronary artery, or stenosis
We use the same hypothesis as the clinicians and evaluate the dynamics of perfusion at the same instant of each cardiac cycle, i.e., heart contraction is not taken into account
Summary
Cardiovascular diseases have a close relation with high blood pressure, smoking, diabetes, lack of exercise, obesity, high blood cholesterol, poor diet, and excessive alcohol (Mendis et al, 2011; Mehta et al, 2015) Many of these conditions can affect myocardial perfusion (MP), which is the distribution process of oxygen and nutrients to the cardiac tissue. The stenosis reduces the supply of oxygen and nutrients (perfusion defect) in the region of the myocardium that should be irrigated by the coronary artery in question This condition may lead to more severe cases, like an infarct, which can provoke irreversible damages to the cardiac tissue, including death. For the heart to have the necessary strength to pump blood throughout the body, it needs a constant supply of oxygen and nutrients This process can be summarized as follows: the blood enters into the myocardium through the epicardial coronary arteries. The present work will not take into account such level of details
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