Alves João R, de Queiroz Rafael A B, Bär Markus, Dos Santos Rodrigo W
Graduate Program in Computational Modeling, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil.
Department of Mathematical Modeling and Data Analysis, Physikalisch-Technische Bundesanstalt, Berlin, Germany.
Front Physiol. 2019 Mar 14;10:177. doi: 10.3389/fphys.2019.00177. eCollection 2019.
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.
这项工作提出了一种新的数学模型，用于描述通过心脏磁共振（CMR）灌注检查获取的心肌中的心脏灌注情况。首次通过（或对比增强CMR）和延迟增强CMR的联合应用是一种广泛使用的非侵入性检查，可通过使用造影剂（CA）识别心脏的异常灌注区域。该检查为缺血和梗死的诊断、管理及预后提供重要信息：不同区域的灌注情况、微血管结构状态、纤维化的存在以及细胞外间隙的相对体积。这些信息是通过从获取的图像中推断心肌组织中造影剂的时空动态来获得的。这些生理参数的评估在心肌活力评估中起着重要作用。然而，心脏生理学的性质在这些参数的估计中带来了巨大挑战。简而言之，目前这些参数是通过对图像的目视检查以及心脏不同区域之间相对亮度的比较进行定性估计的。因此，迫切需要能够帮助量化心脏灌注的技术。在这项工作中，我们提出了一种基于多孔介质中多域流动的新数学模型。该模型基于偏微分方程组。利用达西定律获得压力和速度分布。造影剂动力学通过血管内空间和组织间隙空间中的反应 - 扩散 - 对流方程来描述。还考虑了纤维化与造影剂的相互作用。新模型将这些区域视为各向异性介质，并施加血管内流动的闭环，这对于再现造影剂的再循环是必要的。对模型参数进行了调整以再现临床数据。此外，该模型用于模拟不同场景：正常灌注；由于心外膜冠状动脉狭窄导致的心内膜缺血；以及心肌梗死。因此，该计算模型能够将解剖特征、狭窄和纤维化的存在与功能特征——心脏灌注联系起来。总之，结果表明该模型可以支持非侵入性心脏灌注量化过程。
