Mathematical modelling of cardiac perfusion

心血管疾病是英国和世界范围内导致残疾和死亡的主要原因。英国心脏基金会(BHF)估计，它每年会产生19B GB的经济影响。结构损伤，如缺血性心脏病，即使及时治疗，也可能在一年内导致残余心绞痛。其中一个关键问题是了解治疗后的心肌血流灌注情况。心肌灌注心血管磁共振(CMR)成像[1]使用首过对比增强成像来无创地检测冠脉循环中的缺陷(例如狭窄、阻塞、微血管稀疏)，以评估心肌缺血、心肌存活和心功能，而不需要电离辐射。对于中度到稳定的缺血性心脏病患者和持续性心绞痛患者的评估尤其有价值。然而，冠状动脉血管网络和造影剂性质的巨大差异限制了成像技术；仅凭灌注CMR成像也很难确定灌注不足的确切机制。通过将多孔弹性心肌模型与多尺度冠状动脉血流和自由扩散造影剂的标量传输模型相结合来开发计算框架，将使得能够以时空方法高效而准确地映射生物力学因素(例如渗透性张量)[2]。这个博士项目将专注于开发心肌-冠脉循环耦合模型的数学模型。从活体成像(即冠状动脉造影术)获得的大动脉/大静脉将被用来使用一维(1-D)方程来模拟大血管中的血液流动。对于每个终端血管，将使用一种受约束的构造性优化技术[3]来开发一棵小血管树[3]，该技术将使到灌流区域的总血流阻力最小化。一维大动脉/静脉与优化的小血管树相结合，使用SofTMech基于结构树的网络模型[4]，以量化由大冠状动脉供应的压力驱动的心肌血液灌注量。对于微循环，我们认为心肌是多孔弹性的[5]。3-D患者特有的左心室几何形状将使用该小组开发的成熟方法从MRI数据中得出[6]。对于大血管和小血管，由于心肌收缩，血管外的心肌内压(IMP)会影响血流。对于多孔弹性模型，心肌的供血和引流将从大血管和小血管的耦合血流中获得。我们将使用我们自己开发的新的稳健的孔弹性有限元方法[7]，通过求解一维血液流动模型和心壁内的Darcy流动来模拟耦合冠状动脉循环的三维左心室的非线性变形。

Cardiovascular disease is the leading cause of disability and death in the UK and worldwide. The British Heart Foundation (BHF) estimates it has a £19B annual economic impact. Structural impairment such as Ischaemic heart disease, even when treated in time, can lead to residual angina within one year. One of the key problems is to understand the myocardial blood perfusion after the treatment. Myocardial perfusion cardiovascular magnetic resonance (CMR) imaging [1] uses first- pass contrast-enhanced imaging to invasively detect the defects in the coronary circulation (e.g. stenosis, blockage, microvessel rarefaction) to assess myocardial ischaemia, myocardial viability, and cardiac function without the need for ionizing radiation. It is particularly valuable for the evaluation of patients with moderate to stable ischaemic heart disease, and patients with persisting angina. However, the large variations in coronary vessel networks and contrast agent properties limit imaging technologies; it is also difficult to pin down the exact mechanism of perfusion deficiency from perfusion CMR imaging alone. The development of a computational framework by coupling a poroelastic myocardial model with a multi-scale coronary flow and a scalar transport model for freely- diffusive contrast agents, will enable the efficient and accurate mapping of biomechanical factors (e.g. permeability tensor) in a spatial-temporal approach [2]. This PhD project will focus on developing mathematical models of a coupled myocardial-coronary circulation model. The large arteries/veins obtained from in vivo imaging (i.e. coronary angiograms) will be used to model blood flow in large vessels using one-dimensional (1-D) equations. For each terminal vessel, a tree of small vessels will be developed using a constrained constructive optimization technique [3] that minimises the total blood flow resistance to the perfused territory. The 1-D large arteries/veins are coupled with the optimized trees of small vessels using the SofTMech's structured-tree based network model [4] for quantifying myocardial blood perfusion driven by the pressure supplied by the large coronary arteries. For the microcirculation, we shall consider the myocardium as poroelastic [5]. 3-D patient-specific left ventricle geometry will be derived from MRI data using a well-established approach developed by the group [6]. For the large and small blood vessels, the blood flow is affected by the intramyocardial pressure (IMP) external to the blood vessels due to myocardial contraction. For the poroelasticity modelling, blood supply and drainage to the myocardium will be obtained from the coupled large-vessel/small-vessel blood flow. We shall use our in-house developed novel robust finite-element method for poroelasticity [7] to simulate the nonlinear deformation of the three-dimensional left ventricle coupled with the coronary circulation, by solving the 1-D blood flow model together with the Darcy flow inside the heart wall.