Finite element-immersed boundary method and its application to mitral valves

每年，全世界约有22.5万例心脏瓣膜置换术。特别是二尖瓣（MV）疾病，如二尖瓣返流（渗漏）可能导致左心室（LV）扩张，左室功能下降，心房颤动发生率增加。数学建模可以帮助我们了解中MV疾病及其与左室功能的关系。然而，与主动脉瓣相比，由于其更复杂的解剖结构，对中主动脉瓣的研究还远远不够。我们将提供基于磁共振图像的动态MV模型，该模型将包括流固相互作用和非线性软组织建模等重要特征。这将通过开发新的数值方法来实现；即一种新的有限元版本的自适应网格细化浸入边界法（IBAMR）。这项工作将通过格拉斯哥数学学院、心血管和医学科学研究所以及IBAMR软件的主要开发者、纽约大学的Boyce Griffith教授之间的跨学科合作进行。IBAMR代表了最先进的浸入边界方法，由于其准确性，在美国越来越受欢迎。罗教授是该软件的主要开发人员之一。该项目的一个重要优势是心血管研究中心的直接参与，该中心拥有英国最先进的核磁共振成像设备，并与金禧国家医院和西部医院相连。因此，我们将获得健康和患病患者的瓣膜几何形状。最重要的是，我们将使用最先进的成像技术获得MV在体内的三维时间位移和应变向量场。这将把计算模拟与临床应用结合在一起，并允许我们识别模型中的关键元素和参数。对MV的动力学进行建模，以了解其在健康和疾病中的机械性能，提供了令人兴奋的新机会。我们的发现将为进一步研究其他瓣膜性心脏疾病提供一个跳板，除了解决有关中压功能的重要生理和病理问题外。提高对心脏瓣膜功能基本机制的认识将改善临床治疗，因此具有明显的社会效益。最终，我们的目标是延缓或预防瓣膜疾病的进展，例如，通过调节经瓣血流或采用药物方法来改变心输出量和瓣膜弹性。该项目开发的框架也将立即用于全心脏的多尺度模型，旨在了解急性心肌梗死。

Each year, about 225,000 valve replacements in the heart are performed worldwide. In particular, mitral valve (MV) diseases such as mitral regurgitation (leakage) may lead to left ventricle (LV) dilation, decreased LV function, and increased rates of atrial fibrillation. Mathematical modelling can help us to understand MV diseases and their relationship with LV functions. However, compared to the aortic valves, the MV has been significantly understudied due to its more complex anatomical structure. We will deliver Magnetic Resonance Image based dynamic MV models which will include important features such as fluid-structure interaction and nonlinear soft tissue modelling. This will be achieved by developing novel numerical methods; i.e. a new finite element version of immersed boundary method with adaptive mesh refinement (IBAMR). The work will be carried out through an interdisciplinary collaboration between Mathematics at Glasgow, the Institute of Cardiovascular and Medical Science, and the primary developer of the IBAMR software, Prof. Boyce Griffith from NYU. IBAMR represents the state of the art immersed boundary methods, and is gaining increasing popularity in the USA due to its accuracy. Prof. Luo is one of the leading developers of this software. One of the important strengths of this project is the direct involvement of the Cardiovascular Research centre, which has the most advanced MRI facilities in the UK, and is linked to Golden Jubilee National Hospital and Western Infirmary. Thus we will have access to valve geometries from healthy and diseased patients. Most importantly, we will obtain 3D temporal displacement and strain vector field of the MV in vivo using the state of the art imaging techniques. This will tie the computational simulations with clinical applications together and allow us to identify key elements and parameters in our models.Modelling the dynamics of the MV to understand its mechanical performance in health and disease offers exciting new opportunities. Apart from addressing important physiological and pathological questions about the MV functions, our findings will serve as springboard for further research on other valvular heart disease. Improved understanding of the basic mechanisms of heart valve function will result in improved clinical therapies and therefore has clear social benefit. Ultimately, our aim is to delay or prevent progression of valvular disease, for example, by modulating transvalvular blood flow or engaging pharmacological approaches to modify cardiac output and valve elasticity. The framework to be developed from this project will also be used immediately to multi-scale models of the whole heart aiming at understanding acute myocardial infarction.