Hybrid Adaptive Numerical Methods and Computational Software for Biological Fluid-Structure Interaction

在他早期开发并行和自适应浸没边界(IB)方法来模拟流固耦合(FSI)的基础上，在这个项目中，研究人员的目标是构建一种新的混合FSI方法，该方法结合了IB方法和浸没界面(II)方法的特点。IB方法是一种广泛适用于FSI的方法，已被应用于生物流体动力学的各种问题。尽管IB方法已被证明是解决这类问题的一种有用的方法，但它通常只有一阶精度，因此需要精细的空间网格来获得解析的数值模拟。II方法是一种类似IB的FSI方法，它对某些问题产生二阶精度，但目前仅限于闭合(即没有自由边)的薄弹性界面。该项目的混合FSI方法将结合IB和II方法的特点，以获得“厚”和“薄”弹性体的高阶精度，包括具有自由边缘的薄弹性界面。我们相信，该方法的基本版本将是第一个类似IB的方法，以实现对厚弹性体(如心脏肌壁)的完全二阶精度，而扩展版本的方法将是第一个处理具有自由边缘的界面(如心脏瓣膜的薄叶)的II类方法。这些新方法将被用来模拟心血管流动，特别是主动脉瓣的流体动力学。流体与弹性结构相互作用的问题，如DNA的扭曲和卷曲，或如本项目所述，心脏和血管中的血液流动，在工程、生物和医学中普遍存在。浸没边界(IB)方法是解决这类问题的一种广泛有用的方法，它的引入是为了能够对心脏及其瓣膜的流体动力学进行计算机模拟。事实上，心血管应用推动了许多工作来开发FSI的数学和计算方法，而患有心血管疾病(美国8000万人，约占总人口的30%)的大量且不断增长的患者，如冠心病(1680万人)或心力衰竭(570万人)，使得此类应用变得越来越重要。该项目旨在开发IB方法的改进版本，这将提高方法的准确性，可能导致对心血管动力学的更真实的模拟。由于IB方法非常有用，而且实现该项目方法的软件将免费分发，因此这项工作的潜在影响是相当广泛的，可能会影响到旨在解决基本科学问题(例如，导致输卵管或呼吸道内纤毛跳动的流体-结构相互作用)的研究，以及旨在改进医疗疗法和设备(如人工心脏瓣膜或心力衰竭的治疗)的设计的研究。

Building upon his earlier work in developing parallel and adaptive immersed boundary (IB) methods for simulating fluid-structure interaction (FSI), in this project, the investigator aims to construct a new hybrid FSI methodology which incorporates features of both the IB method and the immersed interface (II) method. The IB method is a broadly-useful approach to FSI which has been applied to diverse problems in biological fluid dynamics. Although the IB method has been demonstrated to be a useful approach to such problems, it is generally only first-order accurate, and fine spatial grids are therefore required to obtain resolved numerical simulations. The II method is an IB-like approach to FSI which yields second-order accuracy for certain problems, but which is currently limited to thin elastic interfaces which are closed (i.e., which do not have free edges). The hybrid FSI methodology of this project will incorporate features of both the IB and II methods to obtain high-order accuracy for both "thick" and "thin" elastic bodies, including thin elastic interfaces with free edges. We believe that the basic version of the methodology will be the first IB-like method to achieve full second-order accuracy for thick elastic bodies such as the muscular walls of the heart, and that the extended version of the methodology will be the first II-like method to treat interfaces with free edges, such as the thin leaflets of the cardiac valves. These new methods will be used to simulate cardiovascular flows, especially the fluid dynamics of the aortic heart valve.Problems in which a fluid flow interacts with an elastic structure, such as the writhing and coiling of DNA or, as addressed within this project, blood flow in the heart and vessels, are ubiquitous in engineering, biology, and medicine. The immersed boundary (IB) method is a broadly-useful approach to such problems which was introduced to enable the computer simulation of the fluid dynamics of the heart and its valves. Indeed, cardiovascular applications have motivated much work to develop mathematical and computational methods for FSI, and the large and growing number of patients suffering from cardiovascular diseases (80 million people in the United States, approximately 30% of the population), such as coronary heart disease (16.8 million people) or heart failure (5.7 million people), make such applications increasingly important. This project aims to develop an improved version of the IB method which will improve the accuracy of the methodology, possibly leading to significantly more realistic simulations of cardiovascular dynamics. Because the IB approach is widely useful, and because the software implementing the methods of this project will be freely distributed, the potential impact of this work is quite broad, possibly affecting studies which aim to address basic scientific questions (e.g., the fluid-structure interactions which result in the beating of cilia within the oviduct or respiratory tract) to studies which aim to improve the design of medical therapies and devices (e.g., prosthetic cardiac valves or treatments for heart failure).