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

基于他早期开发并行和自适应浸没边界（IB）方法模拟流体-结构相互作用（FSI）的工作，在这个项目中，研究者的目标是构建一个新的混合FSI方法，它结合了IB方法和浸没界面（II）方法的特点。 IB方法是一种应用广泛的流固耦合方法，已被应用于生物流体动力学中的各种问题。 虽然IB方法已被证明是一个有用的方法，这样的问题，它通常是只有一阶精度，因此需要精细的空间网格，以获得解决的数值模拟。 II方法是FSI的类似IB的方法，其对于某些问题产生二阶精度，但目前仅限于闭合的薄弹性界面（即，其不具有自由边缘）。 该项目的混合流固耦合方法将结合IB和II方法的特点，以获得高阶精度的“厚”和“薄”弹性体，包括薄弹性界面与自由边缘。 我们认为，该方法的基本版本将是第一个IB类方法，以实现完整的二阶精度厚弹性体，如心脏的肌肉壁，和该方法的扩展版本将是第一个II类方法处理接口与自由边缘，如薄瓣叶的心脏瓣膜。 这些新方法将用于模拟心血管流动，特别是主动脉心脏瓣膜的流体动力学。流体流动与弹性结构相互作用的问题，例如DNA的扭曲和卷曲，或者如本项目所述，心脏和血管中的血液流动，在工程，生物学和医学中普遍存在。 浸没边界（IB）方法是一个广泛有用的方法，这类问题，引入，使计算机模拟的心脏及其瓣膜的流体动力学。 事实上，心血管应用已经激发了许多工作来开发用于FSI的数学和计算方法，并且患有心血管疾病（美国有8000万人，约占人口的30%）（诸如冠心病（1680万人）或心力衰竭（570万人））的患者的大量和不断增长的数量使得这样的应用越来越重要。 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，可能导致心血管动力学的更逼真的模拟。 由于IB方法广泛适用，并且由于实现本项目方法的软件将免费分发，因此这项工作的潜在影响非常广泛，可能会影响旨在解决基本科学问题的研究（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）到旨在改进医学治疗和装置的设计的研究（例如，人工心脏瓣膜或心力衰竭的治疗）。

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).