Collaborative Research: A New Three-Dimensional Parallel Immersed Boundary Method with Application to Hemodialysis

涉及薄壁结构的流固耦合问题在生物和工程应用中普遍存在。然而，到目前为止，用于模拟和模拟流体与薄壁结构之间的相互作用的有效技术和计算能力仍然非常缺乏。研究人员的目标是设计一种新的三维并行浸没边界方法，用于计算模拟一般情况下的流体-薄壁结构相互作用，并将其应用于患者特定的动静脉移植物(AVG)远端吻合口的血液流动，这对许多终末期肾病患者血液透析的血液通路是必不可少的。这种新方法将显著扩大浸没边界方法的适用范围，对于数学生物学社区在血管内膜增生、动脉瘤和动脉粥样硬化等血管疾病的计算研究中将特别有价值。与现有的模型相比，所提出的计算模型在生理上更加逼真：该模型考虑了脉动血流对静脉/移植物的变形，并且将微小但有限厚度的静脉/移植物的壁厚包含在模型中。新的计算结果将澄清现有文献中关于AVG远端吻合口附近的力/流特征的相互矛盾的结果，从而使人们对AVG相关的血管内膜增生有更深入的了解。该项目正在开发的新方法将是通用的，适用于工程中的许多重大问题，包括降落伞打开和街道/公路标志的新设计。这些研究还将提高对透析引起的血管内膜增生的认识，这可能会激励新的血管装置的创造和发展，以延长动静脉曲张的通畅率。这不仅将提高患者的生活质量，还将节省与透析相关的医疗成本。相关的研究和教育活动将为研究生和本科生提供数学、生物学、科学计算、流体/固体力学、血液流动和血管疾病方面的多学科培训和研究机会。新方法的开源实施将使流体-结构-相互作用社区大大提高他们的研究生产力。研究人员将开发数值方法，以提高三维流体-薄壁结构相互作用的计算能力。他们通过集成几个组件来处理这类问题：基于高阶谱/惠普单元技术的结构组件，基于格子Boltzmann方法的流体组件，以及通过浸没边界方法框架的流体与结构的耦合。本项目的目标有三个方面：1)在一般情况下发展一种基于IB的流体与薄壁结构相互作用的三维数值模拟方法。该方法将考虑牛顿流体和非牛顿流体、材料非线性和几何非线性。2)在混合CPU-GPU Linux集群上设计、开发和实现了新的3D方法的并行算法。3)将新的并行方法应用于血液透析动静脉移植物远端吻合口的血液流动建模和模拟。研究人员的外展活动将激励高中生考虑从事数学和计算科学，并提高公众对终末期肾脏疾病的可怕后果、相关医疗成本以及数学和科学计算在研究疾病和促进健康方面所发挥的重要作用的认识。

Fluid-structure interaction problems involving thin-walled structures are ubiquitous in biological and engineering applications. However, to date an efficient and effective technique, and a computational capability, for modeling and simulating the interactions between fluids and thin-walled structures are still sorely lacking. The investigators aim to design a new three-dimensional parallel immersed boundary method for computational simulation of fluid-thin-walled-structure interactions in a generic setting and apply it to blood flow past patient-specific distal anastomosis of arteriovenous grafts (AVG), which are essential to blood access of hemodialysis for numerous patients with end-stage renal disease. The new method, which will significantly broaden the applicability of immersed boundary methods, will be particularly valuable to the mathematical biology community for computational studies of vascular diseases such as vascular intimal hyperplasia, aneurysm, and atherosclerosis. Compared to existing models, the proposed computational model is more physiologically realistic: the simulation accommodates deformation of the vein/graft with the pulsatile blood flow, and it incorporates the small yet finite thickness of the vein/graft walls into the model. New computational results will clarify existing contradictory results in the literature regarding the force/flow characteristics near the distal AVG anastomosis and thus lead to a greater understanding of AVG-associated vascular intimal hyperplasia. The new method under development in this project will be generic and applicable to numerous significant problems in engineering, including parachute opening and novel design for street/highway signs. The studies will also enhance the understanding of vascular intimal hyperplasia due to dialysis, which may inspire the creation and development of novel vascular devices to prolong the patency rate of AVGs. This will not only improve quality of life for patients, but also offer savings in dialysis-related healthcare costs. The associated research and education activities will provide multidisciplinary training and research opportunities in mathematics, biology, scientific computing, fluid/solid mechanics, blood flows, and vascular disease for graduate students and undergraduates. The open source implementation of the new method will enable the fluid-structure-interaction community to dramatically increase their research productivity. The investigators will develop numerical methods to improve computational capability for fluid-thin-walled-structure interaction in three dimensions. They approach this type of problem by integrating several components: a structural component based on the high-order spectral/hp element technique, a fluid component based on the lattice Boltzmann method, and the coupling of the fluid and structure through the framework of the immersed boundary method. The goal of this project is three-fold: 1) Develop a three-dimensional IB-based method for fluid and thin-walled structure interactions in a general setting. The method will account for Newtonian and non-Newtonian fluids, material nonlinearity, and geometric nonlinearity. 2)Design, develop, and implement novel parallel algorithms for the new 3D method on hybrid CPU-GPU linux clusters. 3) Apply the new parallel method to model and simulate blood flow past the distal anastomosis of arteriovenous graft for hemodialysis using patient-specific data. The investigators' outreach activities will inspire high school students to consider careers in mathematical and computational sciences and raise public awareness for the dire consequences of end-stage renal disease, its associated healthcare costs, and the important roles mathematics and scientific computing play in studying disease and promoting health.