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

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，一个有效的和有效的技术，和计算能力，建模和模拟流体和薄壁结构之间的相互作用仍然严重缺乏。研究人员的目标是设计一种新的三维平行浸没边界方法，用于通用环境中流体-薄壁结构相互作用的计算模拟，并将其应用于流经动静脉移植物（AVG）的患者特定远端吻合口的血流，这对于许多终末期肾病患者的血液透析至关重要。新的方法，这将显着拓宽浸入边界方法的适用性，将是特别有价值的数学生物学社区的血管疾病，如血管内膜增生，动脉瘤和动脉粥样硬化的计算研究。与现有的模型相比，所提出的计算模型在生理上更现实：模拟适应静脉/移植物与脉动血流的变形，并且它将静脉/移植物壁的小而有限的厚度结合到模型中。新的计算结果将澄清文献中关于远端AVG吻合附近的力/流量特性的现有矛盾结果，从而更好地理解AVG相关血管内膜增生。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要问题，包括降落伞打开和街道/公路标志的新设计。这些研究还将增强对透析引起的血管内膜增生的理解，这可能会激发新型血管器械的创建和开发，以延长AVG的通畅率。这不仅可以提高患者的生活质量，还可以节省透析相关的医疗费用。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。新方法的开源实现将使流体-结构-相互作用社区能够显着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解决这种类型的问题：基于高阶谱/HP元素技术的结构组件，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和结构的耦合。本项目的目标有三个方面：1）开发一种基于IB的三维流体和薄壁结构相互作用方法。该方法将考虑牛顿和非牛顿流体、材料非线性和几何非线性。2）在混合CPU-GPU Linux集群上设计、开发和实现新的3D方法的并行算法。3)使用患者特定数据，应用新的并行方法对血液透析动静脉移植物远端吻合口的血流进行建模和模拟。 研究人员的外展活动将激励高中生考虑数学和计算科学的职业生涯，并提高公众对终末期肾病的可怕后果，其相关医疗费用以及数学和科学计算在研究疾病和促进健康方面的重要作用的认识。

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.