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

涉及薄壁结构的流固相互作用问题在生物和工程应用中普遍存在。然而，迄今为止，对流体和薄壁结构之间的相互作用进行建模和模拟的高效和有效的技术和计算能力仍然非常缺乏。研究人员旨在设计一种新的三维平行浸入边界方法，用于一般情况下流体-薄壁结构相互作用的计算模拟，并将其应用于通过患者特异性动静脉移植物远端吻合（AVG）的血流，这对于许多终末期肾病患者血液透析的血液通路至关重要。这种新方法将大大拓宽浸入边界方法的适用性，对数学生物学界对血管疾病（如血管内膜增生、动脉瘤和动脉粥样硬化）的计算研究尤其有价值。与现有模型相比，本文提出的计算模型在生理上更真实：模拟了静脉/移植物随脉动血流的变形，并将静脉/移植物壁的小而有限的厚度纳入模型。新的计算结果将澄清文献中关于AVG远端吻合口附近的力/流量特征的现有矛盾结果，从而更好地理解AVG相关的血管内膜增生。在这个项目中开发的新方法将是通用的，适用于许多重要的工程问题，包括降落伞打开和街道/公路标志的新设计。该研究还将加深对透析所致血管内膜增生的认识，从而启发新型血管装置的创造和发展，以延长AVGs的通畅率。这不仅可以提高患者的生活质量，还可以节省与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、血流和血管疾病等多学科的培训和研究机会。新方法的开源实现将使流固相互作用社区能够显著提高他们的研究效率。研究人员将开发数值方法来提高三维流体-薄壁结构相互作用的计算能力。他们通过整合几个组件来解决这类问题：基于高阶谱/高压单元技术的结构组件，基于晶格玻尔兹曼方法的流体组件，以及通过浸入边界方法框架的流体和结构耦合。该项目的目标有三个方面：1)开发一种基于三维流体和薄壁结构相互作用的方法。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CPU-GPU混合linux集群上设计、开发和实现新的3D方法并行算法。3)应用新的并行方法，利用患者特异性数据对血液透析动静脉移植物远端吻合口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从事数学和计算科学的职业，并提高公众对终末期肾病的可怕后果、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.