CAREER: A Local-Nonlocal Coupling Framework for Tissue Damage in Fluid-Structure Interaction

该项目旨在开发一个新的数学框架和相应的高性能开源软件，以解决软组织损伤过程的多尺度和多物理模型的基本开放问题，最终目标是提高对心脏瓣膜损伤机制的理解。由此产生的框架将对心脏瓣膜手术和研究产生重大影响，并可能有助于更严格的介入和外科手术。在这个项目中开发的计算工具和方法也可以有效地用于广泛的物理和生物问题。就教育部分而言，该项目将提供一个极好的研究和外联平台，促进女性和代表性不足的群体在从中学到年轻研究人员研究生院的各级教育中参与科学、技术、工程和数学领域的工作。这些活动包括：（1）在暑期外展计划中引入心脏功能模块，使中学女生接触科学和工程，（2）为主要来自本科院校的本科生提供研究机会，以促进学生参与科学研究，以及（3）组织年度高性能计算（HPC）研讨会和多尺度/多物理建模专题讲习班，以促进女学生和研究人员参与应用数学和科学计算领域。研究部分的一个中心主题是开发一种计算方法，该方法模拟了在长期-术语循环血流动力学负荷，目的是了解组织疲劳机制。重点将放在模拟纤维水平的组织损伤引起的循环血流动力学负荷及其长期进展。具体而言，计算域由三个子区域组成：流体（血液）模拟为不可压缩的牛顿流，断裂薄结构（受损的心脏瓣膜）建模的非局部周壳理论，和薄结构（未受损的心脏瓣膜和主动脉壁）描述的经典超弹性壳模型。这三个子区域将在适当的界面边界条件下相互耦合。将开发新的本构模型和相应的数值方案，并设计新的局部-非局部耦合策略。将开发一个强大的计算开源软件，这不仅将有助于推进软组织损伤的知识，而且还将增加计算机模拟长期问题的能力范围，该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响进行评估，被认为值得支持审查标准。

This project aims to develop a new mathematical framework and the corresponding high-performance open source software for addressing fundamental open questions on multiscale and multiphysics modeling of soft tissue damage process, with the ultimate goal of improving the understanding of heart valve damage mechanisms. The resultant framework will have substantial impacts in heart valve operation and research, and will potentially contribute towards more rigorous interventional and surgical procedures. The computational tool and the methodology developed in this project can also be used efficiently in a wide range of physical and biological problems. For the educational component, this project will provide an excellent research and outreach platform for promoting female and under-represented groups in Science, Technology, Engineering and Mathematics (STEM) fields in a range of educational levels from middle school to young researchers post graduate school. These activities include (1) introducing a heart function module in a summer outreach program to expose middle school girls to science and engineering, (2) providing research opportunities for undergraduate students from primarily undergraduate institutions to promote the students' engagement in scientific studies, and (3) organizing an annual high-performance computing (HPC) workshop and a multiscale/multiphysics modeling topical workshop to promote the participation of female students and researchers in the areas of applied mathematics and scientific computing.Technically, a central theme of the research component is the development of a computational approach which models the physically realistic process of heart valve degradation under long-term cyclic hemodynamic loading with the objective of understanding tissue fatigue mechanisms. Emphasis will be placed on modeling the fiber-level tissue damage induced by cyclic hemodynamic loading and its long-term progression. Specifically, the computational domain is composed of three subregions: the fluid (blood) simulated as incompressible Newtonian flow, the fracture thin structure (damaged heart valves) modeled by the nonlocal peridynamic shell theory, and the thin structure (undamaged heart valves and aortic walls) described by a classical hyperelastic shell model. These three subregions will be numerically coupled to each other with proper interface boundary conditions. Novel constitutive models and corresponding numerical schemes will be developed, and new local-nonlocal coupling strategies will also be designed. A powerful computational open source software will be developed, which not only will contribute to advance the knowledge of soft tissue damage, but also will increase the range of capabilities for computer simulation of problems in long-term materials and manufacturing damage progression in general.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.