Collaborative Research: Using Uncertainty Quantification and Validated Computational Models to Analyze Pumping Performance of Valveless, Tubular Hearts

无瓣膜的管状心脏通过肌肉收缩驱动许多动物的循环流动。这种流动将氧气、营养物质和废物带到身体各处。它还推动脊椎动物胚胎中血管和其他器官的发育。因此，了解这些心脏是如何产生血流的，是了解脊椎动物胚胎的发育和循环系统进化的关键。该项目将开发该系统最基本的特征的计算模型：心脏的电活动，管壁的肌肉收缩，以及心壁和内部血液的流体-结构相互作用。这个计算框架旨在忠实于真实的模型动物(被囊动物或海鞘)的计算框架。然后用数学工具对模型进行分析，以确定抽水系统的物理极限。这一项目的结果将提高对人类心脏发育的早期理解。此外，它还将指出脊椎动物巨大的、多腔的心脏是如何从较小的结构进化而来的。结果将通过大学课程、科学会议和研讨会、在线资源库和定期出版物发布。该项目还将为高中、本科生和研究生提供跨学科培训。建立了无瓣膜管状心脏产生流动的精确计算模型，并通过对孤立的被衣鱼Ciona savignyi的观测和实验进行验证。采用自适应网格加密的浸没边界方法和Windkesel模型对系统内的流体流动进行数学建模。心脏电动力学的Mitchell-Schaeffer模型将使用心脏电活动的光学映射进行调整。用微粒子图像测速仪对活体沙棘环流的测量将作为模型的验证。基于物理约束的广义多项式混沌(GPC)和Dempster-Shafer(DS)理论的不确定性量化(UQ)技术将被用来研究模型上的不确定性并分析模型上的参数敏感性。物理约束的GPC展开可以基于参数空间中适当选择的输入点的流体流动模拟来构造计算成本更低的代理。感兴趣的流体流量中的混合不确定性类型将使用DS理论和GPC方法相结合来确定，并将使用参数的敏感度来开发关于参数演变的假设。收集与活体动物各种参数组合相对应的性能数据，并利用模型修正方法对二维计算流体动力学模型进行改进。改进后的模型可以用来提供更准确的预测。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Valveless, tubular hearts drive many animals' circulatory flow through muscular contractions. This flow carries oxygen, nutrients, and waste around the body. It also drives the development of blood vessels and other organs in vertebrate embryos. So, understanding how these hearts produce flow is key to understanding the development of vertebrate embryos and the evolution of their circulatory systems. This project will develop a computational model of the most essential features of this system: the electrical activity of the heart, muscle contractions of the tube walls, and the fluid-structure interactions of the heart walls and blood within. This computational framework aims to be faithful to that of a real, model animal (tunicate, or sea squirt). The model will then be analyzed with mathematical tools to determine the physical limits of the pumping system. Results of this project will improve the understanding of human heart development at the earliest stages. Also, it will point to how the large, multi-chambered hearts of vertebrates could have evolved from smaller structures. The results will be released through university courses, scientific conferences and seminars, online repositories, and regular publications. This project will also provide interdisciplinary training to high school, undergraduate, and graduate students. An accurate computational model of flow produced by valveless tubular hearts will be developed and validated using observations and experiments on the solitary tunicate, Ciona savignyi. The Immersed Boundary Method with Adaptive Mesh Refinement and a Windkessel model will be used to mathematically model fluid flow within the system. A Mitchell-Schaeffer model of cardiac electrodynamics will be tuned using optical mapping of heart electrical activity. Measurements on live C. savignyi circulatory flow with micro-Particle Image Velocimetry will be used as model validation. With the completed model, uncertainty quantification (UQ) techniques based on physics-constrained generalized polynomial chaos (gPC) and Dempster-Shafer (DS) theory will be used to study the uncertainty and analyze the parameter sensitivity on the model. The physics-constrained gPC expansion can construct a computationally cheaper surrogate based on the fluid flow simulations at the properly chosen input points in the parameter space. The mixed types of uncertainty in the fluid flow quantities of interest will be determined using DS theory combined with the gPC method, and the sensitivity of parameters will be used to develop hypotheses regarding parameter evolution. The performance data corresponding to various parameter combinations in live animals will be collected and used to improve the 2D computational fluid dynamic model by utilizing model correction methods. The improved model can be used to provide more accurate predictions.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.