Collaborative Research: Analysis and Control in Multi-Scale Interface Coupling between Deformable Porous Media and Lumped Hydraulic Circuits

合作研究：可变形多孔介质与集总液压回路多尺度界面耦合分析与控制

• 批准号: 2327640
• 负责人: Giovanna Guidoboni
• 金额: $ 25万
• 依托单位: University of Maine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-01-15 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2327640&HistoricalAwards=false
• 关键词: Collaborative; Research; Analysis; Control; Multi; Collaborative; Research; Analysis; Control; Multi

This project will develop theoretical and computational techniques to advance understanding of the circulation of blood in the cardiovascular system, from large arteries to small vessels embedded within the tissues. This is particularly relevant for the millions of people who suffer from glaucoma, a progressive degenerative disease of the eye that leads to irreversible vision loss; understanding the role of hemodynamic factors could bring new hope to the more than 25% of glaucoma patients who continue to progress to blindness despite medical treatment. The project will cultivate science literacy among a broad audience and diversify the next generation of STEM students. Undergraduate and graduate students will be mentored by the investigators on both the theoretical and applied aspects of this project. The investigators will run Virtual Summits on “The Eye: A Window into Our Body” to build interest in mathematics research and mathematics-related careers among women and underrepresented minorities at the high school level in North Carolina and Missouri.The research program is focused on analysis and control in models of the perfusion of a tissue, a local phenomenon studied in correlation with the global features of the surrounding blood circulation. The models involve multi-scale interface coupling between partial differential equations (quasi-linear Biot model with incompressible constituents and permeability nonlinearly depending on dilation) and ordinary differential equations (nonlinear system describing fluid flow through a vascular network). The research will bridge applied and computational mathematics and apply methods from analysis and control theory, numerical analysis, non-convex optimization, and sensitivity analysis to study how local factors and global features affect the solution of the system. In the application to glaucoma, the study will elucidate the roles played by intraocular pressure (local factor) and blood pressure (global, or systemic, feature) in securing adequate blood flow to the eye, thereby facilitating the development of novel therapeutic approaches coregulating intraocular pressure and blood pressure that could potentially help many glaucoma patients.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.

该项目将开发理论和计算技术，以提高对心血管系统血液循环的了解，从大动脉到嵌入组织内的小vissels。这与数百万患有青光眼的人尤其重要，这是一种渐进的眼睛退行性疾病，导致视力丧失不可逆转。了解血液动力学因素的作用可能会给超过25％的青光眼患者带来新的希望，他们继续发展为失明任务医疗。该项目将在广泛的受众中培养科学素养，并使下一代STEM学生多样化。调查人员将考虑该项目的理论和应用方面的研究生和研究生。 The investigators will run Virtual Summits on “The Eye: A Window into Our Body” to build interest in mathematics research and mathematics-related careers among women and Underrepresented minorities at the high school level in North Carolina and Missouri.The research program is focused on analysis and control in models of the perfusion of a tissue, a local phenomenon studiod in correlation with the global features of the surrounding blood circulation.这些模型涉及部分微分方程之间的多尺度界面耦合（具有不可压缩构成的准线性生物模型和非线性取决于扩张的非线性）和普通的微分方程（非线性系统描述了通过血管网络描述流体流动的非线性系统）。该研究将桥接应用和计算数学，并应用分析和控制理论，数值分析，非凸优化和灵敏度分析的方法，以研究局部因素和全局特征如何影响系统的解决方案。在适用于青光眼的应用中，该研究将阐明眼内压力（局部因素）和血压（全球或全身性或全身性，特征）在确保眼睛充足血液流动方面发挥的作用智力优点和更广泛的影响审查标准。