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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

基本信息

批准号：
2108711
负责人：
Lorena Bociu
金额：
$ 25万
依托单位：
North Carolina State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-08-15 至 2024-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2108711&HistoricalAwards=false
关键词：
Collaborative Research Analysis Control Multi

项目摘要

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，以促进对心血管系统中血液循环的理解，从大动脉到嵌入组织中的小血管。这对于数百万患有青光眼的人来说尤其重要，青光眼是一种导致不可逆视力丧失的渐进性退行性疾病;了解血液动力学因素的作用可以为超过25%的青光眼患者带来新的希望，这些患者尽管接受了药物治疗，但仍继续发展为失明。该项目将在广大受众中培养科学素养，并使下一代STEM学生多样化。本科生和研究生将由研究人员指导本项目的理论和应用方面。研究人员将举办“眼睛：我们身体的一扇窗户”虚拟峰会，以培养北卡罗来纳州和密苏里州高中阶段女性和代表性不足的少数民族对数学研究和医学相关职业的兴趣。研究项目的重点是分析和控制组织灌注模型，这是一种与周围血液循环的全球特征相关的局部现象。该模型涉及偏微分方程（具有不可压缩成分和渗透性非线性地取决于膨胀的准线性毕奥模型）和常微分方程（描述通过血管网络的流体流动的非线性系统）之间的多尺度界面耦合。该研究将桥接应用数学和计算数学，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来研究局部因素和全局特征如何影响系统的解决方案。在青光眼的应用中，该研究将阐明眼内压所起的作用（局部因素）和血压（整体或全身特征）确保足够的血液流向眼睛，从而促进新的治疗方法的发展，共同调节眼内压和血压，这可能有助于许多青光眼患者。该奖项反映了NSF的法定使命，并被认为是值得的。通过使用基金会的知识价值和更广泛的影响审查标准进行评估来提供支持。