Collaborative Research: Tear Film Dynamics: Modeling, Blinking, and Computation

根据2008年的数据，近500万50岁以上的美国人患有中度至重度干眼综合征（DES）。症状包括不适和视觉功能减退。撕裂膜的动力学被认为是DES发展的关键；快速蒸发和/或泪液不足被认为是引起慢性刺激导致DES的原因。这两种机制都可能导致盐份（渗透压）升高，这被认为是理解眼睛表面刺激的关键变量。这个项目的结果将产生对泪膜流动和渗透压动力学的定量洞察，这可能会影响眼科科学家如何解释他们的数据。该团队位于特拉华大学和罗切斯特理工学院，将与领先的验光师密切合作，以实现这一目标。研究人员将培养具有物理和生物医学建模、高级计算和生理应用方面的高级知识和经验的数学科学家。其中本科生5人，研究生2人，博士后1人。所有受训者将通过出版物和前往科学会议，广泛参与向应用数学界和生物医学界传播结果的工作。作为活动的一部分发现的新信息将通过讲座、参与大学的小组研讨会讨论和未来的研究项目纳入研究生和本科生的培训中。特拉华大学（University of Delaware）和罗切斯特理工学院（Rochester Institute of Technology）的研究人员将合作研究人眼泪膜的动力学，以了解其功能，并帮助阐明干眼综合征（DES）的原因和后果。结果将有助于解释和可视化眨眼过程中复杂的泪液运动，并量化泪液盐度（渗透压）等关键量的可变性。为了做到这一点，新的泪膜模型由非线性耦合高阶偏微分方程组成，在移动的二维眼形域上，将使用应用数学和力学的各种方法来制定。然后，该团队将开发两种新的计算技术来解决这些模型。当前的泪膜模型将通过纳入越来越具有挑战性的蒸发和脂质层运动对复杂运动域的影响来推进。该项目将借鉴薄液膜文献，并与实验验光师密切协商，以做出关于数学建模的明智决定，与体内实验数据进行比较，并对结果进行合理的解释。该奖项由数学科学部的数学生物学项目颁发，由化学、生物工程、环境和运输系统部门的流体动力学项目共同资助。

According to data from 2008, nearly 5 million Americans age 50 or older suffer from moderate to severe dry eye syndrome (DES). Symptoms include discomfort and reduced visual function. The dynamics of the tear film is thought to be critical in the development of DES; rapid evaporation and/or insufficient tears are thought to cause chronic irritation leading to DES. Both of these mechanisms can lead to elevated saltiness (osmolarity), which is believed to be a key variable in understanding the irritation to the eye surface. The results from this project will yield quantitative insight into tear film flows and osmolarity dynamics that may impact how ocular scientists interpret their data. The team, which is based at the University of Delaware and the Rochester Institute of Technology, will work closely with leading optometrists to achieve this goal. The investigators will train mathematical scientists with advanced knowledge of and experience with physical and biomedical modeling, advanced computation, and physiological application. These trainees include five undergraduate and two graduate students, and one postdoctoral fellow. All trainees will participate extensively in dissemination of results to the applied mathematical and biomedical communities, via publication and travel to scientific meetings. New information discovered as part of the activity will be incorporated into graduate and undergraduate training through lectures, discussion in group seminars at the participating universities, and future research projects.Investigators based at the University of Delaware and the Rochester Institute of Technology will collaborate to study the dynamics of the tear film on the human eye in an effort to understand its function and to help clarify causes and consequences of dry eye syndrome (DES). The results will help explain and visualize the complex tear motion during blinking and to quantify the variability of critical quantities such as tear saltiness (osmolarity). To do so, new tear film models consisting of nonlinear coupled high-order partial differential equations on moving, two-dimensional eye-shaped domains will be formulated using a variety of methods from applied mathematics and mechanics. The team will then develop two new computational techniques to solve the models. Current tear film models will be advanced by incorporating increasingly challenging effects of evaporation and lipid layer motion on complex moving domains. The project will draw upon the thin liquid film literature and from close consultation with experimental optometrists to make informed decisions about mathematical modeling, comparison with in vivo experimental data, and sensible interpretation of the results.This award by the Mathematical Biology Program in the Division of Mathematical Sciences is co-funded by the Fluid Dynamics Program in the Division of Chemical, Bioengineering, Environmental, and Transport Systems.