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

根据2008年的数据，近500万50岁或50岁以上的美国人患有中重度干眼综合征(DES)。症状包括不适和视觉功能下降。泪膜的动力学被认为是DES发生的关键；快速蒸发和/或泪液不足被认为是导致DES的慢性刺激。这两种机制都会导致盐度升高(渗透压)，这被认为是理解对眼睛表面刺激的一个关键变量。这个项目的结果将对泪膜流动和渗透压动力学产生定量的洞察，这可能会影响眼科科学家解释他们的数据的方式。该团队总部设在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。研究人员将培训具有物理和生物医学建模、高级计算和生理学应用方面的高级知识和经验的数学科学家。这些学员包括五名本科生和两名研究生，以及一名博士后。所有受训人员将通过出版出版物和参加科学会议，广泛参与向应用数学和生物医学界传播成果。作为活动的一部分，新发现的信息将通过讲座、参与大学的小组研讨会讨论以及未来的研究项目纳入研究生和本科生的培训。特拉华大学和罗切斯特理工学院的研究人员将合作研究人眼泪膜的动力学，以努力了解其功能，并帮助澄清干眼综合征(DES)的原因和后果。这些结果将有助于解释和可视化眨眼过程中复杂的泪水运动，并量化泪水盐度(渗透压)等临界量的变异性。为此，将使用应用数学和力学中的各种方法来建立新的泪膜模型，该模型由运动的二维眼形区域上的非线性耦合高阶偏微分方程组组成。然后，该团队将开发两种新的计算技术来求解这些模型。目前的泪膜模型将通过在复杂的运动区域上加入蒸发和脂层运动的日益具有挑战性的影响而得到改进。该项目将利用薄膜液膜文献，并通过与实验验光师的密切磋商，就数学建模、与体内实验数据的比较以及对结果的合理解释做出明智的决定。该奖项由数学科学部门的数学生物学项目获得，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.