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

根据2008年的数据，近500万50岁或以上的美国人患有中度至重度干眼症（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发展的关键;快速蒸发和/或泪液不足被认为会引起慢性刺激，导致DES。这两种机制都可能导致盐度（渗透压）升高，这被认为是理解眼表面刺激的关键变量。该项目的结果将产生对泪膜流动和渗透压动态的定量洞察，这可能会影响眼科科学家如何解释他们的数据。 该团队位于特拉华州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。研究人员将培训数学科学家，他们具有物理和生物医学建模，高级计算和生理应用的先进知识和经验。这些受训人员包括5名本科生、2名研究生和1名博士后研究员。所有受训人员将通过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，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。特拉华州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，以了解其功能，并帮助澄清原因，干眼综合征（DES）这些结果将有助于解释和可视化眨眼过程中复杂的泪液运动，并量化关键量的变化，如泪液盐度（渗透压）。要做到这一点，新的泪膜模型组成的非线性耦合高阶偏微分方程的移动，二维眼形域将制定使用各种方法从应用数学和力学。然后，该团队将开发两种新的计算技术来解决这些模型。 目前的泪膜模型将通过将蒸发和脂质层运动对复杂移动域的日益具有挑战性的影响。该项目将利用液体薄膜的文献，并与实验验光师密切磋商，以做出有关数学建模的明智决定，与体内实验数据进行比较，并对结果进行合理解释。该奖项由数学科学部数学生物学计划共同资助，由化学，生物工程，环境，和运输系统。

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.