Modeling Tear Film Dynamics

泪膜动力学建模

• 批准号: 1022706
• 负责人: Richard Braun
• 金额: $ 44.43万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1022706&HistoricalAwards=false
• 关键词: Modeling; Tear; Film; Dynamics

The spreading and dynamics of the tear film will be studied with a hierarchy of computational models. The starting point is a single liquid layer governed by two partial differential equations (PDEs), one for the tear film thickness and one for the tear film osmolarity. The project progresses to models with additional PDEs involving surfactant transport and multiple liquid layers as well. More detailed understanding of evaporation and lipid layer dynamics, especially as applied to tear film breakup and osmolarity variation, will emerge from this work. Two methods will be used in the computational approaches to these problems. For eye-shaped domains, an overset grid method via the Overture framework from Lawrence Livermore National Laboratory provides much of the software capability needed to manage complex boundaries; some solvers specific to the tear film problems have been and are developed at Delaware. For simpler geometries, the investigators use spectral and adaptive radial basis function (RBF) methods to take advantage of a grid free approach near small regions of rapid variation in some of the problems. Successful application of these methods bring new capabilities for understanding tear film dynamics.New understanding of tear film dynamics would benefit a large number of people. As of 1998, up to ten million Americans required use of artificial tear preparations; nearly 5 million Americans age 50 or older suffer from moderate to severe dry eye symptoms. This project improves accepted mathematical models to include more physiologically important effects, particularly osmolarity, the combined concentration of certain salts and sugars in the tear film. Osmolarity is suspected by physicians of being crucial in thedevelopment of dry eye, and the model yields new insights into tear film and osmolarity dynamics. The project benefits from synergy in the intensive collaboration with optometrists at the Ohio State University. This vital collaboration allows the research team to understand and interpret the computationally-generated results and make close comparisons with images and videos obtained through experiments. The computational approaches benefit from continued collaboration with Lawrence Livermore National Laboratory. Dissemination of results are joint with between the mathematicians and their optometrist collaborators in both the applied-mathematical and biomedical communities; results are presented at major major scientific meetings inmathematics, fluid-dynamics, and eye-related fields. As part of reaching these goals, graduate students are trained in multidisciplinary applications of mathematical modeling and computational mathematics.

泪膜的扩散和动力学将通过一系列计算模型来研究。起始点是由两个偏微分方程组(PDE)控制的单个液层，一个用于泪膜厚度，一个用于泪膜渗透压。该项目进展到带有额外PDE的模型，涉及表面活性剂传输和多个液层。这项工作将对蒸发和脂层动力学，特别是应用于泪膜破裂和渗透压变化，有更详细的理解。在这些问题的计算方法中将使用两种方法。对于眼形区域，来自劳伦斯利弗莫尔国家实验室的Overset网格方法通过Overture框架提供了管理复杂边界所需的大部分软件功能；特拉华州已经并正在开发一些针对泪膜问题的解算器。对于更简单的几何，研究人员使用谱和自适应径向基函数(RBF)方法来利用在一些问题中快速变化的小区域附近的无网格方法。这些方法的成功应用为理解泪膜动力学带来了新的能力，对泪膜动力学的新理解将使许多人受益。截至1998年，多达1000万美国人需要使用人工泪液制剂；近500万50岁或50岁以上的美国人患有中度到重度的干眼症状。这个项目改进了公认的数学模型，以包含更多生理上重要的影响，特别是渗透压，即泪膜中特定盐类和糖类的结合浓度。渗透压被医生怀疑是干眼发生的关键，该模型对泪膜和渗透压动力学产生了新的见解。该项目得益于与俄亥俄州立大学验光师的密切合作。这一至关重要的合作使研究团队能够理解和解释通过计算产生的结果，并与通过实验获得的图像和视频进行近距离比较。计算方法得益于与劳伦斯·利弗莫尔国家实验室的持续合作。数学家和他们的验光师在应用数学和生物医学界的合作者之间共同传播成果；在数学、流体动力学和眼科相关领域的主要科学会议上展示成果。作为实现这些目标的一部分，研究生接受数学建模和计算数学的多学科应用方面的培训。