Abstract

We present a mathematical model to study the influence of a lipid reservoir, seen experimentally, at the lid margin on the formation and relaxation of the tear film during a partial blink. Applying the lubrication limit, we derive two coupled non-linear partial differential equations characterizing the evolution of the aqueous tear fluid and the covering insoluble lipid concentration. Departing from prior works, we explore a new set of boundary conditions (BCs) enforcing hypothesized lipid concentration dynamics at the lid margins. Using both numerical and analytical approaches, we find that the lipid-focused BCs strongly impact tear film formation and thinning rates. Specifically, during the upstroke of the eyelid, we find specifying the lipid concentration at the lid margin accelerates thinning. Parameter regimes that cause tear film formation success or failure are identified. More importantly, this work expands our understanding of the consequences of lipid dynamics near the lid margins for tear film formation.

中文翻译：

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脂质储库对泪膜形成的影响。

摘要

我们提供了一个数学模型来研究脂质储层的影响，以实验方式观察到，在部分眨眼时，眼睑边缘的泪液膜的形成和松弛对眼睑的边缘形成和松弛。应用润滑极限，我们导出了两个耦合的非线性偏微分方程，这些方程描述了水性泪液和覆盖物不溶性脂质浓度的变化。与先前的工作不同，我们探索了一套新的边界条件（BCs），可在盖缘处实施假设的脂质浓度动态。使用数值和分析方法，我们发现以脂质为中心的BCs强烈影响泪膜的形成和稀化率。具体而言，在上睑的上冲程中，我们发现指定眼睑边缘的脂质浓度会加速变薄。确定导致泪膜形成成功或失败的参数范围。更重要的是，这项工作扩大了我们对眼睑盖缘附近脂质动力学对泪膜形成的后果的理解。