The influence of a lipid reservoir on the tear film formation.

IF 0.8 4区 数学 Q4 BIOLOGY Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2020-09-10 DOI:10.1093/imammb/dqz018
Kara L Maki, Richard J Braun, Gregory A Barron
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引用次数: 3

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.

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脂质储层对泪膜形成的影响。
我们提出了一个数学模型来研究实验中看到的眼睑边缘脂质储层对部分眨眼期间泪膜形成和松弛的影响。应用润滑极限,我们推导了两个耦合的非线性偏微分方程,描述了含水泪液和覆盖的不溶性脂质浓度的演变。从先前的工作出发,我们探索了一组新的边界条件(bc),在眼睑边缘强制假设脂质浓度动态。使用数值和分析方法,我们发现脂质聚焦的bc强烈影响泪膜的形成和稀释速率。具体来说,在眼睑上撇期间,我们发现指定眼睑边缘的脂质浓度会加速变薄。确定了导致泪膜形成成功或失败的参数制度。更重要的是,这项工作扩大了我们对眼睑边缘脂质动力学对泪膜形成的影响的理解。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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