Braun Richard J, Driscoll Tobin A, Begley Carolyn G, King-Smith P Ewen, Siddique Javed I
Department of Mathematical Sciences, University of Delaware, Newark, DE, USA.
School of Optometry, Indiana University, Bloomington, IN, USA.
Math Med Biol. 2018 Jun 13;35(2):145-180. doi: 10.1093/imammb/dqw023.
We report the results of some recent experiments to visualize tear film dynamics. We then study a mathematical model for tear film thinning and tear film breakup (TBU), a term from the ocular surface literature. The thinning is driven by an imposed tear film thinning rate which is input from in vivo measurements. Solutes representing osmolarity and fluorescein are included in the model. Osmolarity causes osmosis from the model ocular surface, and the fluorescein is used to compute the intensity corresponding closely to in vivo observations. The imposed thinning can be either one-dimensional or axisymmetric, leading to streaks or spots of TBU, respectively. For a spatially-uniform (flat) film, osmosis would cease thinning and balance mass lost due to evaporation; for these space-dependent evaporation profiles TBU does occur because osmolarity diffuses out of the TBU into the surrounding tear film, in agreement with previous results. The intensity pattern predicted based on the fluorescein concentration is compared with the computed thickness profiles; this comparison is important for interpreting in vivo observations. The non-dimensionalization introduced leads to insight about the relative importance of the competing processes; it leads to a classification of large vs small TBU regions in which different physical effects are dominant. Many regions of TBU may be considered small, revealing that the flow inside the film has an appreciable influence on fluorescence imaging of the tear film.
我们报告了一些用于可视化泪膜动力学的近期实验结果。然后，我们研究了一个关于泪膜变薄和泪膜破裂（TBU，这是眼表文献中的术语）的数学模型。泪膜变薄由一个从体内测量输入的规定泪膜变薄速率驱动。模型中包含了代表渗透压和荧光素的溶质。渗透压导致从模型眼表发生渗透作用，而荧光素用于计算与体内观察结果密切对应的强度。规定的变薄可以是一维的或轴对称的，分别导致泪膜破裂的条纹或斑点。对于空间均匀（平坦）的泪膜，渗透作用会停止变薄并平衡因蒸发而损失的质量；对于这些与空间相关的蒸发剖面，泪膜破裂确实会发生，因为渗透压从泪膜破裂区域扩散到周围的泪膜中，这与先前的结果一致。将基于荧光素浓度预测的强度模式与计算得到的厚度剖面进行比较；这种比较对于解释体内观察结果很重要。引入的无量纲化有助于深入了解竞争过程的相对重要性；它导致了大的和小的泪膜破裂区域的分类，其中不同的物理效应占主导。许多泪膜破裂区域可能被认为是小的，这表明泪膜内部的流动对泪膜的荧光成像有相当大的影响。
