Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA.
School of Optometry, Indiana University, Bloomington, IN, 47405, USA.
Bull Math Biol. 2019 Jan;81(1):39-80. doi: 10.1007/s11538-018-0517-0. Epub 2018 Oct 15.
A previous mathematical model has successfully simulated the rapid tear thinning caused by glob (thicker lipid) in the lipid layer. It captured a fast spreading of polar lipid and a corresponding strong tangential flow in the aqueous layer. With the simulated strong tangential flow, we now extend the model by adding equations for conservation of solutes, for osmolarity and fluorescein, in order to study their dynamics. We then compare our computed results for the resulting intensity distribution with fluorescence experiments on the tear film. We conclude that in rapid thinning, the fluorescent intensity can linearly approximate the tear film thickness well, when the initial fluorescein concentration is small. Thus, a dilute fluorescein is recommended for visualizing the rapid tear thinning during fluorescent imaging.
之前的数学模型成功地模拟了脂质层中 glob(较厚的脂质)引起的快速撕裂变薄现象。该模型捕捉到了极性脂质的快速扩散和水相层中的相应强切向流。有了模拟的强切向流,我们现在通过添加溶质守恒、渗透压和荧光素的方程来扩展模型,以研究它们的动力学。然后,我们将计算得到的强度分布结果与泪膜的荧光实验进行比较。我们得出结论,在快速变薄过程中,当初始荧光素浓度较小时,荧光强度可以很好地线性近似泪膜厚度。因此,建议使用稀荧光素来可视化荧光成像过程中的快速泪膜变薄。