Li Longfei, Braun Richard J, Driscoll Tobin A, Henshaw William D, Banks Jeffrey W, King-Smith P Ewen
Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA.
Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA
Math Med Biol. 2016 Jun;33(2):123-57. doi: 10.1093/imammb/dqv013. Epub 2015 Apr 15.
The concentration of ions, or osmolarity, in the tear film is a key variable in understanding dry eye symptoms and disease. In this manuscript, we derive a mathematical model that couples osmolarity (treated as a single solute) and fluid dynamics within the tear film on a 2D eye-shaped domain. The model includes the physical effects of evaporation, surface tension, viscosity, ocular surface wettability, osmolarity, osmosis and tear fluid supply and drainage. The governing system of coupled non-linear partial differential equations is solved using the Overture computational framework, together with a hybrid time-stepping scheme, using a variable step backward differentiation formula and a Runge-Kutta-Chebyshev method that were added to the framework. The results of our numerical simulations provide new insight into the osmolarity distribution over the ocular surface during the interblink.
泪膜中的离子浓度或渗透压是理解干眼症状和疾病的关键变量。在本手稿中，我们推导了一个数学模型，该模型在二维眼形区域上耦合了泪膜内的渗透压（视为单一溶质）和流体动力学。该模型包括蒸发、表面张力、粘度、眼表润湿性、渗透压、渗透以及泪液供应和引流的物理效应。使用Overture计算框架以及混合时间步长方案来求解耦合的非线性偏微分方程组，该方案采用了添加到框架中的可变步长向后微分公式和龙格-库塔-切比雪夫方法。我们数值模拟的结果为眨眼间隔期间眼表渗透压分布提供了新的见解。
