Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA.
School of Optometry, Indiana University, Bloomington, IN, 47405, USA.
Bull Math Biol. 2020 Jun 6;82(6):71. doi: 10.1007/s11538-020-00745-8.
Many parameters affect tear film thickness and fluorescent intensity distributions over time; exact values or ranges for some are not well known. We conduct parameter estimation by fitting to fluorescent intensity data recorded from normal subjects' tear films. The fitting is done with thin film fluid dynamics models that are nonlinear partial differential equation models for the thickness, osmolarity and fluorescein concentration of the tear film for circular (spot) or linear (streak) tear film breakup. The corresponding fluorescent intensity is computed from the tear film thickness and fluorescein concentration. The least squares error between computed and experimental fluorescent intensity determines the parameters. The results vary across subjects and trials. The optimal values for variables that cannot be measured in vivo within tear film breakup often fall within accepted experimental ranges for related tear film dynamics; however, some instances suggest that a wider range of parameter values may be acceptable.
许多参数会影响泪膜厚度和荧光强度随时间的分布;其中一些参数的确切值或范围尚不清楚。我们通过拟合正常受试者泪膜的荧光强度数据来进行参数估计。拟合采用薄膜流动力学模型,这些模型是用于圆形(斑点)或线性(条纹)泪膜破裂的泪膜厚度、渗透压和荧光素浓度的非线性偏微分方程模型。相应的荧光强度是从泪膜厚度和荧光素浓度计算得出的。计算出的荧光强度与实验荧光强度之间的最小二乘误差决定了参数。结果因受试者和试验而异。在泪膜破裂过程中无法在体内测量的变量的最佳值通常在相关泪膜动力学的可接受实验范围内;然而,有些情况表明,更宽的参数值范围可能是可以接受的。