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Parameter Estimation for Mixed-Mechanism Tear Film Thinning
Bulletin of Mathematical Biology ( IF 2.0 ) Pub Date : 2021-04-09 , DOI: 10.1007/s11538-021-00871-x
Rayanne A Luke 1 , Richard J Braun 1 , Tobin A Driscoll 1 , Deborah Awisi-Gyau 1 , Carolyn G Begley 1
Affiliation  

Etiologies of tear breakup include evaporation-driven, divergent flow-driven, and a combination of these two. A mathematical model incorporating evaporation and lipid-driven tangential flow is fit to fluorescence imaging data. The lipid-driven motion is hypothesized to be caused by localized excess lipid, or “globs.” Tear breakup quantities such as evaporation rates and tangential flow rates cannot currently be directly measured during breakup. We determine such variables by fitting mathematical models for tear breakup and the computed fluorescent intensity to experimental intensity data gathered in vivo. Parameter estimation is conducted via least squares minimization of the difference between experimental data and computed answers using either the trust-region-reflective or Levenberg–Marquardt algorithm. Best-fit determination of tear breakup parameters supports the notion that evaporation and divergent tangential flow can cooperate to drive breakup. The resulting tear breakup is typically faster than purely evaporative cases. Many instances of tear breakup may have similar causes, which suggests that interpretation of experimental results may benefit from considering multiple mechanisms.



中文翻译:

混合机理泪膜减薄的参数估计

泪液破裂的病因包括蒸发驱动、发散流驱动以及这两者的组合。结合蒸发和脂质驱动的切向流的数学模型适合荧光成像数据。脂质驱动的运动被假设是由局部过量脂质或“球体”引起的。目前无法直接测量撕裂过程中的撕裂量,例如蒸发率和切向流速。我们通过将泪液破裂的数学模型和计算的荧光强度与体内收集的实验强度数据拟合来确定这些变量。参数估计是通过使用信任区域反射或 Levenberg-Marquardt 算法对实验数据和计算答案之间的差异进行最小二乘最小化来进行的。撕裂破裂参数的最佳拟合确定支持蒸发和发散切向流可以协同驱动破裂的概念。由此产生的撕裂破裂通常比纯粹的蒸发情况更快。许多撕裂破裂的实例可能有类似的原因,这表明对实验结果的解释可能受益于考虑多种机制。

更新日期:2021-04-09
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