Parameter estimation for evaporation-driven tear film model in two space dimensions

Abstract

The tear film (TF) plays a critical role in maintaining ocular surface health, and its disruption through tear breakup (TBU) is closely associated with dry eye disease. Evaporation-driven thinning is a primary mechanism underlying TBU, yet quantitative in vivo estimates of key physical parameters remain limited. In this work, we fit an evaporation-driven TF thinning model, originally developed by Braun et al. and extended to two dimensions using proper orthogonal decomposition (POD) by Chen et al., to experimental fluorescence (FL) imaging data from normal subjects. The use of dimension reduction enables efficient solution of the governing PDEs and facilitates parameter estimation from imaging data. Our results provide in vivo estimates of evaporation-related and thinning parameters within TBU regions. These findings enhance understanding of TF thinning and dry-spot formation and establish a quantitative baseline for comparison with dry eye patient data.