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Applied & Computational Mathematics seminar: Connecting Experimental Observations To Quantitative Tear Film Dynamics

Oct 24, 2025, 1:30 - 2:30 PM

 

Speaker:  Qinying Chen (University of Delaware)

Title:  Connecting Experimental Observations To Quantitative Tear Film Dynamics


Abstract:  Tear film thinning and breakup (TBU), a key factor in dry eye disease (DED), is difficult to understand in detail at the individual level because important quantities such as osmolarity (i.e., salt concentration) and film thickness cannot easily be measured directly in situ. Fluorescence (FL) imaging experiments are easy and cheap to perform, and mathematical modeling has been used in prior work with zero- and one-dimensional simulations to deduce osmolarity and thickness from FL videos. We investigate a two-dimensional (2D) model of localized evaporative TBU using a Fourier spectral collocation method to simulate how variable evaporation affects tear film dynamics. We find a significant speedup by using a proper orthogonal decomposition (POD) to reduce the dimension of the numerical system. We demonstrate the ability to use optimization to solve inverse problems in the reduced 2D model on several representative cases from experimental videos. Finally, we show how operator learning techniques may be a useful way to map from experiments to deductions quickly, without the need to solve inverse problems at large scale.

 

Time:  Friday, October 24, 1:30pm – 2:30pm

Place:  Exploratory Hall, room 4106 

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