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A Mathematical Model for Tear Drainage Through the Canaliculi

Purpose: Tear drainage through the canaliculi has been extensively studied experimentally but there has been no attempt to develop a quantitative model for this process. In this paper, we develop a mathematical model for the tear drainage through the canaliculi. Methods: The mathematical model is based on the experimental findings of Doane, according to which the muscle action during a blink drives the tear drainage. In this paper, mathematical models are developed for the tear flow and the canalicular deformation, and the model equations are solved to predict the tear drainage rates. Results: The drainage rates depend on various physiological parameters. The time to attain a steady state during the drainage process can vary from about 0.0010 s to 0.0546 s, and the tear drainage rate can vary from 0.10 μ l/min to 4.00 μ l/min for a normal tear film, for physiologically reasonable values of various system parameters. Conclusions: The model predictions agree with various physiological experiments, at least qualitatively. The model also helps resolve the differences between various tear drainage experiments.