A Mathematical Model of Tear Mixing under the Lower Lid

Abstract

Purpose: The degree of tear mixing in various parts of eyes plays an important role in determining some important aspects of tear dynamics. This study develops a mathematical model of tear mixing in the lower conjunctival sac. Method: Tear mixing in the lower conjunctival sac is modeled using Taylor dispersion. The concentration of instilled solutes is obtained numerically from an equation set that integrates the mass balance of solutes in the lower conjunctival sac and the exposed tear film. Results: The time for dye to appear in the exposed tear film and the time for maximal dye concentration after instillation into the lower conjunctival sac vary for different amplitudes and frequencies of lid motion. The time scales for mixing are in qualitative agreement with experiments reported in the literature. Conclusion: This study supports the hypothesis that the tear mixing in the lower conjunctival sac is driven by Taylor dispersion caused by lid/globe movements during blinking.

KEYWORDS:

• conjunctival sac
• drug delivery
• model
• ocular physiology
• Taylor dispersion
• tear dynamics
• tear mixing