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Colin Cerretani, Clayton J. Radke; Periodic Tear Dynamics Model for Healthy and Dry Eyes. Invest. Ophthalmol. Vis. Sci. 2011;52(14):3867.
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A comprehensive model of tear dynamics including osmolarity increase during blinking, osmotic water supply from the cornea and conjunctiva, tear drainage kinetics, and tear evaporation is needed to understand, for example: tear thickness and stability, dry-eye syndrome, and topical drug delivery. We present a periodic-steady quantitative mathematical model to predict tear dynamics.
The tear system is divided into five compartments: upper and lower conjunctival sacs, upper and lower menisci, and preocular tear film. During an interblink, the tear film is perched and does not exchange fluid. We write coupled water, salt, and/or drug balances in the periodic steady state for each compartment. The system of coupled differential equations is solved numerically to predict the periodic salt concentration and tear volumes for each set of lacrimal supply and evaporation rates
Tear dynamics during blinking is a periodic process that repeats identically. This leads to increased salt concentration in the tear film during the interblink only to return to the same values at the next blink. We quantify average tear osmolarity, total tear volume, and tear turnover rate (TTR) in agreement with reported values for healthy and symptomatic individuals [1,2]. For healthy eyes, the model indicates values of 308mOsM, 7.9µL, and 15%, respectively. For ADDE and EDE eyes, the model predicts 318 and 325mOsM, 7.0 and 5.0µL, and 7 and 11%, respectively. Conjunctival secretion is minimal for healthy individuals (0.02µL/min), but is significant in both ADDE (0.06µL/min) and EDE (0.10µL/min).
Lacrimal supply and evaporation greatly affect tear dynamics, especially osmolarity . Both aqueous deficiency and increased evaporation contribute to hypersomolarity, which is a useful indicator of dry eye. In agreement with clinical results by Khanal et al , TTR can be used to differentiate between ADDE and EDE. Osmotic water flow through the ocular surface mitigates hyperosmolarity in dry eye.1. Khanal S, et al., IOVS, 49(4):1407-14, 20082. Khanal S, et al., O&VS, 86(11):1235-40, 20093. Gaffney, E.A., et al. PRER 29 59-78, 2010
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