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H. Zhu, A. Chauhan; Mathematical Modeling of Tear Dynamics . Invest. Ophthalmol. Vis. Sci. 2006;47(13):1958.
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The quantity of tear fluid in an eye under normal circumstances is an important factor in maintenance of comfort and health of ocular tissue. It is thus important to assess the effect of various physiological parameters on the tear volume and to determine the factors that can increase the tear volume. We seek to address these issues by developing mathematical models for various aspects of tear dynamics such as canalicular drainage, conjunctival absorption/secretion, and evaporation.
We perform a tear mass balance on an eye. The mass balance requires mathematical models for the flows from or into the tear film such as canalicular drainage, evaporation and transport across cornea and conjunctiva. The tear drainage model developed is based on the mechanisms proposed by Doane, according to which the muscle action during a blink drives the tear drainage. We also develop a mathematical model for the transport of ions and water through the conjunctival epithelium, using the scheme similar to the corneal endothelium transport model of Fischbarg and Diecke. The drainage and conjunctiva transport models are then incorporated into a tear mass balance, which can predict the steady state tear film thickness and the residence time of fluids and drugs after drop instillation.
The predictions for the mean tear film thickness vary from about 3 to 17 µm. The model also predicts that the drainage time, i.e., the time when 99% of the instilled fluid volume is drained, is 1283 seconds after 15 µL instillation. Similarly, the time for intensity decay for a radioactive tracer after 25 µL instillation is 1566 seconds. Additionally, the time required for the drug concentration to decay to 1% of the value immediately after instillation of drug–laden 40 µL drop is 2480 seconds. Also, the model predicts that the fraction of the instilled drug that reaches the cornea is about 1.3% for topically application of timolol. Each of these predictions is in good agreement with the experiments.
The model predictions agree with various physiological experiments. It also helps resolve the differences between various tear drainage experiments and can be used to design more effective dry eye treatments and also more efficacious ophthalmic drug delivery vehicles.
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