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D. Tang, W. van der Meer; Mathematical Simulation for the Permeation of Hydrophilic Drug Through the Cornea by PEGylated Liposomes. Invest. Ophthalmol. Vis. Sci. 2008;49(13):3174. doi: https://doi.org/.
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To quantitatively determine and mathematically simulate the permeation of hydrophilic drug through the cornea.
A mathematical model was developed describing the time-dependence of the permeation process in terms of rate constants for transfer and diffusion. Four different states were considered: encapsulated drug at the tear film, free drug in the tear film, free drug inside the cornea, and free drug in the antechamber. Transitions between these states were assumed to occur via diffusion and transfer. This model is based on experiments in which the fluorescent dye 8-aminonaphthalene-1,3,6-trisulfonic acid disodium salt (ANTS) was used as a hydrophilic drug model. The permeation of this drug through the cornea when encapsulated in PEGylated liposomes was compared to that when the drug was in a PBS solution and not encapsulated. Drug permeation was measured in vivo in New Zealand rabbits and in vitro using a novel technique in which a drug holder containing an ANTS solution was sealed on the surface of a fresh porcine or rabbit eyeball allowing the measurement of drug at desired time intervals in the cornea and aqueous humor after removal of the drug holder.
Comparing the efficacy of drug penetration through the porcine cornea in vitro for encapsulated drug with that for non-encapsulated drug,the PEGylated liposomes resulted in an average 1.35-fold higher than controls. A similar result, 1.15-fold higher, was found by using rabbit eyeballs in vitro. Data from in vivo experiments show that the amount of drug delivered by PEGylated liposomes is 1.40-fold higher than controls. These data can be satisfactorily simulated by time-dependent equations resulting from the model. Comparison between experimental and theoretical results indicate that the rate of transfer of dye through the cornea is about 4 % per second and the rate of diffusion is about 3% per second.
The hydrophilic drug permeation through the cornea using PEGgylated liposomes can be satisfactorily simulated by time-dependent equations resulting from the model.
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