Model of transient drug diffusion across cornea
Introduction
Topical drug delivery is the most common treatment for diseases of the anterior segment of the eye, such as glaucoma, but is limited by the low permeability of the multilayered cornea, rapid clearance by tear drainage, and absorption into the conjunctiva. Hence, the bioavailability of topically administered drugs is very low. Drug transport processes and methods to improve bioavailability have been studied extensively for the past decades, as reviewed, for example, by Schoenwald [1], Lee and Robinson [2], and Jarvinen et al. [3].
Pharmacokinetic models have been widely used to predict the efficiency of new topical agents. Early physiological models of the eye were developed by Himmelstein et al. [4] and Miller et al. [5]. Compartment models, in which each tissue is represented as a separate compartment and is linked sequentially to the next one as the drug passes through, are commonly employed today. Their underlying assumptions as well as their applications have been previously reviewed [1], [2]. In these pharmacokinetic models, absorption into the cornea and conjunctiva is usually described as a first-order process, and corresponding rate constants are determined by fitting the model to a given set of experimental data. The models are therefore often valid only for a specific group of molecules, and their use for the design of new agents is limited.
Taking a more detailed look at drug transport after topical instillation, drug is absorbed and diffuses in the cornea and conjunctiva/sclera. The cornea consists of three main barriers in series: the epithelium, the stroma, and the endothelium. The corneal stroma and sclera are highly hydrated fibrous acellular tissues. The conjunctiva, corneal epithelium, and endothelium are cellular layers that contain both transcellular and paracellular pathways; lipophilic molecules preferentially diffuse within cells, whereas hydrophilic molecules permeate mostly through the openings between cells. The authors previously developed theoretical approaches to predict solute diffusivity in the cornea and sclera based upon the ultrastructure of these membranes and solute physicochemical properties [6], [7].
Building upon these predictions, in this study, a mathematical model was developed for topical drug delivery across the cornea that accounts for the ultrastructure of ocular membranes, solute molecular size and lipophilicity, tear fluid hydrodynamics, as well as drug distribution and clearance in the anterior chamber. This transient model is built upon the partial differential equation for diffusion across ocular membranes (i.e., Fick's law) rather than the empirical first-order absorption equation commonly used. All the parameters of this model have a physical meaning and can be independently measured or estimated, so that the model can be applied to a variety of compounds. Since the actual mechanisms of drug transport and elimination are explicitly taken into consideration, this approach can yield insights into the main determinants of drug delivery and may therefore guide strategies to improve drug bioavailability.
Section snippets
Mathematical model
The model developed in this study addresses the fate of drug molecules applied topically to the eye. As a drop of solution is instilled into the eyelid sac, it is assumed to mix instantly with the tear fluid due to reflex blinks [8]. As shown in Fig. 1, drug solution thus delivered to the precorneal area (i.e., the conjunctival sac and the tear film, considered as a single, homogeneous compartment) is diluted by lacrimal secretion and cleared by four different mechanisms: drainage with the tear
Results
To address the bioavailability of topical eye drops, the objective of this study was to model the transient absorption of a solute from the precorneal area into the anterior chamber, based upon the morphology and physiology of the eye, and upon the solute properties. Because Cmax (the maximum solute concentration in the anterior chamber), tmax (the time needed to reach Cmax), and Ma (the fractional amount of solute diffusing into the chamber) are important to clinical applications and therefore
Discussion
The theoretical model developed in this study should be considered in the context of previous work. Drug delivery through ocular membranes has been modeled extensively [1], [2], [3]. A semiempirical approach involving compartment models has often been used due to the complicated morphology of the eye, the lack of specific ultrastructural data related to membrane composition, and the difficulty in accounting for certain transport phenomena such as binding, blinking, and tear drainage [4], [5],
Conclusion
The developed model of transient transport across the cornea explicitly considers the ultrastructure and hydrodynamics of the eye as well as the physicochemical properties of diffusing solutes. Predictions in this study are in good agreement with experimental data on topical drug delivery. The model suggests promising strategies to increase the bioavailability of drugs applied topically to the eye, involving (1) increasing corneal permeability without a corresponding increase in conjunctival
Acknowledgements
The authors thank Henry Edelhauser for helpful discussions. This work was supported, in part, by the National Institutes of Health.
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