Analytical and Computational Modeling of Sustained-Release Drug Implants in the Vitreous Humor

Sustained ocular drug delivery systems are necessary for patients needing regular drug therapy since frequent injection is painful, undesirable and risky. One type of sustained-release systems includes pellets loaded with the drug, encapsulated in a porous shell that can be injected into the vitreous humor. There the released drug diffuses while the physiological flow of water provides the convective transport. The fluid flow within the vitreous is described by Darcy's equations for the analytical model and Brinkman flow for the computational analysis, while the drug transport is given by the classical convection-diffusion equation. Since the timescale for the drug depletion is quite large, for the analytical model we consider the exterior surrounding the capsule to be quasi-steady and the interior is time dependent. In the vitreous, the fluid-flow process is relatively slow, and meaningful results can be obtained for small Peclet number whereby a perturbation analysis is possible. For an isolated capsule, with approximately uniform flow in the far-field around it, the mass-transfer problem requires singular perturbation with inner and outer matching. The computational model, besides accommodating the ocular geometry, allows for a fully time-dependent mass-concentration solution and also admits moderate Peclet numbers. As expected, the release rate diminishes with time as the drug depletion lowers the driving potential. The predictive results are sufficient general for a range of capsule permeability values and are useful for the design of the sustained-release microspheres as to the requisite permeability for specific drugs.