Mathematical assessment of drug build-up in the posterior eye following transscleral delivery

Delivery of drugs to the posterior segment of the eye is a significant challenge in the field of opthalmic pharmaceuticals. Several restrictive barriers hinder drug delivery to this district. Static barriers include tissues and limiting membranes, while dynamic barriers include drug clearance mechanism from blood and lymphatics. Strategies for delivering drugs to the posterior segment most often consist in topical ocular medications or systemic administrations, but dose/response profiles are generally very poor. Intravitreal injections and transscleral delivery are new emerging techniques with promising results. Purpose of this study is to develop a mathematical model to assess drug levels subsequent to a transscleral drug implant. Both computational and analytical techniques are adopted. The model comprises sclera, choroid, retina and vitreous along with the retina pigment epithelium at the choroid-retina boundary and the inner blood retinal barrier of the retinal vessels. Darcy equations are used to compute the filtration velocity of the interstitial fluid and a fictitious velocity field is added to model active pumping from the retinal pigmented epithelium. Convective-diffusive-reactive equations for drug concentration are then solved. Permeability parameters and partition coefficients simulate the presence of internal membranes and barriers, with possible different values in outward and inward directions. An important result of the model is the evaluation of the roles of the different physical parameters, which offers key points to improve drug delivery techniques. Namely, the sensitivity study suggests that diffusion in tissue, clearance rates, membrane permeabilities and active pumping play important roles in determining drug peak concentration and time-to-peak. However, their relative influence can be dramatically different depending on the rate-limiting parameter.