Mathematical and numerical methods for modeling drug delivery to the posterior segment of the eye

The high incidence of diseases that affect the posterior segment of the eye (PSE) - here intended as composed by sclera, choroid and retina-prompts for establishing effective and well tolerated therapies. Topical application (instillation of drops) and systemic assumption remain the most widespread drug administration routes. However, the drug achieved levels are not therapeutically sufficient therapeutic, since in the first case the drug is mainly washed away by different pathways (aqueous humor, systemic adsorption, tears) and in the second reaches the PSE target in a minimal fraction. Intravitreal injections and biodegradable episcleral implants have emerged in the last decades as alternative, more effective, administration routes. Whilst these techniques already offer significant improvements, much space is still open to research. The difficulty in delivering drugs to the PSE via the intravitreal (IV) or episcleral (EP) route resides in the several physical and dynamical barriers-including blood retinal barrier, clearance from choriocapillaries and lymphatics-which hinder the passage of the drug molecules. In combination, and in support of clinical experiments, mathematical and computational methods can be used to simulate drug concentration levels in the tissues upon IV or EP administration. In this respect, this short review gives an update of the most recent (from year 2000 to present time) developments on mathematical models for drug delivery to the PSE. We specifically focus our attention on physiological modeling works that include spatial dependency. Our review work is organized in short sections accompanied by detailed tables. We discuss descriptions of the PSE morphology, considering “anatomically accurate” as well as reduced models and we analyze the biophysical phenomena included in the examined models. We present the numerical techniques adopted to solve the resulting systems of partial differential equations and we deal with the delicate issue of parameter choice and validation of the results. Eventually, we examine the main results and scientific achievements of the considered models. Our conclusions point out the absence of a “standard mathematical model” and highlight a significant scattering of the results obtained from the different authors.