P. M. da Silva

Numerical simulation of aqueous humor flow: From healthy to pathologic situations

A mathematical model which simulates drug delivery through the cornea, from a therapeutic lens to the anterior chamber of the eye, is proposed. The model consists of three coupled systems of partial differential equations linked by interface conditions: drug diffusion in the therapeutic lens; diffusion and metabolic consumption in the cornea; diffusion, convection and metabolic consumption in the anterior chamber of the eye. The dependence of intraocular pressure on the obstruction of the trabecular mesh and the production rate of aqueous humor by the ciliary body is modeled. The therapeutic effects of drugs that act on the trabecular mesh or on the ciliary body are analysed. Comparisons between topical administration and drug delivery from a therapeutic lens are included.

Mathematics of aging: Diseases of the posterior segment of the eye

Abstract The changes caused by aging affect all body tissues. The vitreous humor, which fills the space between the lens and the retina, progressively liquefies and shrinks, eventually causing a posterior vitreous detachment. Retinal disorders caused by the breakdown of the blood retinal barrier are also associated with physiological aging. In this work a mathematical model of the pharmacokinetics of a drug eluted from an intravitreal biodegradable implant in an aging eye is presented. The influences of vitreous liquefaction and retina diseases are analyzed. The model is represented by a set of P.D.E’s describing the evolution of the concentration in a drug eluting implant, coupled with two systems of partial differential equations, describing the transport of drug in the vitreous chamber and the retina. Different scenarios of the physiology of vitreous and of inflammation’s degrees of the retina are numerically compared. The numerical results suggest a dominating influence of retina permeability.