Finite and infinitesimal representations of the vasculature: ocular drug clearance by vascular and hydraulic effects.

Abstract

New methods are presented for simulating steady-state drug concentration in vitreous, choroid, and sclera from an intravitreal device. Clearance by choroidal flow and intraocular pressure (IOP) -induced Darcy hydraulic flow are included. Two methods are proposed for modeling the vasculature using simple one-dimensional models for simulating drug concentration profiles from intravitreal devices. The finite choroid method adds a concentration-dependent sink term to the convective diffusion equation, allowing for a continuous but rapid decrease in concentration throughout the choroid region. The infinitesimal choroid method uses a combination of a simple flux boundary condition and a redefinition of the dependent variable to account for the impact of the vascular drain by a discontinuous drop in concentration across the exterior vitreous boundary. This eliminates the need for a choroidal region, reducing finite element memory requirements, enabling the choroid to be made arbitrarily thin. The impact of permeating fluid induced by IOP on convection was examined, using hydraulic coefficients for ocular tissue recently made available [Xu, J. et al., Pharm. Res. 17:664-669 (2000)], allowing for drug efflux through the outer sclera. Transport becomes diffusion limited at high vascular clearance. Hydraulic flow restricts the range in concentration predicted in the vitreous compared to zero flow. Hydraulic influences for small, rapidly cleared drugs can be neglected.