Modeling Intravitreal Drug Transport in Syneretic Eyes

Intravitreal drug delivery is an effective form of treatment for ocular diseases such as Retinal Detachment (RD) and Age Related Macular Degeneration (AMD). Many of these diseases affect the elderly who also experience syneresis. This is condition that comes about with ageing and leads to partial liquefaction of the vitreous that is in general a wholly gel state at birth. We are currently engaged with developing mathematical models of drug transport within the vitreous. In dealing with the elderly, it is therefore essential to include partial liquefaction if the vitreous to properly account for the transport mechanisms. This will contribute to the development of predictive numerical models for intravitreal drug transport leading to improved individualized treatment of patients with ocular diseases. The purpose of the current study is to investigate the effect of a heterogeneity vitreous (partial liquefaction) on the transport of macromolecules. We consider in our model, the gel part of the vitreous as a Darcy-type porous medium. The spherical syneretic zone inside the porous medium of vitreous is considered liquefied and for computational purposes, it is treated as another porous medium but with a much higher permeability coefficient. Physiological flow of water across the vitreous from anterior to posterior is modeled with entry at the hyaloid membrane and exit through the retina into the bloodstream. Using the finite-element method, a time-dependent, three-dimensional, mathematical model has been developed to simulate the transport of intravitreally injected nanoparticles where both convection and diffusion are present in the system. Initial modeling work was developed based on the Galerkin method. Unfortunately, this method does not capture the behavior of the system accurately and the simulation was unstable. To stabilize the model, Petrov-Galerkin method was successfully applied. With this method, a new residual formulation was employed. This formulation includes the original weak formulation with some additional stabilization terms. The computational results for the fluid flow show that for pressure-difference driven water transport across the vitreous, the flow streamlines converge in the liquid region as the flow seeks the fastest path of travel. Not surprisingly, with increasing levels of liquefaction, the volumetric flowrate for the water increases for the same pressure drop. When including convective transport of macromolecules, we see a clear diversion of the drug as it passes through the syneretic region. In considering the targeted retinal region, the presence of syneresis causes some degree of shift in the retinal entry area for the drug.