Mathematical Model of Macromolecular Drug Transport in a Partially Liquefied Vitreous Humor

Abstract

The purpose of this study is to investigate the effect of partial liquefaction (due to ageing) of the vitreous humor on the transport of ocular drugs. In our model, the gel part of the vitreous is treated as a Darcy-type porous medium. A spherical region within the porous part of vitreous is in a liquid state which, for computational purposes, is also treated as a porous medium but with a much higher permeability. Using the finite element method, a time-dependent, three-dimensional model has been developed to computationally simulate (using the Petrov-Galerkin method) the transport of intravitreally injected macromolecules where both convection and diffusion are present. From a fluid physics and transport phenomena perspective, the results show many interesting features. For pressure-driven flow across the vitreous, the flow streamlines converge into the liquefied region as the flow seeks the fastest path of travel. Furthermore, as expected, with increased level of liquefaction, the overall flow rate increases for a given pressure drop. We have quantified this effect for various geometrical considerations. The flow convergence into the liquefied region has important implication for convective transport. One effect is the clear diversion of the drug as it reaches the liquefied region. In some instances, the entry point of the drug in the retinal region gets slightly shifted due to liquefaction. While the model has many approximations and assumptions, the focus is illustrating the effect of liquefaction as one of the building blocks towards a fully comprehensive model.

Advancing treatment of retinal disease through in silico trials

“…Interestingly, it has been shown computationally that in locally liquefied vitreous (e.g. a substitute for the vitreous inserted surgically), fluid flow converges towards the liquefied region as it offers less resistance [154]. This result is of interest in understanding the kinetics of intravitreally injected drugs, especially larger ones such as anti-VEGF which are more subject to convection.…”

“…Rather, these tissues are considered as porous media through which transport is driven by diffusion and a pressure gradient between the IOP in the anterior part of the eye and the lower pressure at the sclera [96,97,135,153,170]. In their noteworthy study, Khoobyar et al determine the depletion of drug from an implant [154]. Through rigorous mathematical analysis of a simplified drug transport model, they derived an analytical formulation for the estimated half-life of an implant in the vitreous which depends on the ratio of convective mass transfer to diffusivity.…”

Computer Modeling of Bevacizumab Drug Distribution After Intravitreal Injection in Rabbit and Human Eyes

“…In this simulation, we considered convective flow due to the aqueous fluid presence in the vitreous, porous domain, influenced by Khoobyar et al [17]. In our model, the vitreous humor is considered a porous structure with a porosity value of ε = 1 [34].…”

“…Khoobyar et al [17] calculated the pressure plot in the human eye considering the vitreous humor divided into two different regions: a liquefied and a gel-type region. They used different permeability values for each area under Darcy's law to simulate vitreous humor convective flow.…”

“…Different investigations have been done to simulate the vitreous humor region. Khoobyar et al [17] considered the vitreous humor as a porous media and divided the vitreous into a low permeability (gel) and high permeability (liquid) region described by the Darcy flow. However, this subdivision of the vitreous humor into a gel and a liquid region, while physiologically relevant, still needs more investigation.…”