Mathematical assessment of drug build-up in the posterior eye following transscleral delivery

Abstract

Delivery of drugs to the posterior segment of the eye is a significant challenge in the field of opthalmic pharmaceuticals. Several restrictive barriers hinder drug delivery to this district. Static barriers include tissues and limiting membranes, while dynamic barriers include drug clearance mechanism from blood and lymphatics. Strategies for delivering drugs to the posterior segment most often consist in topical ocular medications or systemic administrations, but dose/response profiles are generally very poor. Intravitreal injections and transscleral delivery are new emerging techniques with promising results. Purpose of this study is to develop a mathematical model to assess drug levels subsequent to a transscleral drug implant. Both computational and analytical techniques are adopted. The model comprises sclera, choroid, retina and vitreous along with the retina pigment epithelium at the choroid-retina boundary and the inner blood retinal barrier of the retinal vessels. Darcy equations are used to compute the filtration velocity of the interstitial fluid and a fictitious velocity field is added to model active pumping from the retinal pigmented epithelium. Convective-diffusive-reactive equations for drug concentration are then solved. Permeability parameters and partition coefficients simulate the presence of internal membranes and barriers, with possible different values in outward and inward directions. An important result of the model is the evaluation of the roles of the different physical parameters, which offers key points to improve drug delivery techniques. Namely, the sensitivity study suggests that diffusion in tissue, clearance rates, membrane permeabilities and active pumping play important roles in determining drug peak concentration and time-to-peak. However, their relative influence can be dramatically different depending on the rate-limiting parameter.

Hydrodynamics of Intravitreal Injections into Liquid Vitreous Substitutes

“…The prediction of drug distribution within the eye to avoid tissue toxicity and to determine the precise drug levels in target tissues has been a subject of modeling studies. Computational methods have been described to model drug transport following intravitreal injection from a point source [22,23,24,25,26,27] and other models have been developed to simulate drug distribution by an intraocular or periocular implant [25,28,29]. Early models primarily considered diffusion, while more recent models consider both diffusion and convection produced by the aqueous humor flow.…”

Mathematical and Numerical Methods for Modeling Drug Delivery to the Posterior Segment of the Eye

“…On the contrary, the contribution of RPE pumping always appear important, especially when the retina is the therapeutic target. The RPE pumping effect, included in a very limited selection of papers, is modeled as a fictitious advective field or through different inward/outward permeabilities of the RPE membrane [13,19,20]. The inclusion of the significant clearance pathways for a certain drug administration mode is rather varied.…”

“…Choriocapillaries are often treated as a perfect sink [16,21] or they are modeled via porous jump equations [13]. Retinal blood vessels are only considered in [18] and, via a mixture equation approach, in [20]. Generally, the fluid filtration is assumed to be steady state (except for) [15] and not influenced by the drug transport.…”

“…Spatial discretization can be based on finite elements (FEMs) [13,19] or finite volume techniques [15], generally implemented in commercial packages or on finite differences [18]. Different discretization schemes are adopted for time marching, including implicit/semi-implicit finite difference schemes [13,14] and adaptive Runge-Kutta schemes [20]. Three-dimensional problems give rise to large size systems, with a number of degrees of freedom ranging from about 200,000 nodes [13] to 321,000 chamber considered in Jooybar, et al [12] is equal to 4.4 ml , where as in the original model of [13], the volume of the vitreous is about 2.2 ml); iii) what are the significant clearance pathways (for example, blood vessels, periocular structures or lymphatic vessels) for a certain drug administration mode?…”

Preclinical challenges for developing long acting intravitreal medicines

“…Various research with computational modelling has been reported to model drug transport following intravitreal injection. 323,327,[337][338][339][340] Others have reported the effect of drug distribution from intraocular or periocular implant 329,338,341 and for the development of IVIVCs. 342,343 Most studies describe the distribution of injected materials in the vitreous both theoretically and experimentally, but there has been much less described to correlate with real-time data on the distribution and elimination of drugs released from implants or ocular formulations.…”