Compartmental and COMSOL Multiphysics 3D Modeling of Drug Diffusion to the Vitreous Following the Administration of a Sustained-Release Drug Delivery System

Abstract

The purpose of this study was to examine antibiotic drug transport from a hydrogel drug delivery system (DDS) using a computational model and a 3D model of the eye. Hydrogel DDSs loaded with vancomycin (VAN) were synthesized and release behavior was characterized in vitro. Four different compartmental and four COMSOL models of the eye were developed to describe transport into the vitreous originating from a DDS placed topically, in the subconjunctiva, subretinally, and intravitreally. The concentration of the simulated DDS was assumed to be the initial concentration of the hydrogel DDS. The simulation was executed over 1500 and 100 h for the compartmental and COMSOL models, respectively. Based on the MATLAB model, topical, subconjunctival, subretinal and vitreous administration took most (~500 h to least (0 h) amount of time to reach peak concentrations in the vitreous, respectively. All routes successfully achieved therapeutic levels of drug (0.007 mg/mL) in the vitreous. These models predict the relative build-up of drug in the vitreous following DDS administration in four different points of origin in the eye. Our model may eventually be used to explore the minimum loading dose of drug required in our DDS leading to reduced drug use and waste.

Keywords: COMSOL 3D modeling; compartmental modeling; hydrogels; intravitreal delivery; ocular drug delivery; pharmacokinetic modeling; subconjunctival delivery; subretinal delivery; targeted drug delivery; topical delivery.

Figure 1

Vancomycin concentration over time as it diffuses out of the PNIPAAm-PEG-DA hydrogel. An equation of the line was fitted to the data and the equation was extrapolated to describe the change in hydrogel concentration over time for the model described.

Figure 2

The effects of glutathione on release and degradation of 1 mL thermo-responsive PNIPAAm-PEG-DA hydrogel DDS. (A) Release from a 1 mL thermo-responsive PNIPAAm-PEG-DA-based hydrogel and hydrogels containing PEG-PLLA-DA and 1.0 and 1.5 mg/mL glutathione, respectively. Non-degradable hydrogels showed a significantly lower (p < 0.05) initial burst than both biodegradable hydrogels at 5, 12 and 24 h. (B) Hydrogel degradation over time for the non-degradable, 1.0 mg/mL and 1.5 mg/mL hydrogels over 187 days.

Figure 3

Compartment model that considers the layers of tissues that a drug must transverse in order to enter the vitreous chamber following a subconjunctival entry point. The encapsulated drug flows out of the DDS into the subconjunctival space and must pass through the sclera, choroid, and retina before finally reaching the vitreous. Drug loss to the blood and lymph is also considered k_b. C_H, C_Sb, C_S, C_C, C_R, and C_V represent the drug concentration in their respective compartments. All values of k represent the rate of drug flow into and out of their respective compartments. C_o represents the fraction of drug lost from the choroid.

Figure 4

Compartment model that considers the layers of tissues that a drug must transverse in order to enter the vitreous chamber following topical entry. The encapsulated drug flows out of the DDS into the precorneal area where it mixes with the tear fluid. From there, it can pass either through the cornea and the anterior chamber or alternatively, through the conjunctiva, sclera, choroid, and retina before finally reaching the vitreous. Drug loss (K_loss) due to fluid runoff from the eye is also considered. C_H, C_PA, C_Co, C_S, C_Ch, C_R, C_Cr, C_Ac and C_Vb represent the drug concentration in their respective compartments. $$C_o$$ is the fraction of drug lost from the choroid. All values of k represent the rate of drug flow into and out of their respective compartments.

Figure 5

Compartment model that considers the layers of tissues that a drug must transverse in order to enter the vitreous chamber following an intravitreal entry point. The encapsulated drug flows out of the DDS directly into the vitreous. From there, drug exchange can occur between the vitreous and the retina and the vitreous and the aqueous chamber. Additional systemic drug loss (K_loss) is also considered. C_H, C_V, C_R and C_Ac represent the drug concentration in their respective compartments. All values of k represent the rate of drug flow into and out of their respective compartments.

Figure 6

Compartment model that considers the layers of tissues that a drug must transverse in order to enter the vitreous chamber following subretinal entry. The encapsulated drug flows out of the DDS into the subretinal space. From there, it can pass either through the retina into the vitreous or through the retinal pigment epithelium (RPE) and the choroid into the sclera. Drug loss to the blood is also considered (K_b). C_H, C_SS, C_R, C_V, C_RPE, C_C and C_S represent the drug concentration in their respective compartments. C_o represents the fraction of drug lost from the choroid All values of k represent the rate of drug flow into and out of their respective compartments. It should also be noted that loss from the sclera was not considered due to the focus on the vitreous.

Figure 7

Vancomycin concentration in the vitreous over 1500 h as predicted by compartment models of a DDS containing drug originating topically, subconjunctivally, intravitreally and subretinally and simulated used MATLAB version R2019a software.

Figure 8

COMSOL Multiphysics Model simulation of drug entry routes originating from (A) the subconjunctival, (B) topically, (C) the vitreous and (D) the subretina and penetrating into the vitreous. The concentration profile is demonstrated using both streamline and slices. The right color bar represents the concentration spectrum for the streamlines and the left represents the slices.

Figure 9

COMSOL Multiphysics 3D Model simulation of drug concentrations in the vitreous following entry routes originating from (A) the subconjunctival, (B) topically, (C) the vitreous and (D) the subretina; and penetrating into the vitreous.