MAC Poster: Mathematical Modeling of Drug Release from Bi-Layered Drug Delivery Systems in the Eye

Wet age-related macular degeneration (wet AMD) is a chronic disease that involves the formation of new blood vessels in the retina due to overexpression of vascular endothelial growth factor (VEGF). It progressively affects the central retina and can cause vision loss if left untreated. Wet AMD is the leading cause of visual impairment in the Western World and the third leading cause worldwide. There is no cure for this disease; however, there are therapies based on anti-VEGF drugs. The most common administration route of anti-VEGF therapeutics is intravitreal injections, but due to the short half-life of the anti-VEGF drugs, monthly intravitreal injections are needed. These injections are expensive, painful, and can result in poor patient compliance. Furthermore, other complications, such as retinal detachment, can also arise due to repeated intravitreal injections. To address this problem, several drug delivery systems (DDS) have been proposed in the literature to extend anti-VEGF release in the eye and reduce the frequency of injections. In this work, we detail our efforts at mathematical modeling of drug release from chitosan-polycaprolactone (PCL) DDSs with different geometries to help optimize their design and improve wet AMD treatments.

First, we model the prototype chitosan-PCL spherical microparticles consisting of an inner chitosan core and an outer PCL shell [1] with the drug dispersed within the core. Fick’s second law is used to model the unsteady-state drug release into phosphate buffer saline. We assume constant diffusion coefficients in each polymeric layer, no convection or reaction within the DDSs, negligible erosion and swelling effects, and perfect sink conditions at the interface between the DDS and the release medium. We consider the existence of a partition coefficient at the interface between chitosan and PCL. For the drug-loaded chitosan-PCL microspheres, we solve the diffusion equation in spherical coordinates numerically using a finite differences algorithm in MATLAB. Nonlinear least squares curve fitting is used to determine the drug diffusion coefficients in both materials, the initial burst release, the partition coefficient between chitosan and PCL, and the critical time at which burst effects are not significant anymore. We then reconstruct the same system in COMSOL Multiphysics, which uses a finite element algorithm, to compare the capabilities of the MATLAB and COMSOL optimization routines for curve fitting in advance of extending to more complicated geometries. We use this process to verify our numerical techniques for integrating the amount of drug remaining in each layer of the microspheres and for calculating the objective function for minimizing the sum of squared errors between the experimental data and the model predictions for cumulative drug release over time [1].

We then build a COMSOL model with the dimensions of the chitosan-PCL microcapsule, which is a bi-layered cylinder with a hollow core for drug loading. Transport of dilute species was the only physics enabled in COMSOL as we first focused on the diffusive transport of drug from the DDS into the in vitro medium. The boundary condition is set to be a no flow condition on the top and bottom of the DDS, simulating impermeable boundaries, consistent with the fabrication techniques of sealing the end caps of the device. The DDS is assumed to be under perfect sink conditions, therefore the drug concentration on the outside is kept at zero. Fick’s second law is used to model the unsteady-state drug release from the cylinder. Since our fabrication technique of salt-leaching the outer PCL layer allows us to modulate the DDS porosity, we are fitting the experimental data [2] for the various salt leaching conditions to correlate the impacts of the initial porosity on the subsequent drug release trajectories. Following a similar procedure as in the microparticles, we used nonlinear least squares curve fitting to estimate the drug diffusion coefficients in both materials, initial burst release, partition coefficient between polymers, and the critical time.

In parallel, we are developing a 3D human eye geometry model which involves relevant tissues’ dimensions and boundary conditions. This model can be used to predict drug transport within the eye. The model considers both convective and diffusive transport. The vitreous humor of the eye is regarded as a porous media, and therefore Darcy’s law is applied to model the convective flow within the vitreous. Additionally, both anterior and posterior segment elimination pathways are considered.

Our MATLAB and COMSOL models accurately simulated the cumulative drug release behavior from the microspheres for 160 days compared to in vitro experimental data. Furthermore, we observed similar behavior for radial drug concentration profiles within microspheres. For the cylindrical device, we observed large deviations in the initial 50 days, with more accurate predictions after that, implying that other drug-release mechanisms, like erosion, need to be considered for the initial phase. In addition, we used the 3D eye model to study the pharmacokinetic behavior of drug after intravitreal injection in two locations: near the limbus, and at a proposed new target location.

The models can help optimize the design of bi-layered DDSs to improve wet AMD treatment and provide insights into the mechanisms involved in the drug release from these DDSs in the eye. In the future, our refined model will be able to calculate cumulative drug release profile, therapeutic release time, and DDS depletion time from input conditions of drug loading, DDS geometry, and initial porosity. Furthermore, we will consider the effects of porosity over the drug release from the DDS and use the COMSOL optimization module to estimate the relevant parameters. System-level integration will be achieved by combining our model for drug release from DDSs with the human eye geometry model, so that we can simultaneously simulate drug release and drug distribution within the eye. The use of this holistic model alongside with new in vitro and in vivo experimental data will also allow us to optimize the DDS design by tuning its thickness and porosity, so that its drug release is extended as much as possible while keeping the drug concentration in the eye within a therapeutic range.

References:

1. Jiang, P., Jacobs, K. M., Ohr, M. P. & Swindle-Reilly, K. E. Chitosan-Polycaprolactone Core-Shell Microparticles for Sustained Delivery of Bevacizumab. Mol Pharm 17, 2570-2584, doi:10.1021/acs.molpharmaceut.0c00260 (2020).
2. Jiang, P., Chaparro, F. J., Cuddington, C. T., Palmer, A. F., Ohr, M. P., Lannutti, J. J., Swindle-Reilly, K. E. Injectable biodegradable bi-layered capsule for sustained delivery of bevacizumab in treating wet age-related macular degeneration. J Controlled Release 320, 442-456, doi:10.1016/j.jconrel.2020.01.036 (2020).

Acknowledgment: This work was supported by the National Institutes of Health grant R35GM133763 and the University at Buffalo.