Mathematical models of drug delivery via a contact lens during wear

TL;DR

The paper develops a diffusion-based, compartmental framework to predict ophthalmic drug delivery from drug-eluting contact lenses during wear, coupling diffusion inside the lens with transport in the pre-lens and post-lens tear films and eyelid dynamics under blinking. It presents both a vial-model and a dimensional eye-model, along with a nondimensional and a large-diffusion-limit analysis, to derive analytical insights and to validate them against Phan 2021 experimental data. Key contributions include closed-form solutions in the large-D limit, a detailed formulation of blink-reset conditions (squeeze-out and slide-out mechanisms), and comprehensive numerical comparisons showing that post-lens motion and eyelid pathways are essential to reproduce observed eyelid absorption and cumulative drug release. The framework offers a flexible platform to explore parameter regimes, guiding experimental design and the development of more realistic eye models for drug-eluting contact lenses with potential clinical impact.

Abstract

In this work we develop and investigate mathematical and computational models that describe drug delivery from a contact lens during wear. Our models are designed to predict the dynamics of drug release from the contact lens and subsequent transport into the adjacent pre-lens tear film and post-lens tear film as well as into the ocular tissue (e.g. cornea), into the eyelid, and out of these regions. These processes are modeled by one dimensional diffusion out of the lens coupled to compartment-type models for drug concentrations in the various accompanying regions. In addition to numerical solutions that are compared with experimental data on drug release in an in vitro eye model, we also identify a large diffusion limit model for which analytical solutions can be written down for all quantities of interest, such as cumulative release of the drug from the contact lens. We use our models to make assessments about possible mechanisms and drug transport pathways through the pre-lens and post-lens tear films and provide interpretation of experimental observations. We discuss successes and limitations of our models as well as their potential to guide further research to help understand the dynamics of ophthalmic drug delivery via drug-eluting contact lenses.

Figures (20)

• Figure 1: Estimating the model eye diameter from a video still of Phan et al.phan2021development. The red line estimates the contact lens diameter in pixels (known in mm) and the blue line estimates the model eye diameter.
• Figure 2: Estimating the eyelid area from video stills. The blue line in (a) estimates the contact lens diameter in pixels (known in mm) and the blue box in (b) estimates the eyelid area. Image from Phan et al.phan2021development.
• Figure 3: Snapshots at different time points of the concentration in each lens in a vial over time.
• Figure 4: Optimized single-variable vial model solutions with experimental data.
• Figure 5: Schematic that describes the mechanisms/processes occurring between and during blinks. Blue and red ink denote processes affecting tear film thickness and drug concentration, respectively.