Multi-region finite element modelling of drug release from hydrogel based ophthalmic lenses

Understanding the way in which drug is released from drug carrying hydrogel based ophthalmic lenses aids in the development of efficient ophthalmic drug delivery. Various solute-polymer interactions affect solute diffusion within hydrogels as well as hydrogel-bulk partitioning. Additionally, surface modifications or coatings may add to resistance of mass transfer across the hydrogel interface. It is necessary to consider both interfacial resistances as well as the appropriate driving force when characterizing interface flux. Such a driving force is induced by a difference in concentration which deviates from equilibrium conditions. We present a Galerkin finite element approach for solute transport in hydrogels which accounts for diffusion within the gel, storage effects due to polymer-solute interaction, as well as partitioning and mass transfer resistance effects at the interface. The approach is formulated using a rotational symmetric model to account for realistic geometry. We show that although the resulting global system is not symmetric in the case of partitioning, it is similar to a symmetric negative semidefinite system. Thus, it has non-positive real eigenvalues and is coercive, ensuring the validity of the finite element formulation as well as the numerical stability of the implicit backward Euler time integration method employed. Two models demonstrating this approach are presented and verified with release experimental data. The first is the release of moxifloxacin from intraocular lenses (IOLs) plasma grafted with different polyacrylates. The second accounts for both loading as well as the release of diclofenac from disc shaped IOL material loaded for varied time periods and temperature.