Adaptive Finite Element Solutions of a Diffusion Model for Drug Release in PLGA Microspheres (Advances in Applied Mathematics and Mechanics, 2025)
Poly (lactic-co-glycolic acid) copolymer (PLGA) microspheres are crucial in drug delivery due to their ability to provide controlled release of a wide range of therapeutic agents while minimizing side effects and enhancing biocompatibility. In this paper, a mathematical model is proposed and numerically studied for the drug release process in PLGA microspheres. A three-dimensional diffusion model is constructed based on Fick’s law, being different from the traditional one-dimensional model in the past and fitting the configuration from the drug delivery system, while an h-adaptive finite element method is designed and realized using a C++ library AFEPack for numerical solutions of the proposed model. A notable feature is that the h-adaptivity makes the proposed model and numerical method a quality tool for studying concerned phenomena such as initial bursts in drug delivery. In numerical experiments, besides demonstrating the convergence of the numerical method, a case on progesterone release from PLGA is also studied using the proposed model, from which the potential of the model and the method towards the practical application is shown successfully.