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A mathematical model for controlled drug delivery in swelling polymers

Gudiño, Elias; Grassi, Mario; Ferreira, José A.; De Oliveira, Paula

Proceedings of the 13th International Conference on Mathematical Methods in Science and Engineering (CMMSE 2013), 2 (2013), 630-641

We propose a one-dimensional model to describe the sorption of a solvent by a polymeric membrane, followed by polymer swelling and drug release. We assume that the solvent diffuses into the membrane and induces a stress driven diffusion, that causes a non-Fickian mass flux. We assume that the drug is present in two states (dissolved and undissolved) and that its transport occurs by Fickian diffusion and non-linear dissolution. Polymer swelling is tracked with a volume conservation equation. The system of
partial differential equations that define the model is numerically solved.

A qualitative analysis of the dependence of the solutions on the parameters of the model shows a complete agreement with the expected physical behavior.