Drug Release Kinetics from Biodegradable Polymers via Partial Differential Equations Models

In order to achieve prescribed drug release kinetics some authors have been investigating bi-phasic and possibly multi-phasic releases from blends of biodegradable polymers. Recently, experimental data for the release of paclitaxel have been published by Lao et al. (Lao and Venkatraman in J. Control. Release 130:9–14, 2008; Lao et al. in Eur. J. Pharm. Biopharm. 70:796–803, 2008). In Blanchet et al. (SIAM J. Appl. Math. 71(6):2269–2286, 2011) we validated a two-parameter quadratic ordinary differential equation (ODE) model against their experimental data from three representative neat polymers. In this paper we provide a gradient flow interpretation of the ODE model. A three-dimensional partial differential equation (PDE) model for the drug release in their experimental set up is introduced and its parameters are related to the ones of the ODE model. The gradient flow interpretation is extended to the study of the asymptotic concentrations that are solutions of the PDE model to determine the range of parameters that are suitable to simulate complete or partial drug release.