Mathematical modeling of diffusion-mediated release from bulk degrading matrices.

The release of active agent from a bulk degrading matrix is formulated as a linear reaction diffusion problem. Two pools of active agent are assumed to contribute to the release: a pool of mobile active agent which readily diffuses out of the matrix upon immersion in an aqueous medium and a pool of immobilized active agent which can diffuse only after matrix degradation. Due to the linearity of our model, the dynamics of the two pools of active agent can be considered separately, for any mode of bulk degradation kinetics. For definiteness, we consider the case of first order degradation kinetics and a rectangular parallelepiped shaped matrix. A closed form solution is obtained for the release under perfect sink conditions which is then used to describe the in vitro release of the PerioChip¿trade mark omitted¿. This solution can explain the bi-phasic release profile characteristic of many hydrolytically degradable matrices. The case of mass transfer boundary conditions is solved numerically using the finite element method (FEM). This analysis indicates that under ordinary mixing conditions the diffusion layer is not rate limiting and the release is very well approximated by the analytical result for perfect sink conditions.