A mixture model for water uptake, degradation, erosion, and drug delivery
We introduce a general class of mixture models suitable to describe water-dependent degradation and erosion of biodegradable polymers in conjunction with drug release from such matrices. The ability to predict and quantify degradation and erosion has direct impact in a variety of biomedical applications and is a useful design tool for biodegradable implants and tissue engineering scaffolds. The model is based on a finite number of constituents describing the polydisperse polymeric system, each representing chains of an average size, and two additional constituents, water and drug. Hydrolytic degradation of individual chains occurs at the molecular level and mixture constituents diffuse individually accordingly to Fick's 1st law at the bulk level – such analysis confers a multiscale aspect to the resulting reaction-diffusion system. A shift between two different types of behavior, each identified to surface or bulk erosion, is observed with the variation of a single nondimensional parameter measuring the relative importance of the mechanisms of reaction and diffusion. Mass loss follows a sigmoid decrease in bulk eroding polymers, whereas decreases linearly in surface eroding polymers. Polydispersity influences degradation and erosion of bulk eroding polymers and drug release from unstable surface eroding matrices is dramatically enhanced in an erosion controlled release.
