Numerical simulation of drug release from collagen matrices by enzymatic degradation

Biodegradable collagen matrices have become a promising alternative to synthetic polymers as drug delivery systems for sustained release. Previously, a mathematical model describing water penetration, matrix swelling and drug release by diffusion from dense collagen matrices was introduced and tested (cf. Radu et al. in J. Pharm. Sci. 91:964–972, 2002). However, enzymatic matrix degradation influences the drug release as well. Based on experimental studies (cf. Metzmacher in Enzymatic degradation and drug release behavior of dense collagen implants. Ph.D. thesis, LMU University of Munich, 2005), a mathematical model is presented here that describes drug release by collagenolytic matrix degradation. Existence and uniqueness of a solution of the model equations is reviewed. A mixed Raviart–Thomas finite element discretization for solving the coupled system of partial and ordinary differential equations is proposed and analyzed theoretically. The model is verified by a comparison of numerically calculated and experimentally measured data and, in particular, investigated by a parameter sensitivity study. For illustration, some concentration profiles of a two-dimensional simulation are shown.