Diffusion, viscoelasticity and erosion: Analytical study and medical applications

Abstract: In this paper diffusion through a viscoelastic biodegradable material is studied. The phenomenon is described by a set of three coupled partial differential equations that take into account passive diffusion, stress driven diffusion and the degradation of the material. The stability properties of the model are studied. Erodible viscoelastic materials, as biodegradable polymers, have a huge range of applications in medicine to make drug eluting implants. Using the mathematical model the behaviour of a particular ocular drug eluting implant which describes drug delivery into the vitreous chamber of the eye is presented. The model consists of coupled systems of partial differential equations linked by interface conditions. The chemical structure, the viscoelastic properties and the diffusion in the implant as well as the transport in the vitreous are taken into account to simulate the evolution in vivo of released drug. The dependence of the delivery profile on the properties of the material are addressed. Numerical simulations that illustrate the interplay between these phenomena are included.