Modeling the response of nonlinear viscoelastic biodegradable polymeric stents

We analyze the response of nonlinear viscoelastic biodegradable polymers when subject to mechanical loading coupled with the diffusion of a fluid (water) through the polymers and the degradation that occurs over a period of time. We consider the quasi-linear viscoelastic (QLV) model introduced by Fung (1981) that has been found to be reasonably good in modeling tissues undergoing moderate deformations for modeling the nonlinear viscoelastic response of the biodegradable polymer that is being studied, i.e., poly-lactic acid (PLLA). We modify the QLV model to incorporate changes in the material parameters that are a consequence of the degradation that the polymers undergo. We assume that the rate of degradation increases with an increase in the magnitude of strains and concentration of water. We also assume that the degradation softens the polymers and that the rate of stress relaxation (or the rate of creep) of the polymer increases with degradation. Our primary intention is to examine the effect of viscoelasticity on the degradation in virtue of the time-dependent response of such bodies, and also due to the effect of the diffusion of water that leads to degradation. The problem leads to three different time histories associated with the strong coupling between the mechanical loading, diffusion of a fluid (water), and the degradation. As the biodegradable stent is placed inside a nonlinear viscoelastic arterial wall, we further examine the effect of the coupling between the response of the polymeric stent and arterial wall on the degradation of the biodegradable polymeric stent.