A model of polymer degradation and erosion for finite element analysis of bioresorbable implants

Finite element analysis is a powerful tool for the design of bioresorbable medical implants made of aliphatic polyesters such as bioresorbable vascular scaffolds. However polymer erosion has been traditionally modelled using empirical rules rather than differential equations. The rule-based models are difficult to implement in a finite element analysis. Consequently, these models have been limited to simple geometries such as plates or spheres. This paper presents a set of differential equations that govern the hydrolytic chain scission and bulk erosion of bioresorbable implants where polymer erosion is modelled using a differential equation instead of empirical rules. These differential equations can be conveniently solved using a commercial finite element package to calculate the molecular weight and mass loss as functions of time for bioresorbable implant made of aliphatic polyesters. A case study of Absorb bioresorbable vascular scaffolds (BVSs) is presented using data obtained from the literature, where 98 Absorb BVSs were implanted in 40 porcine coronary arteries. It is demonstrated that the finite element model can fit the data of both molecular weight and mass loss as functions of time to an accuracy of approximately 5%. The finite element model and the back-calculated model parameters can be used to design future implants that degrade in a controlled pattern with required mechanical performance.