A mixture theory-based finite element formulation for the study of biodegradation of poroelastic scaffolds

TL;DR

This paper develops a mixture theory-based finite element model to simulate the biodegradation process of poroelastic scaffolds, specifically targeting nerve regeneration implants, incorporating mechanical and transport property evolution.

Contribution

It introduces a novel mathematical model combining mixture theory with FEM for biodegradation of poroelastic scaffolds, including reaction products and fluid interactions.

Findings

Model demonstrates stability and convergence in numerical simulations.

Provides insights into the degradation process of tissue-engineered nerve guides.

Numerical implementation supports future design and analysis of biodegradable implants.

Abstract

We derive a mixture theory-based mathematical model of the degradation of a poroelastic solid immersed in a fluid bath. The evolution of the solid's mechanical and transport properties are also modeled. The inspiration for the model is the study of the temporal evolution of biodegradable Tissue Engineered Nerve Guides (TENGs), which are surgical implants supporting the alignment and re-growth of damaged nerves. The model comprises of the degrading solid, the degradation reaction products, and the fluid in which the solid is immersed. The weak formulation of the partial differential equations (PDEs) so derived is numerically implemented using a Finite Element Method (FEM). The numerical model is studied for stability and convergence rates using the Method of Manufactured Solutions.