A mixture theory based degradation model for poro-elastic nerve guides and its ALE-FEM implementation

Therapies in peripheral nerve injury repairs require that regrowing axonal projections be guided to their targets, which is currently done via nerve autografts. The latter have severe shortcomings such as scarcity of donor sites and possible neuroma development. The development of TENG (Tissue Engineered Nerve Guide) is hence crucial to said therapies. TENGs must be biocompatible, biodegradable, and bioresorbable to avoid repeated surgeries. Degradation rates must match axonal regrowth rates. TENGs must maintain mechanical integrity and function throughout degradation. At the same time, they must have the right transport properties to deliver nutrients and growth factors. Design and optimization of TENGs therefore requires a predictive capability that accounts for the coupling between the material's chemo-mechanical-transport behaviours. Here we present a degradation theory for CUPE (cross linked urethane-doped polyester elastomers) TENGs. The development is based on mixture theory and accounts for reaction, diffusion and convection of a fluid phase and of additional solutes moving within a degrading solid skeleton. In addition to theory formulation we also present numerical implementation via an ALE (arbitrary Lagrangian Eulerian) finite element method.