An Efficient Model for Scaffold-Mediated Bone Regeneration

TL;DR

This paper introduces a computationally efficient 3D model for bone regeneration with porous scaffolds, capable of handling complex microstructures and multiple signaling molecules, validated by numerical simulations matching experimental data.

Contribution

The novel model uses homogenized quantities and abstract relationships, enabling flexible design and reducing computational costs for simulating scaffold-mediated bone regeneration.

Findings

Model shows good agreement with experimental results.

Proves existence and uniqueness of solutions.

Handles multiple signaling molecules and boundary conditions.

Abstract

We present a three dimensional, time dependent model for bone regeneration in the presence of porous scaffolds to bridge critical size bone defects. Our approach uses homogenized quantities, thus drastically reducing computational cost compared to models resolving the microstructural scale of the scaffold. Using abstract functional relationships instead of concrete effective material properties, our model can incorporate the homogenized material tensors for a large class of scaffold microstructure designs. We prove an existence and uniqueness theorem for solutions based on a fixed point argument. We include the cases of mixed boundary conditions and multiple, interacting signalling molecules, both being important for application. Furthermore we present numerical simulations showing good agreement with experimental findings.