Multiscale modelling and homogensation of fibre-reinforced hydrogels for tissue engineering

TL;DR

This paper develops a multiscale homogenisation model for fibre-reinforced hydrogels used in tissue engineering, linking microscale structure to macroscale mechanical behavior and validating with experiments.

Contribution

It introduces a homogenised model for fibre-reinforced hydrogels that captures their orthotropic elastic-poroelastic properties and validates it against experimental compression data.

Findings

Homogenised model accurately predicts mechanical response.

Fibre spacing influences bulk mechanical properties.

Model reveals local cell environment conditions.

Abstract

Tissue engineering aims to grow artificial tissues \emph{in vitro} to replace those in the body that have been damaged through age, trauma or disease. A recent approach to engineer artificial cartilage involves seeding cells within a scaffold consisting of an interconnected 3D-printed lattice of polymer fibres combined with a cast or printed hydrogel, and subjecting the construct (cell-seeded scaffold) to an applied load in a bioreactor. A key question is to understand how the applied load is distributed throughout the construct. To address this, we employ homogenisation theory to derive equations governing the effective macroscale material properties of a periodic, elastic-poroelastic composite. We treat the fibres as a linear elastic material and the hydrogel as a poroelastic material, and exploit the disparate length scales (small inter-fibre spacing compared with construct dimensions) to derive macroscale equations governing the response of the composite to an applied load. This homogenised description reflects the orthotropic nature of the composite. To validate the model, solutions from finite element simulations of the macroscale, homogenised equations are compared to experimental data describing the unconfined compression of the fibre-reinforced hydrogels. The model is used to derive the bulk mechanical properties of a cylindrical construct of the composite material for a range of fibre spacings, and to determine the local mechanical environment experienced by cells embedded within the construct.