A novel micromorphic approach captures non-locality in continuum bone remodelling

Abstract

In continuum bone remodelling, bone is considered as continuous matter on the macroscale. Motivated by i) the underlying trabecular microstructure of bone resulting in size-dependence and ii) the non-local characteristics of osteocyte mechanosensing, a novel phenomenological approach based on a micromorphic formulation is proposed. Via illustrative benchmark examples, i.e. elementary unit cube, rod-shaped bone samples, and a 3D-femur sample, the novel approach is compared to the established local formulation, and the influence of the characteristic size of the microcontinuum and the coupling between macro- and microscale deformation is analysed. Taken together, the interaction between continuum points at the macroscale and their neighbourhood is effectively captured by the micromorphic formulation thus influencing the resulting distribution of nominal bone density at the macroscale.

Keywords:

• Bone remodelling
• density growth
• micromorphic continuum
• non-locality
• finite element method

Disclosure statement

No potential conflict of interest was reported by the authors.

Supporting information

We provide the published figures as well as the scan of a OTC anatomical model of a femoral head via ZENODO: https://doi.org/10.5281/zenodo.7763078.

Additional information

Funding

This research gratefully was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 377472739/GRK 2434/1-2019 and the UK Engineering and Physical Sciences Research Council grant EP/R008531/1. Furthermore, we thank the Bavarian Academic Forum (BayWISS) - Doctoral Consortium ‘Health Research’ for their support.