Assessment of mechanical properties of bone trabeculae as an inverse problem of heterogeneous material modeling

Janc, K.; Tarasiuk, J.; Lipinski, P.; Bonnet, A.-S.; Wronski, S.

Affiliations

¹Faculty of Physics and Applied Computer Science (WFiIS), AGH – University of Science and Technology, 30 Mickiewicza Ave., 30-059 Kraków, Poland

²LEM3, Université de Lorraine, Ecole Nationale d’Ingénieurs de Metz, 1 Route d’Ars Laquenexy, BP 65820, 57 078 Metz Cedex 03, France

Abstract and keywords

In this study, the trabecular bone was treated as a composite material that consists of a bone matrix weakened by ellipsoidal pores. Under the hypothesis that all information concerning the local properties and the microarchitecture are “encrypted” in the apparent properties of a given volume element (VE) of the bone, a method of retrieving these data was proposed. Software based on a genetic algorithm, combined with the incremental scale transition method was developed to this end. To test the approach, µCT measurements of four bone samples were performed providing their real micro-architecture. Tensors of apparent properties of the samples were next computed by numerical (finite element) homogenization method for a large range of the elastic properties of trabeculae. They were considered as the fitness function for the proposed algorithm. Very good agreement was found between the obtained and target values of the apparent elastic properties of the samples and volume fraction of pores. The approach is fast and accurate enough in comparison to the finite element homogenization. As an auxiliary result it was shown that the anisotropy of apparent elastic properties is mainly related to the microarchitecture of the bone, not to the intrinsic properties of trabeculae.

Keywords: bone mechanical properties; inverse problem; computer modelling; incremental scheme

Links

DOI: 10.24423/aom.3469

WoS: 000581832600001

History

Received: 2020-10-22

Revised: 2020-08-25

Online: 2020-10-16

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