Biomechanics and Modeling in Mechanobiology

, Volume 16, Issue 5, pp 1485–1502 | Cite as

Mimetization of the elastic properties of cancellous bone via a parameterized cellular material

  • Lucas ColabellaEmail author
  • Adrián P. Cisilino
  • Guillaume Häiat
  • Piotr Kowalczyk
Original Paper


Bone tissue mechanical properties and trabecular microarchitecture are the main factors that determine the biomechanical properties of cancellous bone. Artificial cancellous microstructures, typically described by a reduced number of geometrical parameters, can be designed to obtain a mechanical behavior mimicking that of natural bone. In this work, we assess the ability of the parameterized microstructure introduced by Kowalczyk (Comput Methods Biomech Biomed Eng 9:135–147, 2006. doi: 10.1080/10255840600751473) to mimic the elastic response of cancellous bone. Artificial microstructures are compared with actual bone samples in terms of elasticity matrices and their symmetry classes. The capability of the parameterized microstructure to combine the dominant isotropic, hexagonal, tetragonal and orthorhombic symmetry classes in the proportions present in the cancellous bone is shown. Based on this finding, two optimization approaches are devised to find the geometrical parameters of the artificial microstructure that better mimics the elastic response of a target natural bone specimen: a Sequential Quadratic Programming algorithm that minimizes the norm of the difference between the elasticity matrices, and a Pattern Search algorithm that minimizes the difference between the symmetry class decompositions. The pattern search approach is found to produce the best results. The performance of the method is demonstrated via analyses for 146 bone samples.


Cancellous bone Parameterized microstructure Elastic properties Homogenization Symmetry classes Optimization 



This work has been supported by projects PIRSES-GA2009_246977 “Numerical Simulation in Technical Sciences” of the Marie Curie Actions FP7-PEOPLE-2009-IRSES of the European Union and by the PICS project “Modeling and Simulation in Multidisciplinary Engineering” MoSiMe funded in the framework of the CAFCI call by CONICET (Argentina) and CNRS (France). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant agreement No. 682001, project ERC Consolidator Grant 2015 BoneImplant).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.INTEMA-School of EngineeringCONICET-National University of Mar del PlataMar del PlataArgentina
  2. 2.Laboratoire Modélisation et Simulation Multiéchelle, UMRS CNRS 8208CNRSCreteilFrance
  3. 3.Institute of Fundamental Technological ResearchPolish Academy of SciencesWarsawPoland

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