title: Mimetization of the elastic properties of cancellous bone via a parameterized cellular material.
abstract: 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.
authors.affiliation: INTEMA-School of Engineering, CONICET-National University of Mar del Plata, Av. Juan B. Justo 4302, B7608FDQ, Mar del Plata, Argentina. lucascolabella@outlook.com.
authors.forename: Lucas
authors.identifier: http://orcid.org/0000-0003-4648-4584
authors.initials: L
authors.lastname: Colabella
authors.affiliation: INTEMA-School of Engineering, CONICET-National University of Mar del Plata, Av. Juan B. Justo 4302, B7608FDQ, Mar del Plata, Argentina.
authors.forename: Adrián P
authors.initials: AP
authors.lastname: Cisilino
authors.affiliation: Laboratoire Modélisation et Simulation Multiéchelle, UMRS CNRS 8208, CNRS, 61 avenue du gal de Gaulle, 94010, Creteil, France.
authors.forename: Guillaume
authors.initials: G
authors.lastname: Häiat
authors.affiliation: Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106, Warsaw, Poland.
authors.forename: Piotr
authors.initials: P
authors.lastname: Kowalczyk
mesh_terms: D000465:Algorithms; D000818:Animals; D001696:Biomechanical Phenomena; D000071556:Cancellous Bone / Q000502:physiology*; D002417:Cattle; D004548:Elasticity; D006801:Humans; D015203:Reproducibility of Results
keywords: Cancellous bone; Elastic properties; Homogenization; Optimization; Parameterized microstructure; Symmetry classes