Parameterized cellular material for the elastic mimetization of cancellous bone

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 (P. Kowalczyk, <i>Comput Meth Biomech Biomed Eng</i>, 9:135–147, 2006) to mimic the elastic response of cancellous bone. An optimization approach is devised to find the geometrical parameters of the artificial microstructure that better mimics the elastic response of target natural bone specimen. This is done via a Pattern Search algorithm that minimizes the difference between the symmetry class decompositions of the elastic tensors. The performance of the method is demonstrated via analyses for 146 bone samples.