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

TL;DR

This study evaluates a parameterized microstructure model's ability to replicate the elastic properties of cancellous bone, using optimization algorithms to match natural bone's mechanical response based on microarchitectural symmetry classes.

Contribution

It introduces and assesses an optimization-based method to design artificial microstructures that mimic the elastic behavior of natural cancellous bone.

Findings

Pattern search algorithm outperforms sequential quadratic programming.

The method successfully replicates the elastic response for 146 bone samples.

Artificial microstructures can match the symmetry class proportions of natural 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 (2006) 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.