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 (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.