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A two-parameter model of the effective elastic tensor for cortical bone.

Abstract：

:Multiscale models of cortical bone elasticity require a large number of parameters to describe the organization and composition of the tissue. We hypothesize that the macro-scale anisotropic elastic properties of different bones can be modeled retaining only two variable parameters, and setting the others to universal values identical for all bones. Cortical bone is regarded as a two-phase composite material: a dense mineralized matrix (ultrastructure) and a soft phase (pores). The ultrastructure is assumed to be a homogeneous and transversely isotropic tissue whose elastic properties in different directions are mutually dependent and can be scaled with a single parameter driving the overall rigidity. This parameter is taken to be the volume fraction of mineral f(ha). The pore network is modeled as an ensemble of water-filled cylinders and described only by the porosity p. The effective macroscopic elasticity tensor C(ij)(f(ha),p) is calculated with a multiscale micromechanics approach starting from existing models. The modeled stiffness coefficients compare favorably to four literature datasets which were chosen because they provide the full stiffness tensors of groups of human samples. Since the physical counterparts of f(ha) and p were unknown for the datasets, their values which allow the best fit of experimental tensors by the modeled ones were determined by optimization. Optimum values of f(ha) and p are found to be unique and realistic. These results suggest that a two-parameter model may be sufficient to model the elasticity of different samples of human femora and tibiae. Such a model would in particular be useful in large-scale parametric studies of bone mechanical response.

journal_name

J Biomech

journal_title

Journal of biomechanics

authors

Grimal Q,Rus G,Parnell WJ,Laugier P

doi

10.1016/j.jbiomech.2011.03.006

subject

Has Abstract

pub_date

2011-05-17 00:00:00

pages

1621-5

issue

8

eissn

0021-9290

issn

1873-2380

pii

S0021-9290(11)00255-7

journal_volume

44

pub_type

杂志文章

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