Micro-computed tomography and compressive characterization of trabecular bone

Abstract Materials with a cellular structure are common in nature and an example of natural solid foam is trabecular bone. As for other materials, the microstructural features of cellular solids affect their mechanical response. The aim of this work is to study how the trabecular bone microarchitecture affects the mechanical properties of two types of bone and compare the results with models existing on the literature for solid cellular materials. In spite of several works which make a more medical analysis, this type of materials-science approach is rare. Two types of trabecular bone were studied, namely from male and female patients with osteoporotic (fragility) fractures and patients with coxarthrosis, that were submitted to total hip arthroplasty. Each sample was first analyzed with micro-computed tomography, micro‑CT, for structural assessment. Several parameters used to characterize the three-dimensional structure of trabecular bone were obtained, including the bone volume fraction. Cylinder samples were also tested under uniaxial compression and the Young’s modulus and the ultimate stress were determined. No statistical differences between the two bone groups in respect to the structural and mechanical properties were found. The structural parameters that correlate better with the mechanical properties are different for each bone assembly, being the trabecular separation on the coxarthrosis group and the trabecular number on the osteoporotic group. However, both trabecular separation and trabecular number are strongly correlated with the bone volume fraction, i.e., to the bone relative density. The existing models of Gibson and Ashby were adapted to the relationship between stiffness and strength with the bone volume fraction. In both bone groups, the Young’s modulus is reduced with the decrease of the bone volume fraction following a quadratic law as happens in bending dominated open-cell foams. The ultimate strength is related to the bone volume fraction by a relationship with an exponent between 1 and 2, which indicates that during cell collapse, there is a mixture of two mechanisms: elastic buckling and brittle crushing.