CORTICAL OSTEON STIFFNESS: A COMPARATIVE MICROMECHANICS-BASED HOMOGENIZATION STUDY

Abstract

This work utilizes a novel combination of automated image segmentation and numerical homogenization solutions to provide accurate estimates of stiffness of cortical bone. Segmentation of actual cortical bone digital images (20×) pro-vides for high-fidelity capture of lacunar-canaliculi (L-C) microstructure which, in turn, serves as geometric input to the numerical homogenization solution of osteon stiffness. Osteons are treated as lamella matrix punctuated by porous L-C inclusions namely: Haversian canals, lacunae, and canaliculi clusters. Using image segmentation, extracted geometric attributes are calculated for each individual pore within the matrix including the inclusion’s area, elliptical major–minor axis length (aspect ratio), orientation, and location coordinates. Consequently, aggregate secondary os-teons attributes such as area and volume fractions are calculated. Numerically, solutions of the axial Young’s modulus of the cortical osteon are obtained using the established homogenization methods of Mori–Tanaka (MT) and the generalized self-consistent method (GSCM). Solutions are also obtained using the authors’ own recent development dubbed the generalized stiffness formulation (GSF). To corroborate the numerical results, experimental micro-indentations hardness measurements are conducted on the same image locations in the secondary osteons. It is found that the axial Young’s modulus of the cortical osteon’s matrix decreases with increasing porosity (volume fraction) and aspect ratio. Although all three homogenization methods returned numerical estimates close to experimentally measured stiffness values from micro-indentation tests, the GSF stiffness results exhibit closer agreements. This is attributed to the fact that GSF, in addition to considering the inclusions’ classical variables of area and shape, accounts for the geometric attributes of orientation and position of each of the actually segmented porosities in the osteon. © 2021 by Begell House.