Orientation and size-dependent mechanical modulation within individual secondary osteons in cortical bone tissue

Abstract

Anisotropy is one of the most peculiar aspects of cortical bone mechanics; however, its anisotropic mechanical behaviour should be treated only with strict relationship to the length scale of investigation. In this study, we focus on quantifying the orientation and size dependence of the spatial mechanical modulation in individual secondary osteons of bovine cortical bone using nanoindentation. Tests were performed on the same osteonal structure in the axial (along the long bone axis) and transverse (normal to the long bone axis) directions along arrays going radially out from the Haversian canal at four different maximum depths on three secondary osteons. Results clearly show a periodic pattern of stiffness with spatial distance across the osteon. The effect of length scale on lamellar bone anisotropy and the critical length at which homogenization of the mechanical properties occurs were determined. Further, a laminate-composite-based analytical model was applied to the stiffness trends obtained at the highest spatial resolution to evaluate the elastic constants for a sub-layer of mineralized collagen fibrils within an osteonal lamella on the basis of the spatial arrangement of the fibrils. The hierarchical arrangement of lamellar bone is found to be a major determinant for modulation of mechanical properties and anisotropic mechanical behaviour of the tissue.