A first estimation of prestress in so-called circularly fibered osteonic lamellae

The existence and role of prestress in the various hierarchical structures of long bone are long standing questions. In this study, the prestress and associated strain that exist in a component of human bone microstructure, circularly fibered osteonic lamella, are estimated. Such estimates allow the formulation of hypotheses on prestress formation and lamellar stiffness. Dimensional measurements were obtained for eight fully calcified lamellae. These dimensions, before isolation from the surrounding alternate osteon and after strain relief by isolation and axial sectioning, furnish data upon which a geometric lamellar model is constructed. A material model is based on the most likely hypothesis as to lamellar structure. This geometric-material model allows estimation of the preexisting strain. The largest strains occur in shear circumferential-axial and normal axial strain directions, averaging 0.08 and 0.05, respectively. The geometric-material model expresses prestress in terms of as yet unknown elastic moduli. The average prestress magnitude is the largest in shear circumferential-axial direction, compensating for alternate osteon weakness in this direction. The estimated axial prestress confirms long hypothesized alternate osteon precompression, which impedes fractures of areas of collagen bundles transverse to the osteon axis at low stresses. The results of the model support the formulation of the following biological hypotheses: (a) lamellar prestress occurs at a supra-molecular level, namely through collagen bundles which are themselves likely to be prestressed; (b) collagen bundles oblique to the lamellar axis are responsible for shear prestress; (c) prestress ranges up to 0.11 GPa; and (d) the lamella is less stiff than alternate osteon.