The effect of porosity on the elastic properties of cortical bone and ultrasound propagation

This paper focuses on the modeling of the effect of different porosity on the overall elastic properties of saturated cortical bone and ultrasound wave propagation in such bone. We first utilize micromechanical model of Zhou, Cui and Sevostianov (2020) to model anisotropic effective elastic stiffness of saturated cortical bone and evaluate the effect of partial porosities. It is shown that the moduli C₃₃^satand C₄₄^satof saturated bone are more sensitive to canalicular porosity, while the moduli C₁₁^satand C₆₆^satof saturated bone are more sensitive to Haversian porosity. This model has been validated by experimental data. We compare the extents of anisotropy of the saturated bones for different levels of partial porosity. Last but not the least, we apply this micromechanical model to the elastic field of saturated cortical bone to evaluate the effect of partial porosity on the velocity of different bulk waves and guided waves. Results show that the velocity of the fast longitudinal wave and the slower SH wave along the horizontal direction are more sensitive to Haversian porosity ϕ_Hav, but the velocity of the fast longitudinal wave and SH wave along the vertical direction and the velocity of the SV wave along the horizontal direction are more sensitive to the canalicular porosity ϕ_Can. Further, it is found that, the plateau region of the axisymmetric longitudinal guided waves mode L(0, 1) and L(0, 2) phase velocity are more sensitive to canalicular porosity ϕ_Can, and the phase velocity of the lowest nonaxisymmetric flexural mode F(1, 1) in low frequencie is more sensitive to Haversian porosity ϕ_Hav.