The Effect of Porosity on the Elastic Properties of Dry Long Cortical Bone and Ultrasound Propagation

Abstract When osteoporosis occurs, the long cortical bone shows increased porosity. The effect of porosity on the ultrasonic body wave and axial ultrasonic guided wave propagation in the long cortical bone has not been fully investigated. In this article, in order to evaluate the effects of partial porosity on the elastic properties and the ultrasonic wave propagation in the dry long cortical bone, the relation between the partial porosity and the effective anisotropic elastic modulus of the dry cortical bone has been established using the stiffness contribution tensor and the Maxwell homogenization scheme. The anisotropic porous long cortical bone model has been constructed, the acoustic field is analytically solved, and the effects of different levels of partial porosities on the elastic properties of long cortical bone are studied. The effects of porosity on the ultrasonic body wave propagation velocity and guided wave dispersion characteristics are carefully investigated. The results show that the elastic moduli C33d, C44d, the body waves (including longitudinal wave, SH wave (shear wave motion in a vertical plane), and SV wave (shear wave motion in a horizontal plane) propagating along the vertical direction (perpendicular to the isotropic plane of long cortical bone), longitudinal guided wave modes L1andL2 in the low-frequency plateau region are more sensitive to the canalicular porosity; However, the elastic moduli C11d, C66d, the body waves (including longitudinal wave, SH wave) propagating along the horizontal direction (along the isotropic plane of long cortical bone) are more sensitive to the Haversian porosity. Flexural guided wave modes are sensitive to both types of porosity. This article provides a theoretical basis for nondestructive evaluation of osteoporosis using ultrasonic waves.