Nonlinear Inversion of Ultrasonic Guided Waves for in Vivo Evaluation of Cortical Bone Properties

Ultrasonic guided waves (UGW), which propagate throughout the whole thickness of cortical bone, are attractive in the early diagnosis of osteoporosis. However, it is challenging due to the impact of soft tissue and the inherent difficulties related to the multiparametric inversion of cortical bone quality factors, such as cortical thickness and bulk wave velocities. Therefore, an UGW based multiple-parameter inversion algorithm is developed to predict strength-related factors in this research. In simulation, a free plate (cortical bone) and a bilayer plate (soft tissue and cortical bone) are used to validate the proposed method. The inverted cortical thickness (CTh), longitudinal velocity (V L ) and transverse velocity (V T ) are in accordance with the true value. Then four bovine cortical bone plates are used in the in vitro experiments. Compared with the reference values, the relative errors for cortical thicknesses are 3.96%, 0.83%, 2.87% and 4.25% respectively. In the in vivo measurements, ultrasonic guided waves are collected from ten volunteers’ tibia. The theoretical dispersion curves depicted by the estimated parameters (V T , V L , CTh) match well with the extracted experimental ones. In comparison to the dual-energy x-ray absorptiometry (DXA), the results show that the estimated transverse velocity and cortical thickness are highly sensitive to the osteoporosis. Therefore, these two parameters (CTh and V T ) of long bones have potential to diagnose bone status in clinical applications.