Robust guided wave inversion for estimating bone thickness and elasticity

Accurately characterizing bone properties using quantitative ultrasound remains a significant challenge due to the dispersive nature of guided waves, limited observations, irregularity of bone structure, and heterogeneity of bone tissues. In this paper, an inversion technique is proposed that combines weighted mean absolute criteria and the simulated annealing algorithm to extract the thicknesses and elastic properties of a bilayer bone model. By utilizing the L1 norm with an appropriate weighting parameter, this method effectively reduces the influence of outliers and noises commonly encountered in ultrasonic data, leading to more accurate estimation. This paper also introduces an asymptotic scheme to significantly reduce the search domain, improving the speed and precision of the inversion process. This approach employs a spectral collocation method as a forward modeling technique to simulate guided waves in a bone plate coated by a soft tissue layer. This paper validates the inversion using simulated and ex vivo data and demonstrates its ability to estimate features of cortical bone and soft tissue with high accuracy. Results are presented for the isotropic model. These findings hold great promise for the accurate characterization of bone properties using quantitative ultrasound, with potential applications in clinical diagnosis and treatment of bone-related diseases and injuries.