Thickness detection of anisotropic variable cross-section bone based on ultrasonic guided waves

We measured cortical bone thickness of long bones by ultrasonic guided waves for diagnosis of osteoporosis. Current studies were limited to the detection of isotropic cortical bone with uniform thickness, which did not reflect the actual situation. This paper considered the anisotropic cortical bone and proposed an inversion method for measuring the thickness of variable cross-section cortical bone. Firstly, the propagation characteristics of guided waves in cortical bone could be verified by experimentally measuring the guided wave velocity. Then, the inversion method used the A0 mode wavenumber distribution to characterize the thickness of bone plates. Through error analysis, when the signal frequency remains constant, the thinner the cortical bone thickness to be measured, the more accurate the measurement results are. For the thickness inversion of the quantitative experiments in vitro bovine tibia, the error was within 1.1 mm for the oblique bone plate and within 0.9 mm for the concave bone plate. The thickness inversion error of the transverse isotropic assumption decreased by 7.8% compared to the isotropic assumption, which is more realistic for the cortical bone. The method can effectively invert the local thickness of cortical bone, thus providing a reliable basis for evaluating bone health status.