Material and geometric effects on ultrasonic guided wave propagation in long bone

During the last couple of decades, ultrasonic guided waves have been shown to be increasingly capable of interrogating long bones in the human skeleton in order to characterize osteoporosis. Their diagnostic role is promising as the established gold-standard diagnostic techniques of dual-energy x-ray absorptiometry (DXA) and quantitative computed tomography (QCT) do not provide information about the material properties. Ultrasonic guided waves can provide information about the material properties as well as the geometry (i.e., cortical bone thickness) and cracks. Wave propagation in cortical bone is much different than in soft tissue. Likewise, there are similarities and differences between wave propagation in bone and mechanical components such as pipes and plates. While steel pipes and plates typically are homogeneous, prismatic, isotropic, uniform thickness, and essentially lossless; long bones are heterogeneous, non-prismatic, anisotropic, variable thickness, and very lossy. Thus, guided wave propagation in long bones is quite complicated, and yet it is not uncommon to use Lamb wave propagation as a surrogate for wave propagation in long bones. The aim of this work is to compare and contrast wave propagation in a long bone with that in a plate to point out where the surrogate Lamb wave analog is useful and where it is not. The semi-analytical finite element (SAFE) method is used to obtain dispersion curves for a cross-section of the plate, and mid-diaphyseal cross-section of the tibial cortex. The frequency domain finite element (FDFE) method is used to account for the non-prismatic nature of the bone and damping.