Guided ultrasound wave propagation in intact and healing long bones.

Ultrasonic evaluation of bone fracture healing has been traditionally based on the measurement of the propagation velocity of the first arriving signal (FAS). However, the FAS in general corresponds to a lateral wave that propagates along the bone's subsurface. In this work, we study guided ultrasound propagation in intact and healing bones. We developed a 2-D model of a bone-mimicking plate in which the healing process was simulated as a 7-stage process, and we also carried out ex vivo experiments on an intact tibia. Guided waves were represented in the time-frequency (t-f) domain of the signal by incorporating the Lamb wave theory. Three t-f distribution functions were examined, namely the reassigned Spectrogram, the smoothed-pseudo Wigner-Ville, and the reassigned version of it. For the intact plate case, we found that the S2, A3 Lamb modes were the dominant waves for a broadband 1-MHz excitation, and the S2, S0 for a 500-kHz excitation. During the simulated healing process, the mechanical and geometrical callus properties affected the theoretically anticipated Lamb modes. The propagation of guided waves throughout the thickness of the cortical bone and their sensitivity to both the mechanical and structural changes during healing can supplement velocity measurements so as to enhance the monitoring capabilities of ultrasonic evaluation. Nevertheless, the applicability of the Lamb wave theory to real bones has several limitations mostly associated with neglecting the inhomogeneity, anisotropy and irregular geometry of bone.