Axial Transmission Method for Long Bone Fracture Evaluation by Ultrasonic Guided Waves: Simulation, Phantom and in Vitro Experiments

Mode conversion occurs when the ultrasonic guided waves encounter fractures. The aim of this study was to investigate the feasibility of fracture assessment in long cortical bone using guided-mode conversion. Mode conversion behavior between the fundamental modes S0 and A0 was analyzed. The expressions proposed for modal velocity were used to identify the original and converted modes. Simulations and phantom experiments were performed using 1.0-mm-thick steel plates with a notch width of 0.5 mm and notch depths of 0.2, 0.4, 0.6 and 0.8 mm. Furthermore, in vitro experiments were carried out on nine ovine tibias with 1.0-mm-wide partial transverse gap break and cortical thickness varying from 2.10 to 3.88 mm. The study confirmed that mode conversion gradually becomes observable as fracture depth increases. Energy percentages of the converted modes correlated strongly with fracture depth, as illustrated by the frequency-sweeping experiments on steel phantoms (100-1100 kHz, r2 = 0.97, p < 0.0069) and the fixed-frequency experiments on nine ovine tibias (250 kHz, r2 = 0.97, p < 0.0056). The approaches described, including mode excitation, velocity expressions and energy percentage criteria, may also contribute to ultrasonic monitoring of long bone fracture healing.