Quantitative ultrasound has drawn considerable interests in the assessment of osteoporosis and bone fracture evaluation. Currently, ultrasonic evaluation of the fractured long bone is primarily based on axial detection of the First Arriving Signals (FAS), corresponding to the lateral wave propagating along the surface between the soft-tissue and cortex. Owing to the pipe-shaped geometry, long cortical bone can also support ultrasonic guided waves propagation. In particular, when the guided modes propagate throughout the fracture site, newly converted modes come out apart from the reflection and transmission. The aim of this study is to investigate the mode conversion on the fracture site and analyze the feasibility of mode conversion based long bone fracture evaluation.
Guided waves theory and numerical simulation were employed to analyze the mode conversion in the fractured long bone. Acrylic pipes were used as phantoms in the experiments, where the pipe thicknesses were of 1.5 mm, 2.5 mm and 3.0 mm. The artificial notches were circumferentially sawed on the pipes to imitate different fracture status. Under the narrowband excitation of 200 kHz, five low-order modes, i.e. longitudinal modes L(0,1) and L(0,2) and the flexural modes F(1,1), F(1,2) and F(1,3), were discussed. Finally, group velocity and modal energy were in vitro assessed in sheep tibias by the axial transmission method.
In simulation, it was demonstrated that obvious mode conversion phenomena occurred on the fracture site, generating the newly converted modes. The velocity of the converted package followed the proposed velocity relations and existed between the faster and slower original guided modes. Original and converted wave packages were then extracted from the measured signals of the phantoms. An energy criterion was established to quantitatively describe the mode conversion degree. It was illustrated that mode conversion enlarged monotonically with the circumferential notch-depth increasing. Energy percentages of the converted and original packages presented linear exchange relations with fracture percentage increasing. In the in vitro experiments, it was demonstrated that the energy percentages can be used to evaluate the fractures in the sheep tibias.
These results suggest that mode conversion theory of the guided waves can be utilized to interpret the ultrasound propagation in the fractured long cortical bone. The proposed energy criteria enable to reflect the mode conversion degree, which highly correlates to the long bone fracture status. We conclude that the energy percentages of ultrasound guided mode conversion may offer great potentials of the long cortical bone fracture evaluation.