Using ultrasonic guided waves to assess long bone fractures and fracture healing has become a promising diagnostic issue. But the multimode overlap of the guided waves challenges the quantitative evaluation and clinical application. In the preformed study, in order to simplify the signal interpretation, the low-frequency sinusoidial signals were used to only excite SO and A0 modes in fractured long bones. The amplitudes of SO and A0 modes were numerically analyzed with variation in crack width and fracture angle. Numerical simulation, based on the two-dimension finite-difference time-domain （2D-FDTD） reveals that both SO and A0 amplitudes decrease with the fracture widening. However, the increase in fracture angle gradually enhances the A0 amplitude, while with respect to the SO mode, its amplitude shows a non-monotonic trend to the variation in fracture angle with a turning point around 45°. The amplitude ratio between S0 and A0 can reflect the variations in crack width and fracture angles. The simulation illustrates that ultrasonic guided SO and A0 modes are sensitive to the degree of both vertical and oblique fractures in the long cortical bone. These findings may be helpful for fractures diagnosis and healing evaluation of the long bone.
The quadratic transformation method is proposed to estimate the trabecular spac- ing （Tb.Sp）, an important index for osteoporosis diagnosis. The performance of this algorithm was investigated by scatter model, two-dimension finite difference time domain （2D-FDTD） simulation and in vitro experiments of bovine cancellous bone specimens. Comparing with the other four methods autoregressive cepstrum （AR）, adaptive filter- autoregressive cepstral （AFAR）, inverse filter-autoregressive eepstrum （InvAR）, and simplified inverse filter tracking （SIFT）, quadratic transformation is much more stable and accurate. The results demonstrated that quadratic transformation is a great algorithm for Tb.SD estimation.
