An experimental study on the ultrasonic wave propagation in cancellous bone: Waveform changes during propagation

Abstract

Wave propagation in a trabecular bone was experimentally investigated using an acoustic tube. For the purposes of this study, a cubic sample was gradually filed so the waveform change due to the sample thickness could be observed. The initial sample showed clear two-wave separation. As the sample became thinner, the fast and slow waves gradually overlapped. The apparent frequencies and amplitudes of the fast waves obtained from the time domain data decreased significantly for the smaller thicknesses. This indicates an increase in the apparent attenuation at the initial stage of the propagation. Next the authors investigated the distribution of the ultrasonic field after the transmission through the cancellous bone sample. In addition to a large aperture receiver, a needle-type ultrasonic transducer was used to observe the ultrasonic field. Within an area of the same size of the large transducer, the waveforms retrieved with the needle sensor exhibited high spatial variations; however, the averaged waveform in the plane was similar to the waveform obtained with the large aperture receiver. This indicates that the phase cancellation effect on the surface of the large aperture receiver can be one of the reasons for the strong apparent attenuation observed at the initial stages of the propagation.

Conventional, Bayesian, and Modified Prony's methods for characterizing fast and slow waves in equine cancellous bone

“…The data acquisition process has been described previously in Fujita et al (2013). A brief overview will be given here.…”

“…At the longest sample thickness, the center frequency of the slow wave was $814 kHz. The results of the (frequency-domain) centroid frequencies were compared to both the time-domain apparent frequencies, determined using the methods reported in Fujita et al (2013), and the predicted center frequencies, f c , determined by Eq. (6).…”

“…In Fujita et al (2013), the apparent center frequencies of the fast waves and slow waves at each sample length were determined using time intervals of peaks and zero-crossings in the time-domain signals. As discussed in Nelson et al (2011), time-domain analysis methods may be inappropriate for broadband ultrasonic wave propagation.…”

“…Since the angle of insonification was parallel to the predominant trabecular orientation and the bone volume fraction of the specimen was quite high, the separation between the fast wave and slow wave velocities was rather large. In the present study, we analyzed data acquired in the same laboratory from a specimen adjacent to the specimen used to acquire the data presented in Fujita et al (2013). In the current study, conventional, Bayesian, and MLSP þ CF analysis techniques were employed to analyze the data over a wide range of sample thicknesses.…”

“…Therefore, there was no appropriate standard for comparison with the Bayesian method available. Fujita et al (2013) performed through-transmission measurements on equine cancellous bone that was gradually and systematically shortened. Since the angle of insonification was parallel to the predominant trabecular orientation and the bone volume fraction of the specimen was quite high, the separation between the fast wave and slow wave velocities was rather large.…”