Determining attenuation properties of interfering fast and slow ultrasonic waves in cancellous bone

Abstract

Previous studies have shown that interference between fast waves and slow waves can lead to observed negative dispersion in cancellous bone. In this study, the effects of overlapping fast and slow waves on measurements of the apparent attenuation as a function of propagation distance are investigated along with methods of analysis used to determine the attenuation properties. Two methods are applied to simulated data that were generated based on experimentally acquired signals taken from a bovine specimen. The first method uses a time-domain approach that was dictated by constraints imposed by the partial overlap of fast and slow waves. The second method uses a frequency-domain log-spectral subtraction technique on the separated fast and slow waves. Applying the time-domain analysis to the broadband data yields apparent attenuation behavior that is larger in the early stages of propagation and decreases as the wave travels deeper. In contrast, performing frequency-domain analysis on the separated fast waves and slow waves results in attenuation coefficients that are independent of propagation distance. Results suggest that features arising from the analysis of overlapping two-mode data may represent an alternate explanation for the previously reported apparent dependence on propagation distance of the attenuation coefficient of cancellous bone.

Cancellous bone fast and slow waves obtained with Bayesian probability theory correlate with porosity from computed tomography

“…3 This method has been validated with simulated data 4 and with experimental data from phantoms. 5 It has been applied to data from cancellous bone, and the resulting separated fast and slow waves are consistent and plausible.…”

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

“…We have previously demonstrated an approach utilizing Bayesian probability theory that is capable of isolating the fast and slow waves, even in cases of extreme overlap and interference . This Bayesian technique has proven successful at separating the two wave modes in experimental data from plastic phantoms (Anderson et al, 2010) and from cancellous bone (Nelson et al, 2011;Hoffman et al, 2012). However, in the previous studies using Bayesian methods on measurements of cancellous bone, the fast and slow waves overlapped in time and frequency domains, thus, not permitting the use of conventional analysis methods.…”

“…In Fujita et al (2013) and in other studies (Nagatani et al, 2008;Nelson et al, 2011), the reported attenuation properties of the fast and slow waves were for thin slabs, or segments, of the bone sample instead of for the entire bulk of the bone specimen, as was employed in this study. In both Fujita et al (2013) and Nagatani et al (2008), a timedomain method comparing the peak amplitudes of the fast and slow waves for successive sample thickness was employed to determine the apparent (segmental) attenuation for the fast and slow waves.…”

“…As discussed in Nelson et al (2011), time-domain analysis methods may be inappropriate for broadband ultrasonic wave propagation. Since the Bayesian probability theory technique can recover the individual fast and slow waves, it permits the spectral content of the individual fast and slow waves to be determined using frequencydomain methods.…”

“…This method has been described in previous publications from our laboratory Anderson et al, 2010;Nelson et al, 2011;Hoffman et al, 2012). Bayesian probability theory was used to estimate the six fast and slow wave ultrasonic parameters, {A fast , A slow , b fast , b slow , c fast ðf 0 Þ, c slow ðf 0 Þ}, in the wave propagation model detailed above.…”