Single mode analysis appears to overestimate the attenuation of human calcaneal bone based on Bayesian-derived fast and slow wave mode analysis

Abstract

Our laboratory in St. Louis previously demonstrated that a signal transmitted through cancellous bone might be comprised of two interfering (fast and slow wave) modes even though it appears to consist of only a single mode. We also showed that a Bayesian probability technique permits separation of ultrasonic fast and slow waves in cancellous bone even when the modes overlap substantially in time. In this study, the effects of interfering fast and slow waves on measurements of the phase velocity and normalized broadband ultrasonic attenuation were addressed. Ultrasonic measurements were taken on 8 human calcaneal samples in vitro at 9 sites each. The data were analyzed two ways: 1) assuming that the received signal contained only a single wave mode and 2) assuming that the received signal contained both fast and slow wave modes. A Bayesian analysis method was implemented to recover the individual properties of the fast and slow waves. For all eight samples, the phase velocity obtained from the one-mode analysis always lay between the fast and slow wave phase velocities. The overall mean ± SD phase velocities at 500 kHz for the eight samples were (1645 ± 68) m/s, (1523 ± 40) m/s, and (1565 ± 52) m/s for the fast, slow, and one mode waves, respectively. normalized broadband ultrasound attenuationFor all samples, the normalized broadband ultrasound attenuation (nBUA) value obtained from the one-mode analysis was consistently larger than the corresponding values from either the fast or slow waves. The overall mean ± SD normalized broadband ultrasound attenuation for the eight samples for the fast, slow, and single mode waves were (5.6 ±4.0) dB/cm/MHz, (4.1 ± 3.0) dB/cm/MHz, and (19.3 ± 8.2) dB/cm/MHz, respectively. Microarchitectural parameters were also measured using microCT. The phase velocities and nBUAs for both the fast and slow waves showed moderate inverse correlations with porosity and trabecular spacing (r = -0.70 to -0.93).