Sample thickness dependence of Bayesian and modified least squares Prony’s analysis methods on systematically shortened bovine cancellous bone

Abstract

The goal of this study was to compare the results from two proposed methods for separating fast and slow waves from mixed-mode signals, one using Bayesian probability theory and one using modified least-squares Prony’s (MLSP) [Wear, J. Acoust. Soc. Am. 133, 2490–2501 (2013)], on measurements of cancellous bone. Ultrasonic through-transmission data were acquired on a bovine femoral head specimen for thicknesses ranging from 15 mm to 6 mm. The thickness was reduced in 1 mm increments and measurements were acquired at each sample thickness [Nagatani et al., Ultrasonics 48, 607–612 (2008)]. A Bayesian parameter estimation analysis was performed on the experimentally acquired signals to isolate the fast and slow waves and to obtain estimates of the fast and slow wave’s ultrasonic properties. Results for the corresponding ultrasonic properties were estimated using the modified least squares Prony’s method plus curve fitting (MLSP + CF) on the same bovine sample by Wear et al. (J. Acoust. Soc. Am. 136, 2015–2024). The results show good agreement between the phase velocities estimated by Bayesian and MLSP + CF analysis methods for both the slow wave and the fast wave. Both analysis methods yielded fast and slow wave phase velocities that depended on sample thickness. This may imply that the propagation model, which is used in both methods, may be incomplete.