Conventional, Bayesian, and the modified least-squares Prony's plus curve-fitting (MLSP + CF) methods were applied to data acquired using 1 MHz center frequency, broadband transducers on a single equine cancellous bone specimen that was systematically shortened from 11.8 mm down to 0.5 mm for a total of 24 sample thicknesses. Due to overlapping fast and slow waves, conventional analysis methods were restricted to data from sample thicknesses ranging from 11.8 mm to 6.0 mm. In contrast, Bayesian and MLSP + CF methods successfully separated fast and slow waves and provided reliable estimates of the ultrasonic properties of fast and slow waves for sample thicknesses ranging from 11.8 mm down to 3.5 mm. Comparisons of the three methods were carried out for phase velocity at the center frequency and the slope of the attenuation coefficient for the fast and slow waves. Good agreement among the three methods was also observed for average signal loss at the center frequency. The Bayesian and MLSP + CF approaches were able to separate the fast and slow waves and provide good estimates of the fast and slow wave properties even when the two wave modes overlapped in both time and frequency domains making conventional analysis methods unreliable.
This study was supported, in part, by NIH Grant No. R01 AR057433, NIH Grant No. R01 HL040302, and by the Regional Innovation Strategy Support Program of the Ministry of Education, Culture, Sports, and Technology, Japan, and a Grant-in Aid for Scientific Research (B) from the Japan Society for Promotion of Science.
I. INTRODUCTION II. METHODS A. Data acquisition B. Model of wave propagation in cancellous bone C. Bayesian parameter estimation D. Conventional analysis E. MLSP+CF method F. Estimation of apparent frequency III. RESULTS A. Radiofrequency data B. Apparent frequency C. Separation using time gates D. Bayesian estimation E. Comparison of conventional, Bayesian, and MLSP + CF results IV. DISCUSSION A. Trends with sample thickness B. Segmental attenuation V. CONCLUSION