Comparison of Conventional and Bayesian Analysis for the Ultrasonic Characterization of Cancellous Bone

This dissertation investigates the physics underlying the propagation of ultrasonic waves in cancellous bone. Although quantitative ultrasound has the potential to evaluate bone quality even better than the current gold standard X-ray based modality, its clinical utility has been hampered by the incomplete understanding of the mechanisms governing the interaction between ultrasound and bone. Therefore, studies that extend the understanding of the fundamental physics of the relationship between ultrasound and trabecular bone tissue may result in improved clinical capabilities. Ultrasonic measurements were carried out on excised human calcaneal specimens in order to study the effects of overlapping fast and slow compressional mode waves on the ultrasonic parameters of attenuation and velocity. Conventional analysis methods were applied to received sample signals that appeared to contain only a single wave mode. The same signals were also analyzed using a Bayesian parameter estimation technique that showed that the signals, which appeared to be only a single wave, could be separated into fast and slow wave components. Results demonstrated that analyzing the data under the assumption that only a single wave mode is present, instead of two interfering waves, yielded a phase velocity that lay between the fast and slow wave velocities and a broadband ultrasound attenuation that was much larger than the ultrasound attenuations of the individual fast and slow waves. The fast and slow wave ultrasonic parameters were found to correlate with microstructural parameters, including porosity, determined by microCT measurements. Simulations of fast and slow wave propagation in cancellous bone were carried out to demonstrate the plausibility of a proposed explanation for an anticipated sample-thickness dependence of the apparent attenuation in bovine bone. The results showed that an apparent sample-thickness dependence could arise if the fast and slow waves are not separated sufficiently and if frequency-domain analysis is not performed on broadband data. The sample-thickness dependence of the ultrasonic parameters was explored further using experimental data acquired on an equine cancellous bone specimen that was systematically shortened. The thickness of the sample varied the degree to which the fast and slow waves overlapped, permitting the use of conventional analysis methods for sufficiently long sample lengths. Bayesian parameter estimation was performed successfully on data from all sample lengths. The ultrasonic parameters obtained by both conventional and Bayesian analysis methods were found unexpectedly to display small, systematic variations with sample thickness. A very thorough and systematic series of studies were carried out on one-mode Lexan phantoms to investigate the potential cause of the observed sample-thickness dependence. These studies ruled out a series of potential contributors to the sample-thickness dependence, but yielded no clear cause. Although the clinical implications of the small but systematic sample-thickness dependence may be negligible, these studies may provide additional insights into the propagation of ultrasonic waves in cancellous bone and how to maximize the quality of information obtained

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

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