Ultrasonic characterization of bone quality based on Bayesian probability theory.

Abstract

The hypothesis that underlies the approach to be reported is that ultrasonic properties obtained using Bayesian probability theory can produce reliable estimates of bone quality and fracture risk. A key factor in this approach is to provide quantitative estimates of the confidence to be associated with the derived values of speed of sound (SOS) and frequency dependence of attenuation or broadband ultrasonic attenuation (BUA). Our laboratory demonstrated that when overlapping fast and slow compressional wave mode data are processed using phase spectroscopy and spectral subtraction techniques, interference effects may result in artifacts. In previous reports of studies of bone conducted in vitro, Bayesian probability theory was shown to be an effective method for extracting the ultrasonic properties of the individual fast and slow waves, even in the presence of substantial interference, whereas the same signals processed using conventional methods often exhibited anomalous features including non-causal negative dispersion. The focus of the present report is on the distribution of the probability density functions about their maximum values as a means for providing meaningful estimates of the confidence to be associated with the reported values for SOS and BUA for fast and slow wave modes. [Work supported by NIH R01HL40302, R01AR057433, and NSF CBET-0717830.]