Incorporation of explicit transmission coefficients in the wave propagation model enhances the results of Bayesian analysis of fast and slow wave propagation in cancellous bone

Abstract

Ultrasonic propagation in cancellous bone is a challenging coupled-mode problem as a result of the existence of two compressional modes, a fast wave and a slow wave. In previous reports, we demonstrated that Bayesian probability theory combined with a simple wave propagation model permits the estimation of fast and slow wave velocities and slopes of attenuation (nBUA), even in cases where the two waves overlap significantly. The hypothesis that underlies the current work is that by explicitly specifying the functional forms of the transmission coefficients at the entry and exit surfaces additional information that might further characterize bone structure could be obtained. This extension of the propagation model leads directly to the introduction of fast wave and slow wave effective mass densities, ρl <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fast</sub> and ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">slow</sub> . In the long view, this work represents a step toward improving the utility of bone sonometry for monitoring pharmacological treatment designed to reverse osteoporosis.