Parameter Estimation in Ultrasonic Measurements on Trabecular Bone

Ultrasonic tissue characterization has shown promise for clinical diagnosis of diseased bone (e.g., osteoporosis) by establishing correlations between bone ultrasonic characteristics and the state of disease. Porous (trabecular) bone supports propagation of two compressional modes, a fast wave and a slow wave, each of which is characterized by an approximately linear-withfrequency attenuation coefficient and monotonically increasing with frequency phase velocity. Only a single wave, however, is generally apparent in the received signals. The ultrasonic parameters that govern propagation of this single wave appear to be causally inconsistent [1]. Specifically, the attenuation coefficient rises approximately linearly with frequency, but the phase velocity exhibits a decrease with frequency. These inconsistent results are obtained when the data are analyzed under the assumption that the received signal is composed of one wave. The inconsistency disappears if the data are analyzed under the assumption that the signal is composed of superposed fast and slow waves. In the current investigation, Bayesian probability theory is applied to estimate the ultrasonic characteristics underlying the propagation of the fast and slow wave from computer simulations. Our motivation is the assumption that identifying the intrinsic material properties of bone will provide more reliable estimates of bone quality and fracture risk than the apparent properties derived by analyzing the data using a one-mode model.