Influence of the precision of spectral backscatter measurements on the estimation of scatterer size in cancellous bone

Abstract

Ultrasonic backscatter measurements can be used to characterize trabecular bone structure and to estimate trabecular thickness (Tb.Th, i.e., the size of the scatterers). Our objective was to evaluate the performance of this estimator as well as others spectral estimators, like the frequency dependence and the mid-band amplitude of the backscatter coefficient. The performance of these estimators is degraded mainly by two factors: interference noise due to random positioning of the scatterers and attenuation. We have simulated rf-lines backscattered from trabecular bone assuming a random positioning of the trabeculae (leading to a fully developed speckle), a Gaussian form factor for the scatterers and a linear-frequency dependent attenuation. It is found that the variance in the estimation of the frequency dependence of the backscatter coefficient is as high as the variance due the biological variability in Tb.Th, in agreement with the results showed by K. Wear [J. Acoust. Soc. Am. SA, 110 (2001)]. In contrast, the variances on the mid-band amplitude and on the estimated trabecular thickness are lower than the variance due the biological variability. We also show that the effect of attenuation may be compensated by using an appropriate attenuation-compensation function. These results suggest that the inverse problem can be appropriately addressed.