Ultrasonic backscatter characterization of cancellous bone using a general Nakagami statistical model**Project supported by the National Natural Science Foundation of China (Grant Nos. 11874289, 11827808, 11504057, 11525416, and 81601504) and the Fundamental Research Funds for the Central Universities.

Abstract

The goal of this study is to analyze the statistics of the backscatter signal from bovine cancellous bone using a Nakagami model and to evaluate the feasibility of Nakagami-model parameters for cancellous bone characterization. Ultrasonic backscatter measurements were performed on 24 bovine cancellous bone specimens in vitro and the backscatter signals were compensated for the frequency-dependent attenuation prior to the envelope detection. The statistics of the backscatter envelope were modeled using the Nakagami distribution. Our results reveal that the backscatter envelope mainly followed pre-Rayleigh distributions, and the deviations of the backscatter envelope from Rayleigh distribution decreased with increasing bone density. The Nakagami shape parameter (i.e., m) was significantly correlated with bone densities (R=0.78–0.81, ) and trabecular microstructures (, ). The scale parameter (i.e., ) and signal-to-noise ratio (SNR) also yielded significant correlations with bone density and structural features. Multiple linear regressions showed that bone volume fraction (BV/TV) was the main predictor of the Nakagami parameters, and microstructure produced significantly independent contribution to the prediction of Nakagami distribution parameters, explaining an additional 10.2% of the variance at most. The in vitro study showed that statistical parameters derived with Nakagami model might be useful for cancellous bone characterization, and statistical analysis has potential for ultrasonic backscatter bone evaluation.