Predictions of the modified Biot–Attenborough model for the dependence of phase velocity on porosity in cancellous bone

Abstract

The modified Biot–Attenborough (MBA) model for acoustic wave propagation in porous media has been found useful to predict wave properties in cancellous bone. The present study is aimed at applying the MBA model to predict the dependence of phase velocity on porosity in cancellous bone. The MBA model predicts a phase velocity that decreases nonlinearly with porosity. The optimum values for input parameters of the MBA model, such as compressional speed c m of solid bone and phase velocity parameter s 2, were determined by comparing the predictions with previously published measurements in human calcaneus and bovine cancellous bone. The value of the phase velocity parameter s 2 = 1.23 was obtained by curve fitting to the experimental data for 53 human calcaneus samples only, assuming a compressional speed c m = 2500 m/s of solid bone. The root-mean-square error (RMSE) of the curve fit was 15.3 m/s. The optimized value of s 2 for all 75 cancellous bone samples including 22 bovine samples was 1.42 with a value of 55 m/s for the RMSE of the curve fit. The latter fit was obtained by using of a value of c m = 3200 m/s. Although the MBA model relies on the empirical parameters determined from experimental data, it is expected that the model can be usefully employed as a practical tool in the field of clinical ultrasonic bone assessment.