Dependence of phase velocity on porosity in cancellous bone: Application of the modified Biot-Attenborough model

Abstract

This study aims to apply the modified Biot-Attenborough (MBA) model to predict the dependence of phase velocity on porosity in cancellous bone. The MBA model predicted that the phase velocity decreases nonlinearly with porosity. The optimum values for input parameters of the MBA model, such as compressional speed cm of solid bone and phase velocity parameter s2, were determined by comparing the prediction with the previously published measurements in human calcaneus and bovine cancellous bones. The value of the phase velocity parameter s2=1.23 was obtained by curve fitting to the experimental data only for 53 human calcaneus samples with a compressional speed cm=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 s2 for all 75 cancellous bone samples (53 human and 22 bovine samples) was 1.42 with the rmse of 55 m/s. The latter fit was obtained by using cm=3200 m/s. Although the MBA model relies on empirical parameters determined from the experimental data, it is expected that the model can be usefully employed as a practical tool in the field of clinical ultrasonic bone assessment.