Application of Waterman-Truell theory and the Dynamic Generalised Self-Consistent model to the study of the trabecular bone case

The trabecular bones is a highly inhomogeneous scattering medium composed by a trabecular network surrounded by fluid-like medium (marrow). A simplistic model of this two-phase system can be approximated as cylindrical-shaped inclusions (trabeculae) in a marrow matrix. The ultrasonic wave propagation into a trabecular bone is analysed using the multiple scattering theory of Waterman-Truell (WT) and the Dynamic Generalized Self-Consistent model (DGSCM). The effective phase velocity and attenuation as a function of frequency and inclusions concentration were computed, using the WT and the DGSCM. It is shown that for this simplified bone model with concentration less than 20%, the calculated phase velocity values produced by WT are consistent with published results.