Phase velocity analysis of acoustic propagation in trabecular bone

The trabecular bones are highly dispersive acoustic media composed by randomly shaped trabeculae (considered as scatterers) and surrounded by bone marrow. An acoustic wave generated by an incident ultrasonic pulse with respect to the media under study, shows that its velocity and amplitude are a function of the density size and shaped of the scatterers. Two different methods were used to theoretically study this scattering phenomena: i) a self-consistent model proposed by Sabina and Willis, and ii) the multiple-scattering theory of Waterman-Truell. These methods were able to compute the phase velocity and amplitude as a function of operating frequency, density and size of scatterers. The theoretical results were compared with experimental data already published and the phase velocity shows a good agreement for low concentration of scatterers.