Phase and group velocities of fast and slow compressional waves in trabecular bone

This Letter is an extension to a multilayer model of porous bone first proposed by Hughes et al. [Ultrasound Med. Biol. 25, 811-821 (1999)]. Both slow and fast compressional waves propagate when the acoustic wave propagation is parallel to the trabecular alignment. However, a slow wave disappears at high refraction angles. To explain this phenomenon, the multilayer model is extended to compute group velocity surface and arrival times with an angle. Two major effects are highlighted as the refraction angle increases. First, the energy of the slow wave is refracted from the phase propagation direction. Second, the signals of fast and slow waves overlap. As a consequence, the slow wave may not be observed for a refraction angle greater than 40 degrees, which is in agreement with previous experimental data published by Hughes et al. and others.