(Received November 15, 2004; accepted January 22, 2005; published June 24, 2005)
In previous studies, two longitudinal waves, the fast and slow waves, were observed in cancellous bone. The propagation speed of the fast wave increases with bone density and that of the slow wave remains almost constant. The attenuation constant of the fast wave is much higher than that of the slow wave and is independent of bone density, but the attenuation constant of the slow wave increases with bone density. In the present study, experimental results on ultrasonic waves transmitted through cancellous bone show that the fast wave amplitude increases proportionally and the slow wave amplitude decreases inversely with bone density. The dependence of the fast wave amplitude on bone density cannot be explained by the attenuation constant. The ultrasonic wave propagation path through cancellous bone is modeled to specify the causality between ultrasonic wave parameters and bone density. Then bone density and bone elasticity are quantitatively formulated.