Effects of the structural anisotropy and the porosity on ultrasonic wave propagation in bovine cancellous bone

Ultrasonic wave propagation in water-saturated bovine cancellous (spongy) bone has been experimentally studied in vitro by a pulse transmission technique. In earlier investigation, fast and slow longitudinal waves have been clearly observed when the acoustic wave propagates in the direction of the trabeculm orientation. In the present study, the propagation speeds of the fast and the slow waves were measured as a function of the propagation angle to the trabecular orientation. Experimental results show that the propagation speed of the fast wave and the amplitude of the slow wave depend greatly on the angle to the trabecular orientation .The speed of the slow wave and the amplitude of the fast wave are little affected by the angle. The propagation speeds of the both waves were also experimerrtaIly examined as a function of porosity. Measured results are discussed in relation to the structural arrisotropy and the porosity using Biot’s theory. 1NTRODUCTION Cancellous bone is a porous material comprised of a connected network of trabeculae, and can be considered as an anisomopic material due to the trabecular mangement, in a previous study,’ it was shown that both fast and slow longitudinal waves propagate through bovine cancellous bone along the trabecular orientation, with the two waves corresponding to “waves of the first and second kind’ as predicted by Biot’s theory.2’3 In the present study, the effect of the trabecular structure on the propagation of the two waves is examined. ACOUSTIC ANISOTROPY IN CANCELLOUS BONE The amplitudes and propagation speeds of the fast and slow waves in water-saturated cacellous bone (porosity ~0.83) were measured as a function of the propagation angle O to the trabecular orientation, and are respectively shown in Fig. 1(a) and ~). In Fig. 1(a), the amplitude of the fast wave gradually increases with the propagation angle, but that of the slow wave rapidly decreases. According to Biot’s theory,2’3 the propagation of the slow wave is related to the motion of the fluid (water) in the pore spaces relative to the trabecular frame. This indicates that the slow wave propagation depends on the structure of the trabecular frame and that fluid in the spaces parallel to the trabeculae moves-more smoothly than that in the perpendicular space. In Fig. 1(b), the propagation speed of the slow wave is almost constant (1400 ds). The speed of the fast wave, however, decreases from 2500 to 1900 m/s and approaches to a value close to that of the slow wave as the angle increases. g + Fast wave \ ~ ~ ‘. : D Slow wave ~ & ~ -5 ~..................~!i...................j....................j u :, > E .“~ z z ; ‘“h : I z -10 ;-..................j ........t ..............................{ f :*, : $! ,: ,: -15 /------------------; --~h-j--------------. ! o 20 40 60 Propagation angle 9 (a) FIGURE 1. Changes in amplitudes and propagation speeds of fast and slow waves in water-saturated bovine carrcellous bone with propagation angle to the trabeculm alignment: (a) amplitude; (b) propagation speed. 4M0