Abstract:

This work is an attempt to measure the nonlinear parameter of porous trabecular bone. Two different methods were applied. One method involves an AM ultrasonic signal transmitted through a bone submerged into water. A part of the signal energy transforms into the low-frequency (the frequency of modulation) signal due to the nonlinearity of the sample. The larger the nonlinear parameter of the sample, the more intensive such a transformation. This low-frequency signal is then picked up with a hydrophone and measured. The other method employs the effect of modulation of higher-frequency ultrasound by lower-frequency vibration applied directly to the bone. The same high frequencies and low frequencies were used in both tests, so the independently measured nonlinear parameters of the samples (cut from the same bone) could be compared. High dissipation of ultrasonic waves in trabecular bone in the frequency range above 100 kHz made it difficult to measure the nonlinear effects. We were able to reliably measure the nonlinear parameter in the frequency range below 100 kHz. Thus the nonlinear parameters were measured for three ultrasonic frequencies 26, 37, and 60 kHz modulated by the vibration frequencies 4.6 and 9.8 kHz. In vitro determined values of the nonlinear parameter for bovine bone used in these tests were in the range 80--120, which is an order of magnitude higher than for nonporous media (e.g., compact bone and liquid). [Work supported by NASA.]