The nonlinear transition period of broadband ultrasound attenuation as bone density varies

The purpose of this study was to determine whether a transition period occurs between cortical and cancellous bone in the relationship between ultrasound parameters [broadband ultrasound attenuation (BUA), and ultrasonic velocity] and density. Twenty-two cancellous bone discs were obtained from proximal bovine tibiae. Also included were three samples of human vertebral cancellous bone from an elderly female and four samples of bovine cortical bone. Ultrasonic velocity did not show any transition period as density varied from cancellous to cortical bone. Ultrasonic velocity exhibited a definite linear dependence on density over the entire range examined. However, BUA has shown a transition period as density varied. Although BUA increased linearly with density for a low density cancellous bone tested (below 0.64 gcm-3), the dependence of BUA on density is nonlinear with a downwardly inflected parabola shape when covering a wide density range (0.130-0.913 gcm-3), of cancellous bone. When one includes cortical bone, the parabola tends to level off in a slow exponential decay. This nonlinear dependence may help to understand the characteristics of BUA measurement.