A numerical method to predict the effects of frequency-dependent attenuation and dispersion con speed of sound estimates in cancellous bone

Many studies have demonstrated that time-domain speed-of-sound (SOS) measur ements in calcaneus are predictive of osteoporotic fracture risk. However, there is a lack of standardization fur this measurement. Consequently, diff erent investigators using different measurement systems and analysis algori thms obtain disparate quantitative values for calcaneal SOS, impairing and often precluding meaningful comparison and/or pooling of measurements. A nu merical method has been developed to model the effects of frequency-depende nt attenuation and dispersion on transit-time-based SOS estimates. The nume rical technique is based on a previously developed linear system analytic m odel for Gaussian pulses propagating through linearly attenuating, weakly d ispersive media. The numerical approach is somewhat more general in that it can be used to predict the effects of arbitrary pulse shapes and dispersio n relationships. The numerical technique, however, utilizes several additio nal assumptions (compared with the analytic model) which would be required for the practical task of correcting existing clinical databases. These inc lude a single dispersion relationship for all calcaneus samples, a simple l inear model relating phase velocity to broadband ultrasonic attenuation, an d a constant calcaneal thickness. Measurements on a polycarbonate plate and 30 human calcaneus samples were in good quantitative agreement with numeri cal predictions. In addition, the numerical approach predicts that in cance llous bone, frequency-dependent attenuation tends to be a greater contribut or to variations ire transit-time-based SOS estimates than dispersion. This approach may be used to adjust previously acquired individual measurements so that SOS data recorded with different devices using different algorithm s may be compared in a meaningful fashion.