Application of the Kramers-Kronig relations to measurements of attenuation and dispersion in cancellous bone


Ultrasonic (US) assessment of fracture risk in osteoporotic patients is based on measurements of broadband ultrasonic attenuation and speed of sound (SOS) of cancellous bone. Discrepancies in estimates of SOS can result from dispersion and frequency-dependent attenuation. An improved understanding of the relation between attenuation and dispersion in cancellous bone could benefit both numerical and experimental investigations of the effects of these properties on estimates of SOS. The Kramers-Kronig (K-K) dispersion relations are used to investigate the relation between attenuation and dispersion. We consider a finite-bandwidth form of the K-K relations that uses the US properties over only the experimental bandwidth. In vitro measurements of cancellous bone were performed to validate this technique. Cancellous bone specimens were obtained from the proximal end of four bovine tibia and prepared with the axis of measurement along the medial-lateral (ML) and superior-inferior (SI) directions. Measurements were performed by use of a through-transmission, immersion technique. The attenuation coefficient and phase velocity were determined for each specimen. We found that dispersion correlated well with apparent density for ML specimens (r = 0.95) but less so for SI specimens (r = 0.61). Finite-bandwidth KK analysis of the attenuation coefficient predicted the corresponding phase velocity. We observed good agreement between the measured and K-K predicted dispersion (r = 0.99) for all specimens. Keywords-attenuation; cancellous bone; dispersion; fracture risk; Kramers-Kronig relations; osteoporosis; ultrasound characterization

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@inproceedings{Waters2004ApplicationOT, title={Application of the Kramers-Kronig relations to measurements of attenuation and dispersion in cancellous bone}, author={Kendall R. Waters and Brent K Hoffmeister and Julie A Javarone}, year={2004} }