Application of the Kramers-Kronig relations to Measurements of Attenuation and Dispersion in Cancellous Bone
Kendall Waters, B K. Hoffmeister, J A. Javarone
Ultrasonic (U5) assessment of fracture risk in osteoporotic patients is based on measurements of broadband ultrasonic attenuation and speed-of-sound (505) of cancellous bone. Discrepancies in estimates of 505 can result from dispersion and frequency-dependent attenuation. An improved understanding of the relation between attenuation and dispersion in cancellous bone could benefit numerical and experimental investigations of the effects of these properties on estimates of 505. The Kramers- Kronig (K-K) dispersion relations are used for the investigation of attenuation and dispersion. We consider a finite-bandwidth form of the K-K relations that uses the U5 properties over only the experimental bandwidth. In vitro measurements of cancellous bone are 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-Iateral (ML) and superior-inferior (51) directions. Measurements were performed using a through-transmission, immersion technique. The attenuation coefficient and phase velocity were determined for each specimen. Dispersion correlated well with apparent density for ML specimens (r=-0.95) but less so for 51 specimens (r=0.61). Finite-bandwidth K-K analysis of the attenuation coefficient predicted the corresponding phase velocity. Good agreement was observed between the measured and K-K predicted dispersion (r=0.99) for all specimens.
, Hoffmeister, B.
and Javarone, J.
Application of the Kramers-Kronig relations to Measurements of Attenuation and Dispersion in Cancellous Bone, Proc., IEEE Intl. Ultrasonics Symp., Montreal, CA, USA, [online], https://doi.org/10.1109/ULTSYM.2004.1417787
(Accessed December 3, 2023)