A restricted-bandwidth form of the Kramers-Kronig dispersion relations is applied to in vitro measurements of ultrasonic attenuation and dispersion properties of trabecular bone specimens from bovine tibia. The Kramers-Kronig analysis utilizes only experimentally measured properties and avoids extrapolation of ultrasonic properties beyond the known bandwidth. Compensation for the portions of the Kramers-Kronig integrals over the unknown bandwidth is partially achieved by the method of subtractions, where a subtraction frequency acts as an adjustable parameter. Good agreement is found between experimentally measured and Kramers-Kronig reconstructed dispersions. The restricted-bandwidth approach improves upon other forms of the Kramers-Kronig relations and may provide further insight into how ultrasound interacts with trabecular bone.
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December 2005
December 01 2005
Kramers-Kronig analysis of attenuation and dispersion in trabecular bonea) Available to Purchase
Kendall R. Waters;
Materials Reliability Division,
National Institute of Standards and Technology
, Boulder, Colorado 80305
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Brent K. Hoffmeister
Brent K. Hoffmeister
Department of Physics,
Rhodes College
, Memphis, Tennessee 38112
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Materials Reliability Division,
National Institute of Standards and Technology
, Boulder, Colorado 80305
Brent K. Hoffmeister
Department of Physics,
Rhodes College
, Memphis, Tennessee 38112c)
Current affiliation is Volcano Corp., Advanced Technology Laboratory, Cleveland, Ohio, 44195.
a)
Portions of this work were presented in “Application of the Kramers-Kronig relations to measurements of attenuation and dispersion in cancellous bone,” in Proceedings of IEEE International Ultrasonics, Ferroelectrics, and Frequency Control 50th Anniversary Joint Conference, Montréal, Canada, August, 2004.
J. Acoust. Soc. Am. 118, 3912–3920 (2005)
Article history
Received:
May 31 2005
Accepted:
September 29 2005
Citation
Kendall R. Waters, Brent K. Hoffmeister; Kramers-Kronig analysis of attenuation and dispersion in trabecular bone. J. Acoust. Soc. Am. 1 December 2005; 118 (6): 3912–3920. https://doi.org/10.1121/1.2126934
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