Kramers-Kronig analysis of attenuation and dispersion in trabecular bone.
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.
Waters
Kendall R
KR
Materials Reliability Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA.
Hoffmeister
Brent K
BK
D000162:Acoustics; D000818:Animals; D002417:Cattle; D066298:In Vitro Techniques; D008954:Models, Biological; D010024:Osteoporosis / Q000000981:diagnostic imaging; D013977:Tibia / Q000000981:diagnostic imaging*; D014129:Trabecular Meshwork / Q000000981:diagnostic imaging*; D014465:Ultrasonics; D014463:Ultrasonography