Velocity dispersion of acoustic waves in cancellous bone

Abstract

Measurement of ultrasonic attenuation and velocity in cancellous bone are being applied to aid diagnosis of women with high fracture risk due to osteoporosis. However, velocity dispersion in cancellous bone has received little attention up to now. The overall goal of this research was to characterize the velocity dispersion of human cancellous bone based on a spectral analysis of ultrasound transmitted through the bone specimens. We have followed a systematic approach, beginning with the investigation of a test material, moving on to the investigation of bone specimens. Particular attention is given to diffraction effect, a potential source of artifacts. Parametric images of phase velocity (measured at the center frequency of the pulse spectrum), slope of attenuation coefficient (dB/cm/MHz) and velocity dispersion were obtained by scanning 15 bone specimens. We have demonstrated that the diffraction effect is negligible in the useful frequency bandwidth, and that the ultrasonic parameters reflect intrinsic acoustic properties of bone tissue. The measured attenuation showed approximately linear behavior over the frequency range 200 to 600 kHz. Velocity dispersion of cancellous bone in the frequency range 200 to 600 kHz was unexpectedly found to be either negative or positive and not correlated with the slope of attenuation coefficient. There was a highly significant correlation between the slope of attenuation coefficient and phase velocity at the center frequency of the spectrum. This behavior contrasts with other biological or nonbiological materials where the local form of the Kramers-Kronig relationship provides accurate prediction of velocity dispersion from the experimental frequency dependent-attenuation for unbounded waves.

Dependences of quantitative ultrasound parameters on frequency and porosity in water-saturated nickel foams

“…This apparent negative dispersion observed in the nickel foams is consistent with the behavior in human calcaneal trabecular bone in vitro and in vivo. [13][14][15][16][17] Similar negative dispersion was also observed in trabecular-bone-mimicking phantoms consisting of parallel nylon wires and randomly distributed nylon filaments. 4,7 In contrast, Zhang et al found that the seven aluminum foams exhibited the positive dispersion at frequencies from 0.7 to 1.3 MHz while the other two foams displayed the minor negative dispersion.…”

Determining attenuation properties of interfering fast and slow ultrasonic waves in cancellous bone

“…14,15,17 Previous work has demonstrated, however, that when decomposed, the fast wave and slow wave each exhibit positive dispersion. 19,27 Negative dispersion has been measured not only in trabecular bone [29][30][31][32][33] and cortical bone 34 in vitro but also in trabecular bone-mimicking phantoms. 35,36 Several models have been proposed that predict negative dispersion including multilayer models, 31,37 multiple scattering models, 38 and independent scattering models.…”

Bayesian estimation of the underlying bone properties from mixed fast and slow mode ultrasonic signals

“…Measurements of the ultrasonic characteristics of bone to assess the risk of fracture due to osteoporosis are often based on the frequency dependence of attenuation ͑Droin et al, 1998;Langton et al, 1984;Wear and Armstrong, 2001͒. Bone attenuates ultrasound in a manner that is approximately linear with frequency ͑Droin et al., 1998;Wear, 2000a͒ so that the attenuation characteristics can be reported as a rate of change with frequency of the attenuation coefficient times the distance traveled, known as broadband ultrasound attenuation ͑BUA͒, or, if normalized with bone thickness, the normalized broadband ultrasound attenuation ͑nBUA͒.…”