The effects of frequency-dependent attenuation and dispersion on sound speed measurements: Applications in human trabecular bone

Sound speed may be measured by comparing the transit time of a broadband ul trasonic pulse transmitted through an object with that transmitted through a reference water path. If the speed of sound in water and the thickness of the sample are known, the speed of sound in the object may be computed. To measure the transit time differential, a marker such as a zero-crossing, m ay be used. A sound speed difference between the object and water shifts al l markers backward or forward. Frequency-dependent attenuation and dispersi on may alter the spectral characteristics of the waveform, thereby distorti ng the locations of markers and introducing variations in sound-speed estim ates. Theory is derived to correct for this distortion for Gaussian pulses propagating through linearly attenuating, weakly dispersive media. The theo ry is validated using numerical analysis, measurements on a tissue mimickin g phantom, and on 24 human calcaneus samples in vitro. Variations in soft t issue-like media are generally not exceptionally large for most application s but can be substantial, particularly for high bandwidth pulses propagatin g through media with high attenuation coefficients. At 500 kHz, variations in velocity estimates in bone can be very substantial, on the order of 40 t o 50 m/s because of the high attenuation coefficient of bone. In trabecular bone, the effects of frequency-dependent attenuation are considerable, and the effects of dispersion are negligible.