An investigation of pulse-timing techniques for broadband ultrasonic velocity determination in cancellous bone: a...

Berlage wavelets are used to simulate ultrasonic pulses in an unbounded, homogeneous, isotropic and absorptive medium. Intrinsic absorption of the medium is properly described by Kolsky's attenuation, which considers velocity dispersion to meet the causality condition. Several current time-domain velocity measurement techniques have been investigated using numerically simulated pulses for three normalized BUA values: 20, 40 and 60 dB MHz(-1) cm(-1), which mimic experimentally determined values for cancellous bone. The velocities, calculated using first motion transit times, are used as references supported by the Fermat principle of least time. The simulated results for fixed sample thickness indicate that pulse-broadening increases with the transit time of the reference point and the intrinsic absorption of the medium. Comparison shows that the first zero-crossing method yields 3-6% errors in velocity results, better than the cross-correlation method. However, the zero-crossing method gives inconsistent velocity measurement for a medium of 40 dB MHz(-1) cm(-1)1 absorption and three different thicknesses: 0.2, 0.4 and 0.6 cm. A novel technique for velocity measurement is presented using the peak of the envelope of a signal as a reference point to measure transit time difference. The envelope of a signal represents the instantaneous amplitude of the associated analytic signal. The velocities derived using this method differ from the true velocities by only 1.2-2.4%, more accurate than those obtained by the first zero-crossing method. The envelope peak has the additional merits of easy detection and robustness. Most importantly, the envelope technique may be used to yield accurate velocity measurement in cases where an accurate determination of the first motion transit time is sometimes prohibited due to the presence of noise.