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TECHNICAL PAPERS: Bone/Orthopedics

# Determination of Ultrasound Phase Velocity in Trabecular Bone Using Time Dependent Phase Tracking Technique

[+] Author and Article Information
Wei Lin, Erik Mittra, Yi-Xian Qin

Department of Biomedical Engineering, State University of New York at Stony Brook, Stony Brook, NY 11794

J Biomech Eng 128(1), 24-29 (Aug 16, 2005) (6 pages) doi:10.1115/1.2132369 History: Received December 30, 2004; Revised August 16, 2005

## Abstract

Ultrasound velocity is one of the key acoustic parameters for noninvasive diagnosis of osteoporosis. Ultrasound phase velocity can be uniquely measured from the phase of the ultrasound signal at a specified frequency. Many previous studies used fast Fourier transform (FFT) to determine the phase velocity, which may cause errors due to the limitations of FFT. The new phase tracking technique applied an adaptive tracking algorithm to detect the time dependent phase and amplitude of the ultrasound signal at a specified frequency. This overcame the disadvantages of FFT to ensure the accuracy of the ultrasound phase velocity. As a result, the new method exhibited high accuracy in the measurement of ultrasound phase velocity of two phantom blocks with the error less than 0.4%. 41 cubic trabecular samples from sheep femoral condyles were used in the study. The phase velocity of the samples using the new method had significantly high correlation to the bulk stiffness of the samples $(r=0.84)$ compared to the phase velocity measured using fast Fourier transform FFT $(r=0.14)$. In conclusion, the new method provided an accurate measurement of the ultrasound phase velocity in bone.

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## Figures

Figure 1

The top signal contained two tone bursts at 500kHz at different times. The bottom sinusoidal wave was the reference signal with an initial phase of zero. The preset delay of the first tone burst was 2.16μs and the second tone burst was 17.44μs. The tracked amplitude and phase of the tone bursts were also shown.

Figure 2

The anatomic position of the cubic trabecular bone from a sheep femoral condyle

Figure 3

The ultrasound wave was generated by the transmitter driven by the pulse generator and was received by the receiver on the other side. The ultrasound signal was then collected by the oscilloscope and computer. The trabecular sample was surrounded by sound proof material to prevent the ultrasound wave from bypassing the sample.

Figure 4

(a) The original broadband pulse. (b) The correlation of the broadband pulse to sinusoidal tone burst (500kHz). (c) The amplitude of (b) from the phase tracking algorithm. (d) The phase of (b) from the phase tracking algorithm. The average value of phase in the flat region was the measured phase value.

Figure 5

The correlation coefficient (r=0.14, p=0.38) between the ultrasound phase UV at 500kHz using FFT algorithm and the mechanical stiffness of the trabecular sample. The low correlation coefficient indicated that the phase UV from FFT may not be the true phase velocity.

Figure 6

The correlation coefficient (r=0.84, p<0.0001) between the ultrasound phase UV at 500kHz using the phase tracking algorithm and the mechanical stiffness of the trabecular sample

Figure 7

The reference signal (above) and sample signal (below) were aligned at the onset of the pulse for easy comparison. The pulse in the sample signal was wider than the reference signal. Zero crossing point A and point B were the locations where the pulse was extracted for FFT analysis.

Figure 8

The relationship between the error of UV and the error of measured time delay. The X axis was the real time delay and the Y axis was the error of UV if an error of 0.5μs is present. Errors in samples of five different sizes from 1.0cmto3.0cm were shown.

## Errata

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