Fast characterization of two ultrasound longitudinal waves in cancellous bone using an adaptive beamforming technique

Abstract

The received signal in through-transmission ultrasound measurements of cancellous bone consists of two longitudinal waves, called the fast and slow waves. Analysis of these fast and slow waves may reveal characteristics of the cancellous bone that would be good indicators of osteoporosis. Because the two waves often overlap, decomposition of the received signal is an important problem in the characterization of bone quality. This study proposes a fast and accurate decomposition method based on the frequency domain interferometry imaging method with a modified wave transfer function that uses a phase rotation parameter. The proposed method accurately characterized the fast and slow waves in the experimental study, and the residual intensity, which was normalized with respect to the received signal intensity, was less than -20 dB over the bone specimen thickness range from 6 to 15 mm. In the simulation study, the residual intensity was less than -20 dB over the specimen thickness range from 3 to 8 mm. Decomposition of a single received signal takes only 5 s using a laptop personal computer with a single central processing unit. The proposed method has great potential to provide accurate and rapid measurements of indicators of osteoporosis in cancellous bone.

Fast decomposition of two ultrasound longitudinal waves in cancellous bone using a phase rotation parameter for bone quality assessment: Simulation study

“…In this section, we explain the simulation settings used to construct the received signals that pass through bone specimens with various BV/ TV values and transducer sizes. We then briefly describe the modified transfer function and the decomposition strategy that was reported in our previous work (Taki et al, 2015).…”

“…c i f and jd i f denote the attenuation and the time shift, respectively. h i is a phase rotation parameter that is independent of f. In a linear-with-frequency attenuation model, the modified wave transfer function that accounts for the PLV effect is expressed using the following formula (Taki et al, 2015):…”

“…The MV range beamformer uses each of the candidate waves as a reference wave, and it then calculates the rise time and the estimated intensity for each candidate wave separately. The received signal is then normalized using a reference signal to adjust the intensities and phases of all frequency components uniformly (Taki et al, 2012;Taki et al, 2015):…”

“…However, in medical ultrasound imaging, the signal intensity is commonly variable and speckle is signal correlated noise. In the present study, we followed our previous study (Taki et al, 2015) and introduced the assumption that the expectation of the noise intensity is 40 dB lower than the average intensity of the reference signal, that is, g was set to be 40 dB lower than the average intensity of the reference signal X Rl . The MV range beamformer minimizes the output intensity under the constraint of a constant response for the reference signal at a specific measurement depth (Taki et al, 2012).…”

“…We recently reported a fast decomposition method that was based on a minimum variance (MV) range beamformer, called the MV beamformer for range resolution improvement (Taki et al, 2015). The method introduces a modified wave transfer function with a phase rotation parameter that can compensate for the arrival time distribution that is caused by path-length variations within a bone specimen.…”