Accurate characterization of ultrasonic guided waves propagating in cortical bone acquired by a single transmitter–receiver pair using adaptive signal processing

Abstract

The characterization of Lamb waves propagating in cortical bone is important for diagnosing bone quality. Using fewer transmitters and receivers is desirable for low-cost diagnosis. Thus, in this study, we propose a method based on an adaptive beamforming technique to characterize Lamb waves using a single transmitter-receiver pair. We begin by estimating the longitudinal and shear wave velocities as these are the primary determinants of the Lamb wave transfer function. The frequency domain interferometry (FDI) with Capon method, which is one of the adaptive signal processing methods, accurately estimates the position of the wave having the same frequency components as the reference wave. The high-frequency components of the zeroth-order modes of the Lamb wave are almost non-dispersive. Therefore, we use the transmitted wave as the reference and apply the Capon method to the high-frequency components where the phase velocity is converge to the Rayleigh wave velocity. Because the Rayleigh wave velocity is determined by the longitudinal and shear wave velocities, we can estimate candidates of the velocities by using estimated Rayleigh wave velocity. Finally, we calculate the transfer function using a least squares method (LSM) applied to the estimated velocities. We conduct 2-D numerical simulations using a semi-analytical finite element method. The center frequency of the transmitted wave is 1.0 MHz, the thickness of cortical bone is 5.0 mm, signal-to-noise ratio is 20 dB, longitudinal and shear wave velocities are 4430 and 2120 m/s, respectively, and the distance from the transmitter to the receiver is 21 mm. We use eight candidates in the fitting process using LSM. The predicted longitudinal and shear wave velocities were 4458 and 2116 m/s, respectively, and the residue normalized with respect to the received signal intensity was −16 dB. The proposed method accurately predicts the waveforms and longitudinal and shear wave velocities.