Accurate measurement of guided modes in a plate using a bidirectional approach

Abstract

International audienceMeasuring guided wave propagation in long bones is of interest to the medical community. When an inclination exists between the probe and the tested specimen surface, a bias is introduced on the guided mode wavenumbers. The aim of this study was to generalize the bidirectional axial transmission technique initially developed for the first arriving signal. Validation tests were performed on academic materials such a bone-mimicking plate covered with either a silicon or fat-mimicking layer. For any inclination, the wavenumbers measured with the probe parallel to the waveguide surface can be obtained by averaging the wavenumbers measured in two opposite directions

Predicting bone strength with ultrasonic guided waves

“…The three arrays of piezocomposite elements, aligned along the x 3 -axis (i.e., main fibers orientation for the bone-mimicking phantoms and main bone axis in vivo ), were in contact with the samples and ultrasonic gel was used for coupling. This configuration permits the propagation of GWs in two opposite directions, thus allowing the correction of the bias induced by the eventual inclination between the probe and the samples, which could result from the presence of uneven overlying soft tissue in the measurements area30.…”

“…In short, (1) for each propagation direction, the 120 radio-frequency signals were Fourier transformed with respect to time and stored in a response matrix; (2) a singular value decomposition was applied to the response matrix at each frequency; (3) signal-to-noise ratio enhancement was achieved by removing the singular vectors corresponding to the lowest singular values; (4) a testing vector (i.e., an attenuated spatial plane wave with a complex wave number32) was projected onto the singular vector basis, delivering the so-called Norm function , whose maxima correspond to the wave numbers of the guided modes; (5) combining the data acquired from the two propagation directions, a bidirectional correction was applied to the measurements30; (6) the ( f, k )–pairs were extracted from the corrected Norm function using a dilation operator21; (7) outliers were removed from those pairs by applying statistical denoising over 10 measurement repetitions (successively recorded without moving the probe); and (8) the resulting denoised data on each direction were grouped together, yielding a single set of dispersion curves for each sample. For further details on the data processing, the reader is referred to our previous studies213132.…”

Ultrasound-Based Estimates of Cortical Bone Thickness and Porosity Are Associated With Nontraumatic Fractures in Postmenopausal Women: A Pilot Study

“…The probe was specifically designed to measure guided waves propagating in two opposite directions and thus correct the bias on the guided modes wavenumbers induced by the inclination angle between the probe and the bone due to uneven overlying soft tissues. (39,43) Second, there is an electronic device used to transmit, receive, and digitize signals (Althaïs, Tours, France). The electronic device allows for the excitation of each transmitter successively with a wideband pulse (170 V, 1-MHz central frequency) of -6 dB power spectrum spanning the frequency range from 0.4 to 1.6 MHz.…”

A free plate model can predict guided modes propagating in tubular bone-mimicking phantoms

“…The experimental dispersion curves, representing the frequency-dependent wave numbers of guided modes propagating in the waveguide, were extracted using a method described in our previous publications. 16,17 Briefly, (1) the rf signals were Fourier transformed; (2) a singular value decomposition was applied to the response matrix at each frequency; (3) enhancement of signal-to-noise ratio was achieved by eliminating the singular vectors associated with the lowest singular values; (4) the projection of a testing vector (an attenuated spatial plane wave with a complex wave number 16 ) onto the singular vector basis yielded the so-called Norm function, whose maxima correspond to the wave numbers of the guided modes. The bidirectional correction, combining the data acquired from the two transmitting arrays, was applied to the measurements.…”