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Resonant ultrasound spectroscopy (RUS) allows identification of the elastic properties of solid materials vibrating under an ultrasonic excitation from the measurement of their inherent frequencies. Retrieving the resonant frequencies is therefore a key signal processing step in RUS, which is generally addressed using a linear prediction filter. In this study, the Empirical Mode Decomposition (EMD) was proposed to retrieve the inherent resonant frequencies of materials with low Q-factor (quality factor). EMD was used to decompose the frequency response of the tested sample into intrinsic mode functions (IMF). The relevant IMF was selected from which the resonant frequencies could be computed. A bovine cortical bone sample was measured and its resonant frequencies were identified with EMD and with linear prediction for comparison. The elastic constants were also derived using both approaches. The number of resonant frequencies (45) extracted with EMD was larger than the number of frequencies (26) identified using the classical linear prediction approach. In particular, EMD proved to be more effective in detecting resonance in the higher frequency range (i.e., between 235 kHz and 400 kHz), i.e., on the weak excitation side where the spectral amplitude is low. The number of measured frequencies matching with the calculated ones was also larger for EMD (39) compared to linear prediction (17). If these results are confirmed in further studies on more samples, EMD combined with RUS, by improving the extraction of resonant frequencies for low Q-factor materials, may be considered to be useful not only to improve the reliability of the estimation of elastic parameters, but also to extend the application range of RUS., (Copyright © 2019 Elsevier B.V. All rights reserved.)

Guided waves-based techniques are currently under development for quantitative cortical bone assessment. However, the signal interpretation is challenging due to multiple mode overlapping. To overcome this limitation, dry point-contact transducers have been used at low frequencies for a selective excitation of the zeroth order anti-symmetric Lamb A0 mode, a mode whose dispersion characteristics can be used to infer the thickness of the waveguide. In this paper, our purpose was to extend the technique by combining a dry point-contact transducers approach to the SVD-enhanced 2-D Fourier transform in order to measure the dispersion characteristics of the flexural mode. The robustness of our approach is assessed on bone-mimicking phantoms covered or not with soft tissue-mimicking layer. Experiments were also performed on a bovine bone. Dispersion characteristics of measured modes were extracted using a SVD-based signal processing technique. The thickness was obtained by fitting a free plate model to experimental data. The results show that, in all studied cases, the estimated thickness values are in good agreement with the actual thickness values. From the results, we speculate that in vivo cortical thickness assessment by measuring the flexural wave using point-contact transducers is feasible. However, this assumption has to be confirmed by further in vivo studies., (Copyright © 2017 Elsevier B.V. All rights reserved.)

The development of novel quantitative ultrasound (QUS) techniques to measure the hip is critically dependent on the possibility to simulate the ultrasound propagation. One specificity of hip QUS is that ultrasounds propagate through a large thickness of soft tissue, which can be modeled by a homogeneous fluid in a first approach. Finite difference time domain (FDTD) algorithms have been widely used to simulate QUS measurements but they are not adapted to simulate ultrasonic propagation over long distances in homogeneous media. In this paper, an hybrid numerical method is presented to simulate hip QUS measurements. A two-dimensional FDTD simulation in the vicinity of the bone is coupled to the semi-analytic calculation of the Rayleigh integral to compute the wave propagation between the probe and the bone. The method is used to simulate a setup dedicated to the measurement of circumferential guided waves in the cortical compartment of the femoral neck. The proposed approach is validated by comparison with a full FDTD simulation and with an experiment on a bone phantom. For a realistic QUS configuration, the computation time is estimated to be sixty times less with the hybrid method than with a full FDTD approach., (Copyright © 2013 Elsevier B.V. All rights reserved.)

Velocity of ultrasound waves has proved to be a useful indicator of bone biomechanical competence. A detailed understanding of the dependence of ultrasound parameters such as velocity on bone characteristics is a key to the development of bone quantitative ultrasound (QUS). The objective of this study is to investigate the relative contributions of porosity and mineralized matrix properties to the bulk compressional wave velocity (BCV) along the long bone axis. Cross-sectional slabs from the diaphysis of four human femurs were included in the study. Seven regions of interest (ROIs) were selected in each slab. BCV was measured in through-transmission at 5 MHz. Impedance of the mineralized matrix (Z(m)) and porosity (Por) were obtained from 50 MHz scanning acoustic microscopy. Por and Z(m) had comparable effects on BCV along the bone axis (R=-0.57 and R=0.72, respectively)., (Copyright © 2011 Elsevier B.V. All rights reserved.)

Finite-difference numerical simulation of ultrasound propagation in complex media such as cancellous bone represents a fertile alternative to analytical approaches because it can manage the complex 3D bone structure by coupling the numerical computation with 3D numerical models of bone microarchitecture obtained from high-resolution imaging modalities. The objective of this work was to assess in silico the sensitivity of ultrasound parameters to controlled changes of microarchitecture and variation of elastic constants. The simulation software uses a finite-difference approach based on the Virieux numerical scheme. An incident plane wave was propagated through a volume of bone of approximately 5 x 5 x 8 mm(3). The volumes were reconstructed from high-resolution micro-computed tomography data. An iterative numerical scenario of "virtual osteoporosis" was implemented using a dedicated image processing algorithm in order to modify the initial 3D microstructures. Numerical computations of wave propagation were performed at each step of the process. The sensitivity to bone material properties was also tested by changing the elastic constants of bone tissue. Our results suggest that ultrasonic variables (slope of the frequency-dependent attenuation coefficient and speed of sound) are mostly influenced by bone volume fraction. However, material properties and structure also appear to play a role. The impact of modifications of the stiffness coefficients remained lower than the variability caused by structural variations. This study emphasizes the potential of numerical computations tools coupled to realistic 3D structures to elucidate the physical mechanisms of interaction between ultrasound and bone structure and to assess the sensitivity of ultrasound variables to different bone properties.

Two hundred-MHz time-resolved scanning acoustic microscopy was applied for the investigation of acoustic and structural bone properties of mice from two inbred strains. Transverse sections of femur taken from 5 C57BL/6J@Ico and 5 C3H/HeJ@Ico mice were explored. Both strains had the same bone diameter, but the C3H/HeJ@Ico mice had greater cortical thickness, smaller cancellous diameter, and greater acoustic impedance values than C57BL/6J@Ico mice. The strong differences in the measured acoustic impedances among the two inbred strains indicate that the impedance is a good parameter to detect genetic variations of the skeletal phenotype in small animal models.