Simon Bernard

Bio: Simon Bernard is an academic researcher from University of Le Havre. The author has contributed to research in topics: Resonant ultrasound spectroscopy & Cortical bone. The author has an hindex of 9, co-authored 21 publications receiving 371 citations. Previous affiliations of Simon Bernard include École Normale Supérieure & University of Paris.

Accurate measurement of cortical bone elasticity tensor with resonant ultrasound spectroscopy.

Abstract: Resonant ultrasound spectroscopy (RUS) allows to accurately characterize the complete set of elastic constants of an anisotropic material from a set of measured mechanical resonant frequencies of a specimen. This method does not suffer from the drawbacks and limitations of the conventional sound velocity approach, but has been reported to fail to measure bone because of its strong viscoelastic damping. In this study, we take advantage of recent developments of RUS to overcome this limitation. The frequency response of a human cortical bone specimen (about 5×7×7 mm 3 ) was measured between 100 and 280 kHz. Despite an important overlapping of the resonant peaks 20 resonant frequencies could be retrieved by using a dedicated signal processing method. The experimental frequencies were progressively matched to the frequencies predicted by a model of the sample whose elastic constants were adjusted. The determined diagonal elastic constants were in good agreement with concurrent sound velocity measurements performed in the principal directions of the specimen. This study demonstrates that RUS is suitable for an accurate measurement of cortical bone anisotropic elasticity. In particular, precision of measured Young and shear moduli is about 0.5%.

Ultrasonic computed tomography based on full-waveform inversion for bone quantitative imaging

Abstract: We introduce an ultrasonic quantitative imaging method for long bones based on full-waveform inversion. The cost function is defined as the difference in the L 2-norm sense between observed data and synthetic results at a given iteration of the iterative inversion process. For simplicity, and in order to reduce the computational cost, we use a two-dimensional acoustic approximation. The inverse problem is solved iteratively based on a quasi-Newton technique called the Limited-memory Broyden-Fletcher-Goldfarb-Shanno method. We show how the technique can be made to work fine for benchmark models consisting of a single cylinder, and then five cylinders, the latter case including significant multiple diffraction effects. We then show pictures obtained for a tibia-fibula bone pair model. Convergence is fast, typically in 15 to 30 iterations in practice in each frequency band used. We discuss the so-called 'cycle skipping' effect that can occur in such full waveform inversion techniques and make them remain trapped in a local minimum of the cost function. We illustrate strategies that can be used in practice to avoid this. Future work should include viscoelastic materials rather than acoustic, and real data instead of synthetic data.

Ultrasound Shear Wave Viscoelastography: Model-Independent Quantification of the Complex Shear Modulus

Abstract: Ultrasound shear wave elastography methods are commonly used for estimation of mechanical properties of soft biological tissues in diagnostic medicine. A limitation of most currently used elastography methods is that they yield only the shear storage modulus ( $G^{\prime }$ ) but not the loss modulus ( $G^{\prime \prime }$ ). Therefore, no information on viscosity or loss tangent (tan $\delta )$ is provided. In this paper, an ultrasound shear wave viscoelastography method is developed for model-independent quantification of frequency-dependent viscoelastic complex shear modulus of macroscopically homogeneous tissues. Three in vitro tissue-mimicking phantoms and two ex vivo porcine liver samples were evaluated. Shear waves were remotely induced within the samples using several acoustic radiation force pushes to generate a semicylindrical wave field similar to those generated by most clinically used elastography systems. The complex shear modulus was estimated over a broad frequency range (up to 1000 Hz) through the analytical solution of the developed inverse wave propagation problem using the measured shear wave speed and amplitude decay versus propagation distance. The shear storage and loss moduli obtained for the in vitro phantoms were compared with those from a planar shear wave method and the average differences over the whole frequency range studied were smaller than 7% and 15%, respectively. The reliability of the proposed method highlights its potential for viscoelastic tissue characterization, which may improve noninvasive diagnosis.

Resonant ultrasound spectroscopy for viscoelastic characterization of anisotropic attenuative solid materials

Abstract: Resonant ultrasound spectroscopy (RUS) is an accurate measurement method in which the full stiffness tensor of a material is assessed from the free resonant frequencies of a small sample, and the viscoelastic damping is measured from the resonant peaks width. High viscoelastic damping causes the resonant peaks to overlap and therefore complicate the measurement of the resonant frequencies and the inverse identification of material properties. For that reason, RUS has been known to be fully applicable only to low damping materials. The purpose of this work is to adapt RUS for the characterization of highly attenuating viscoelastic materials. Spectrum measurement using shear transducers combined with dedicated signal processing is employed to retrieve the resonant frequencies despite overlapping. A probabilistic (Bayesian) formulation of the inverse problem, tackling the problem of correctly pairing the measured and predicted frequencies, is proposed. Applications to polymethylmethacrylate (isotropic) and glass/epoxy transversely isotropic samples are presented. The full set of viscoelastic properties is obtained with good repeatability. Particularly, elastic moduli of the isotropic samples are obtained within 1%.

Elasticity–density and viscoelasticity–density relationships at the tibia mid-diaphysis assessed from resonant ultrasound spectroscopy measurements

Abstract: Cortical bone tissue is an anisotropic material characterized by typically five independent elastic coefficients (for transverse isotropy) governing shear and longitudinal deformations in the different anatomical directions. It is well established that the Young’s modulus in the direction of the bone axis of long bones has a strong relationship with mass density. It is not clear, however, whether relationships of similar strength exist for the other elastic coefficients, for they have seldom been investigated, and the results available in the literature are contradictory. The objectives of the present work were to document the anisotropic elastic properties of cortical bone at the tibia mid-diaphysis and to elucidate their relationships with mass density. Resonant ultrasound spectroscopy (RUS) was used to measure the transverse isotropic stiffness tensor of 55 specimens from 19 donors. Except for Poisson’s ratios and the non-diagonal stiffness coefficient, strong linear correlations between the different elastic coefficients $$(0.7 < {r^{2}} < 0.99)$$ and between these coefficients and density $$(0.79 < {r^{2}} < 0.89)$$ were found. Comparison with previously published data from femur specimens suggested that the strong correlations evidenced in this study may not only be valid for the mid-tibia. RUS also measures the viscous part of the stiffness tensor. An anisotropy ratio close to two was found for damping coefficients. Damping increased as the mass density decreased. The data suggest that a relatively accurate estimation of all the mid-tibia elastic coefficients can be derived from mass density. This is of particular interest (1) to design organ-scale bone models in which elastic coefficients are mapped according to Hounsfield values from computed tomography scans as a surrogate for mass density and (2) to model ultrasound propagation at the mid-tibia, which is an important site for the in vivo assessment of bone status with axial transmission techniques.