Assessing the Elasticity of Child Cortical Bone.

A better understanding of the mechanical behaviour of child bone is essential to improve the diagnosis of pediatric bone disorders that may influence bone development. Even though the process of bone growth is well described, there are still lacks of knowledge on intrinsic material properties of child bone and particularly on child bone considered as "non-pathological". Geometry, material properties, microstructure and biochemical components are associated with child bone fragility and remain difficult to assess for two main reasons: the scarcity of the bone samples and their small dimensions. In this context, ultrasonic methods offer interesting possibilities by exploiting in particular their non-destructive character. In this chapter, the elasticity properties of Non Pathological Child Cortical Bone (NPCCB) obtained by ultrasonic methods are presented. The objective was to contribute to the construction of a reference database on NPCCB that would serve as a point of comparison for analyzing the effect of a pathology or treatment. After the presentation of the hypotheses on the elasticity and anisotropy of NPCCB, ultrasonic transmission-mode and resonance spectroscopy methods are described. Results are presented and discussed with respect to microstructural and biochemical properties.

Acoustical characterisation and monitoring of microbubble clouds.

Argon microbubbles will exist in the primary sodium of the next generation of sodium-cooled fast reactors (SFR). Due to its opacity, acoustic methods will be used for the in-service inspection in these reactors, but the presence of such bubbles will greatly affect ultrasonic wave propagation. Moreover, these bubbles can lead to the formation of gas pockets in the reactor and impact cavitation and boiling phenomena. It is therefore necessary to characterise what is called the 'microbubble cloud' by providing the volume fraction and the bubble size distribution. Safety requirements in this field call for robust inspection methods based on very few assumptions about the bubble populations. The objective of this study is to assess the performance of spectroscopic methods in the presence of bubbles with high polydispersity and to monitor an evolving cloud of microbubbles. The histogram and void fractions were estimated according to the regularised inversion of the complex wave number's integral equation. To reduce the need for prior information on the bubble cloud, a specific procedure was used to estimate the maximum radius of the population. The results are presented on the basis of the experimental data obtained and then compared with optical measurements.

Bubbly flow velocity measurement in multiple scattering regime.

We propose a technique to measure the velocity of a bubble cloud based on the coda correlation. The method is founded on successive recordings of multiple scattered waves from a bubble cloud. Our model predicts the dependence between the correlation coefficient of these coda waves and the velocity of the bubble cloud under diffusion approximation. The Acoustic experiments are validated by simultaneous optical measurements in a water tank, with a good agreement between the acoustical and the optical methods (relative difference smaller than 7%). This technique can be transposed to any particle flow velocity problems involving multiple scattering effects in acoustics.

Assessment of elastic coefficients of child cortical bone using resonant ultrasound spectroscopy.

The assessment of the anisotropic elastic properties of non-pathological child cortical bone remains a challenge for the biomechanical engineering community and an important clinical issue. Resonant ultrasound spectroscopy (RUS) can be used to determine bone stiffness coefficients from the mechanical resonances of bone specimens. Here, a RUS protocol was used on 7 fibula specimens from children (mean age 14 ±â€¯3 years) to estimate the whole elastic stiffness tensor of non-pathological child cortical bone considered as orthotropic. Despite a small number of sample, results are consistent with this hypothesis, even if a trend towards transverse isotropy is discussed. Indeed, the average values of the 9 independent stiffness coefficients obtained in this study for child bone are: C11 = 16.73 ±â€¯0.19 GPa, C22 = 16.19 ±â€¯0.12 GPa, C33 = 24.47 ±â€¯0.30 GPa, C44 = 4.14 ±â€¯0.08 GPa, C55 = 4.16 ±â€¯0.07 GPa, C66 = 3.13 ±â€¯0.05 GPa, C12 = 10.14 ±â€¯0.20 GPa, C13 = 10.67 ±â€¯0.27 GPa, C23 = 10.25 ±â€¯0.14 GPa.

Nonlinear ultrasound parameter to monitor cell death in cancer cell samples.

A scaling subtraction method was proposed to analyze the radio frequency data from cancer cell samples exposed to an anti-cancer drug and to estimate a nonlinear parameter. The nonlinear parameter was found to be well correlated (R2 = 0.62) to the percentage of dead cells in apoptosis and necrosis. The origin of the nonlinearity may be related to a change in contacts between cells, since the nonlinear parameter was well correlated to the average total coordination number of binary packings (R2 ≥ 0.77). These results suggest that the scaling subtraction method may be used to early quantify chemotherapeutic treatment efficiency.

From local to global measurements of nonclassical nonlinear elastic effects in geomaterials.

In this letter, the equivalence between local and global measures of nonclassical nonlinear elasticity is established in a slender resonant bar. Nonlinear effects are first measured globally using nonlinear resonance ultrasound spectroscopy (NRUS), which monitors the relative shift of the resonance frequency as a function of the maximum dynamic strain in the sample. Subsequently, nonlinear effects are measured locally at various positions along the sample using dynamic acousto elasticity testing (DAET). After correcting analytically the DAET data for three-dimensional strain effects and integrating numerically these corrected data along the length of the sample, the NRUS global measures are retrieved almost exactly.

Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types.

In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. This result could lead to further understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.

Analyzing the anisotropic Hooke's law for children's cortical bone.

Child cortical bone tissue is rarely studied because of the difficulty of obtaining samples. Yet the preparation and ultrasonic characterization of the small samples available, while challenging, is one of the most promising ways of obtaining information on the mechanical behavior of non-pathological children׳s bone. We investigated children׳s cortical bone obtained from chirurgical waste. 22 fibula or femur samples from 21 children (1-18 years old, mean age: 9.7±5.8 years old) were compared to 16 fibula samples from 16 elderly patients (50-95 years old, mean age: 76.2±13.5 years old). Stiffness coefficients were evaluated via an ultrasonic method and anisotropy ratios were calculated as the ratio of C33/C11, C33/C22 and C11/C22. Stiffness coefficients were highly correlated with age in children (R>0.56, p<0.01). No significant difference was found between C11 and C22 for either adult or child bone (p>0.5), nor between C44 and C55 (p>0.5). We observe a transverse isotropy with C33>C22=C11>C44C55>C66. For both groups, we found no correlation between age and anisotropy ratios. This study offers the first complete analysis of stiffness coefficients in the three orthogonal bone axes in children, giving some indication of how bone anisotropy is related to age. Future perspectives include studying the effect of the structure and composition of bone on its mechanical behavior.

Microbubble dynamics monitoring using a dual modulation method.

An experimental method for characterizing microbubbles' oscillations is presented. With a Dual Frequency ultrasound excitation method, both relative and absolute microbubble size variations can be measured. Using the same experimental setup, a simple signal processing step applied to both the amplitude and the frequency modulations yields a two-fold picture of microbubbles' dynamics. In addition, assuming the occurrence of small radial oscillations, the equilibrium radius of the microbubbles can be accurately estimated.

Depth profile of a time-reversal focus in an elastic solid.

The out-of-plane velocity component is focused on the flat surface of an isotropic solid sample using the principle of time reversal. This experiment is often reproduced in the context of nondestructive testing for imaging features near the surface of the sample. However, it is not clear how deep the focus extends into the bulk of the sample and what its profile is. In this paper, this question is answered using both numerical simulations and experimental data. The profiles of the foci are expressed in terms of the wavelengths of the dominant waves, based on the interpretation of the Lamb's problem and the use of the diffraction limit.