Fabric dependence of wave propagation in anisotropic porous media

Current diagnosis of bone loss and osteoporosis is based on the measurement of the Bone Mineral Density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction, 2) only the first wave arriving to the ultrasound probe is characterized, and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as Speed of Sound (SOS) and Broadband Ultrasound Attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot’s poroelastic wave propagation theory. In this paper the governing equations for wave motion in the linear theory of anisotropic poroelastic materials are developed and extended to include the dependence of the constitutive relations upon fabric - a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. This fabric-dependent anisotropic poroelastic approach is a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of trabecular bone, and thus represents an alternative for bone quality assessment beyond BMD alone

The exterior gravitational potential of toroids

ABSTRACT We perform a bivariate Taylor expansion of the axisymmetric Green function in order to determine the exterior potential of a static thin toroidal shell having a circular section, as given by the Laplace equation. This expansion, performed at the centre of the section, consists in an infinite series in the powers of the minor-to-major radius ratio e of the shell. It is appropriate for a solid, homogeneous torus, as well as for inhomogeneous bodies (the case of a core stratification is considered). We show that the leading term is identical to the potential of a loop having the same main radius and the same mass – this ‘similarity’ is shown to hold in the ${\cal O}(e^2)$ order. The series converges very well, especially close to the surface of the toroid where the average relative precision is ∼10−3 for e = 0.1 at order zero, and as low as a few 10−6 at second order. The Laplace equation is satisfied exactly in every order, so no extra density is induced by truncation. The gravitational acceleration, important in dynamical studies, is reproduced with the same accuracy. The technique also applies to the magnetic potential and field generated by azimuthal currents as met in terrestrial and astrophysical plasmas.</jats:p

Improvement of the PLD process assisted by RF plasma for AlN growth

International audienceThe pulsed-laser-deposition (PLD) method is particularly well suited for the growth of oxide thin films, but in the case of other compounds, such as nitrides, PLD presents some limitations which are mainly due to the low reactivity of nitrogen in comparison with oxygen. A possible way to overcome this problem is to increase the reactivity of the constituent species, via plasma assisted-pulsed-laser deposition. A plasma is coupled to the ablation chamber, in order to increase the density of reactive atomic species, which can be further incorporated in the growing film. This approach is described in this paper as well as the nature, energy, and concentration of the atomic and molecular species in the plasma as determined by various plasma diagnostics. These results are correlated to the growth of thin films in the particular case of the aluminum nitride compound. The composition and structure of the films are studied as a function of the growth conditions, and the positive effects of the additional discharge are evidenced on the film purity and properties. The fundamental problem with the PLD technique, especially with metallic targets, is the production of unwanted droplets that significantly worsen the properties of the films. To eliminate these droplets, a thin film has been grown with an experimental setup using two targets and crossed laser beams which gave positive results

The exterior gravitational potential of toroids

International audienceWe perform a bivariate Taylor expansion of the axisymmetric Green function in order to determine the exterior potential of a static thin toroidal shell having a circular section, as given by the Laplace equation. This expansion, performed at the centre of the section, consists in an infinite series in the powers of the minor-to-major radius ratio $e$ of the shell. It is appropriate for a solid, homogeneous torus, as well as for inhomogeneous bodies (the case of a core stratification is considered). We show that the leading term is identical to the potential of a loop having the same main radius and the same mass | this "similarity" is shown to hold in the ${\cal O}(e^2)$ order. The series converges very well, especially close to the surface of the toroid where the average relative precision is $\sim 10^{-3}$ for $e\! = \!0.1$ at order zero, and as low as a few $10^{-6}$ at second order. The Laplace equation is satisfied {\em exactly} in every order, so no extra density is induced by truncation. The gravitational acceleration, important in dynamical studies, is reproduced with the same accuracy. The technique also applies to the magnetic potential and field generated by azimuthal currents as met in terrestrial and astrophysical plasmas

Comparison of synchrotron radiation and conventional X-ray microcomputed tomography for assessing trabecular bone microarchitecture of human femoral heads

articleMicrocomputed tomography (microCT) produces three-dimensional (3D) images of trabecular bone. We compared conventional microCT (CmicroCT) with a polychromatic x-ray cone beam to synchrotron radiation (SR) microCT with a monochromatic parallel beam for assessing trabecular bone microarchitecture of 14 subchondral femoral head specimens from patients with osteoarthritis (n=10) or osteoporosis (n=4). SRmicroCT images with a voxel size of 10.13 microm were reconstructed from 900 2D radiographic projections (angular step, 0.2 degrees). CmicroCT images with a voxel size of 10.77 microm were reconstructed from 205, 413, and 825 projections obtained using angular steps of 0.9 degrees, 0.45 degrees, and 0.23 degrees, respectively. A single threshold was used to binarize the images. We computed bone volume/ tissue volume (BV/TV), bone surface/bone volume (BS/BV), trabecular number (Tb.N), trabecular thickness (Tb.Th and Tb.Th*), trabecular spacing (Tb.Sp), degree of anisotropy (DA), and Euler density. With the 0.9 degrees angular step, all CmicroCT values were significantly different from SRmicroCT values. With the 0.23 degrees and 0.45 degrees rotation steps, BV/TV, Tb.Th, and BS/BV by CmicroCT differed significantly from the values by SRmicroCT. The error due to slice matching (visual site matching +/- 10 slices) was within 1% for most parameters. Compared to SRmicroCT, BV/TV, Tb.Sp, and Tb.Th by CmicroCT were underestimated, whereas Tb.N and Tb. Th* were overestimated. A Bland and Altman plot showed no bias for Tb.N or DA. Bias was -0.8 +/- 1.0%, +5.0 +/- 1.1 microm, -5.9 +/- 6.3 microm, and -5.7 +/- 29.1 microm for BV/TV, Tb.Th*, Tb.Th, and Tb.Sp, respectively, and the differences did not vary over the range of values. Although systematic differences were noted between SRmicroCT and CmicroCT values, correlations between the techniques were high and the differences would probably not change the discrimination between study groups. CmicroCT provides a reliable 3D assessment of human defatted bone when working at the 0.23 degrees or 0.45 degrees rotation step; the 0.9 degrees rotation step may be insufficiently accurate for morphological bone analysis

Chemical structure of films grown by AIN laser ablation: an X-ray photoelectron spectroscopy study

We report on a study of the compositional and chemical properties of films deposited on silicon by quadrupoled Nd:YAG pulsed laser ablation of a ceramic AlN target. The ablation has been performed either in a vacuum or in the presence of a gas atmosphere. The effect of oxygen incorporation in the films on their chemical structure was investigated. The binding energy of the aluminium 2p, nitrogen 1s and oxygen 1s core electrons indicate the formation of near-stoichiometric aluminum nitride in films grown under vacuum (10-7 - 10-5 mb) while in films grown under 0.1 mbar oxygen partial pressure only aluminum oxide formation was observe