Propagation des ultrasons en milieux poreux anisotropes : Application à l’os trabéculaire

Abstract : Understanding ultrasound propagation through a porous, heterogeneous and anisotropic structure as trabecular bone is a real theoretical challenge. Biot’s theory can predict the propagation and velocities of the two longitudinal waves observed experimentally under some conditions. However, this theory fails to predict the observed attenuation as it does not take into account the multiple scattering occurring in cancellous bone. Multiple scattering theories could provide an alternative, but are hardly suitable to such a complex structure. We thus ran numerical simulations in simplified and controlled bone-like structures consisting of solid ellipsoids randomly distributed in a fluid. These simulations highlighted the role of some key parameters (porosity, anisotropy, …) in the apparition of the two waves. Our results suggest that the fast wave would be guided by the trabeculae, while the slow one essentially propagates through the fluid phase. Furthermore, Biot’s theory was applied for the first time in bone-like structures without fitted parameters. In the context of these simulations, we showed that the semi-analytic processing of the field scattered by high aspect ratio elliptical cylinders is very instable but can be improved by performing arbitrary precision calculations. Finally, with the use of 3D printing, we have replicated at scale 1:1 a sample of horse cancellous bone, opening the way to trabecular bone phantoms controlled numerically. Thus, by increasing the anisotropy prior to printing, we experimentally observed for the first time the propagation of two longitudinal waves in bone-like samples.
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Fabien Mézière. Propagation des ultrasons en milieux poreux anisotropes : Application à l’os trabéculaire. Rhumatologie et système ostéo-articulaire. Université Paris.Diderot (Paris 7), 2014. Français. ⟨tel-01128763⟩

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