Identification of the probabilistic model for a non-homogeneous cortical bone using in vivo measurements in ultrasonic range

Abstract : The mean elasticity properties of the cortical bone in the thickness is not a constant but have spatial fluctuations due to damages in the cortical bone microstructure near the interface between the cortical bone and the marrow (osteoporosis). The uncertainties introduced in the construction of such a simplified model and the random nature of such a material are taken into account in introducing, as a prior probabilistic model, a non Gaussian non-homogeneous elasticity tensor-valued random field of the cortical bone. This prior probabilistic model exhibits a minimum number of parameters which are the mean function (not constant in the thickness direction), a spatial correlation length in the thickness direction and a space dependent dispersion parameter controlling the level of the random fluctuations. We present a method and an application for this identification using axperimen-tal measurements in ultrasonic range. The stochastic inverse problem is carried out by solving an optimization problem based on a new adapted cost functions and on in vivo observations.