Identification of the probabilistic model for a nonhomegeneous cortical bone using in vivo measurements in ultrasonic range

Abstract : The uncertainties introduced in the construction of such a simplified model and the random nature of such a heterogeneous medium are taken into account in introducing a probabilistic model of the elasticity tensor of the cortical bone medium. This probabilistic model is then a non-Gaussian tensor-valued random field which is non-homogeneous in space, for which the mean field has a gradient in the thickness direction and for which the random fluctuations are defined by a spatial correlation length in the thickness direction and by a space dependent dispersion parameter controlling the level of the random fluctuations. The parameters which have to be identified by solving an inverse stochastic problem related to the wave propagation prediction model are then those relative to the mean value function of the random field, the correlation length and the dispersion function of the elasticity tensor random field of the cortical layer. The purpose is to present a method for this identification using experimental measurements in ultrasonic range.