Experimental identification of a prior tensor-valued random field for the elasticity properties of cortical bones using in vivo ultrasonic measurements

Abstract

International audienceA cortical bone layer is a biomechanical system which is difficult to model due to the complexity level of its microstructure. The experimental identification of its effective mechanical properties at the macroscale is usually carried out using the axial transmission technique which is often modeled with a mean mechanical model. In this paper, the mean mechanical model is made up of a fluid-solid semi- infinite multilayer system (skin and muscles/cortical layer/marrow). It is also assumed that the effective elasticity properties of the solid layer (cortical bone) have spatial variations in the thickness (osteoporosis). The uncertainties introduced in the mean mechanical model are taken into account in introducing a prior stochastic model in which the elasticity tensor is modeled by a non- homogeneous non-Gaussian tensor-valued random field. The parameters of the random field are a spatial correlation length, a space dependent dispersion parameter and the values of the elasticity tensor of the simplified mean mechanical model. A method and an application are presented for the identification of these parameters using in vivo experimental measurements in ultrasonic range with the axial transmission technique