Probabilistic model of the human cortical bone with mechanical alterations in ultrasonic range

The biomechanical materials are among the most complex mechanical systems. Most often, their microstructure is heterogeneous and random. This is the case for the human cortical bones which are considered in this paper. For such systems, a gradient of porosity can be observed in the thickness direction but, in this case, none of the usual theories of porous materials can be applied. For this reason, a simplified model with gradient for the elasticity tensor is presented. The predictability of this model is improved by taking into account uncertainties. We propose a prior stochastic model of the tensor-valued elasticity field corresponding to an extension of a previous work in which the random elasticity field was constant in space. This extension consists in introducing two ingredients: the introduction of a spatial gradient for the mean elasticity tensor and spatial statistical fluctuations in the thickness direction. The stochastic model which is constructed shows that the observed responses are effectively sensitive with respect to the values of the gradient and to the level of statistical fluctuations. In this sense, this stochastic model will be well adapted to perform its identification solving a stochastic inverse problem that is not the purpose of the present paper.

► We construct a mean simplified model (multilayer) for human bones.
► We introduce a model to take into account the degradation of the cortical bone in the neighborhood of the marrow (osteoporosis).
► A mesoscale model is constructed by modeling the elasticity tensor with a nonhomogeneous tensor-valued random field.
► An application presents an observation that exhibits sensitivity with respect to the thickness of the cortical layer.