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

Christophe Desceliers (1) , Christian Soize (1) , S. Naili (1) , Q. Grimal (2) , M. Talmant (2)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 LIP - Laboratoire d'Imagerie Paramétrique

The biomechanical materials are among the most complex mechanical systems. Most often, their microstructure are complex and random. This is the case for the human cortical bones which are considered in this paper. For such a system, the micro-structure can be altered near its interface with the marrow (osteoporosis). A gradient of porosity is then observed in the thickness direction but, in this case, none of the usual theories of porous materials can be applied. For this reason, we present a simplified model with gradient for the elasticity tensor. The predictability of this model is improved by taking into account uncertainties. The elasticity tensor is then modelled by a random field. This random model is well adapted for the modelling of the random experimental measurements in ultrasonic range for the human cortical bone.

Mots clés: uncertainty quantification; biomechanical materials; human cortical bone; ultrasonic range

Domaines: Mécanique [physics.med-ph]; Probabilités [math.PR]; Statistiques [math.ST]; Biomécanique [physics.med-ph]

Christophe Desceliers, Christian Soize, S. Naili, Q. Grimal, M. Talmant. Probabilistic model of the human cortical bone with mechanical alterations in ultrasonic range. Third International Conference on Uncertainty in Structural Dynamics, USD2010, Katholieke Universiteit Leuven, Sep 2010, Leuven, Belgium. pp.1-7. ⟨hal-00692871⟩