2D calculation method based on composite beam theory for the determinationof local homogenised stiffnesses of long bones

A calculation method using the finite element technique is presented. Its m ain objective was to determine strains, stresses and more particularly stif fnesses in any cross section of a tibia, thus enabling the localisation of tibial torsion in vivo. Each tibial cross section was considered to be a no n-uniform cross section of a composite beam with arbitrary orientation of f ibres. The determination of stresses, strains and stiffnesses within a comp osite beam cross section has been defined by solving a variational problem. The validation of this method was performed on a tibial diaphysis of which each cross section was assumed to be the cross section of a composite beam made of orthotropic materials with orthotropic axes of any orientation wit h respect to the principal axis of the bone. The comparison of the results, From our model and that of a three-dimensional one, was performed on each nodal value (strains, stresses) of the meshed cross section as it was impos sible to obtain local stiffnesses by experimentation. The good agreement be tween the results has validated our finite element program. Actually, this method has enabled to treat directly 2D geometric reconstructions from CT s can images with a good accuracy to determine locally the homogenised mechan ical characteristics of human tibia in vivo, and particularly to quantify t orsional tibial abnormalities of children without approximation of the shap e of the cross section and by calculating the real moment of inertia J. The importance of the fibre orientation with regards to the stiffness values h as been emphasised. This 2D method has also allowed to reduce CPU time of t he 3D modelling and calculation. (C) 2001 Elsevier Science Ltd. All rights reserved.