Recovering young moduli in heterogeneous stenosed carotid arteries: a numerical plane strain study

International audiencei) The regions' boundaries having the same mechanical properties are detected with a new mechanical criterion based on a comparison of the experimental and calculated stress distributions. Both distributions are obtained with homogeneous elastic properties either from the measured displacements or from a complete finite element (FE) simulation, respectively. The heterogeneity only affects the measured displacement field. ii) A cost function defined as the distance between experimental and a finite elements displacement fields is minimized for finding the elastic properties of the different regions. Minimization is performed with two algorithms: Levenberg-Marquardt ([3, 4]) and Covariance Matrix Adaptation- Evolution Strategy (CMA-ES, [5]). In order to reduce the computation time, an alternative approach is considered for this step: the Virtual Fields Method ([6, 7]). This study is a numerical validation of the method. Using finite elements, we model the deformation of a cross section of the carotid artery between diastole and systole (variation of the blood pressure of about 5 kPa), assuming linear elasticity and plane strain. The plaque is made of an inclusion surrounded by material having the same properties as the carotid wall. The blood pressure onto the wall is assumed to be uniform. The displacement field provided by a FE model of the artery with a single inclusion is used as pseudo-experimental data of our inverse method (figure 2). We focus on the case of a single heterogeneity in a matrix representing the healthy part of the artery (figure 1). A high ratio, r, between the Young moduli of the artery and the inclusion is assumed (typically r = Ematrix=Eheterogeneity = 50), and the materials are assumed to be almost incompressible (nheterogeneity = nmatrix = 0:49)