3D heterogeneous stiffness reconstruction using MRI and the Virtual Fields Method

The first extension of the virtual fieldsmethod to the reconstruction of heterogeneous stiffnessproperties from 3D bulk full-field displacementdata is presented in this paper. Data are provided byMagnetic Resonance Imaging (MRI). Two main issuesare addressed: 1. the identification of the stiffness ratiobetween two different media in a heterogeneoussolid; 2. the reconstruction of stiffness heterogeneitiesburied in a heterogeneous solid. The approach is basedon a finite element discretization of the equilibriumequations. It is tested on experimental full-field dataobtained on a phantom with the stimulated echo MRItechnique. The phantom is made of a stiff sphericalinclusion buried within a lower modulus material. Preliminaryindependent tests showed that the material ofthe inclusion was four times stiffer than the surroundingmaterial. This ratio value is correctly identified byour approach directly on the phantom with the MRIdata. Moreover, the modulus distribution is promisinglyreconstructed across the whole investigated volume.However, the resulting modulus distribution ishighly variable. This is explained by the fact that the approach relies on a second order differentiation of thedata, which tends to amplify noise. Noise is significantlyreduced by using appropriate filtering algorithms