Application of the virtual fields method to magnetic resonance elastography data

This paper deals with the application of the Virtual Fields Method to the identification of the shear modulus of a gel from Magnetic Resonance Elastography data. Volume deformation fields in the cube were recorded at different times during the harmonic loading and the full harmonic response has been reconstructed using Fast Fourier Transform. Strains were then obtained by direct spatial differentiation, without any smoothing. The VFM was then applied with inertial forces balancing out elastic forces, without including the loading force which was not measured here. It has been shown that the choice of the virtual field is critical with such a spatial wave deformation field. A wide range of spatially harmonic virtual fields has been tested at different times within the loading period. The identified shear modulus has been shown to be consistent and to correlate with the value obtained from a simplified approach based on the shear wave solution. This is a feasibility study, it will be extended in the future to heterogeneous materials with a more thorough procedure to build up relevant virtual fields.