Extension of the optimised virtual fields method to estimate viscoelastic material parameters from 3D dynamic displacement fields

In vivo measurement of the mechanical properties of soft tissues is essential to provide necessary data in biomechanics and medicine (early cancer diagnosis, study of traumatic brain injuries, etc.). Imaging techniques such as magnetic resonance elastography can provide 3D displacement maps in the bulk and in vivo, from which, using inverse methods, it is then possible to identify some mechanical parameters of the tissues (stiffness, damping, etc.). The main difficulties in these inverse identification procedures consist in dealing with the pressure waves contained in the data and with the experimental noise perturbing the spatial derivatives required during the processing. The optimised virtual fields method (OVFM) (Comput. Mech. 34, 2004, 439), designed to be robust to noise, presents natural and rigorous solution to deal with these problems. The OVFM has been adapted to identify material parameter maps from magnetic resonance elastography data consisting of 3D displacement fields in harmonically loaded soft materials. In this work, the method has been developed to identify elastic and viscoelastic models. The OVFM sensitivity to spatial resolution and to noise has been studied by analysing 3D analytically simulated displacement data. This study evaluates and describes the OVFM identification performances: Different biases on the identified parameters are induced by the spatial resolution and experimental noise. The well-known identification problems in the case of quasi-incompressible materials also find a natural solution in the OVFM. Moreover, an a posteriori criterion to estimate the local identification quality is proposed. The identification results obtained on actual experiments are briefly presented.