Virtual fields-based method for mechanical parameter reconstruction in quasi-static ultrasound elastography: Assessment with numerical simulations and phantom data

Quasi-static ultrasound elastography mainly provides images of the axial strain that biological tissues experience when compressed. In this study, a virtual fields–based method is investigated to reconstruct Young’s modulus maps from compression-induced 2D displacements and the knowledge of the force applied. The media examined are supposed to be linear elastic and isotropic, and because only 2D data are available, the plane stress assumption is used. To perform Young’s modulus imaging, the domain of interest is partitioned into multiple subdomains and, for each of them, a modulus value needs to be estimated. The proposed approach is based on the virtual work principle and determines for each modulus to be computed, the virtual field to be used. The method was evaluated using numerical simulations and a CIRS phantom. Results showed accurate Young’s modulus reconstruction when the plane stress conditions were satisfied, whereas a decrease in stiffness contrast was noted in the other cases. Finally, a progressive evolution of the modulus maps with increasing subdomain size was also observed.