Elastic Modulus Imaging for Breast Application Using a Virtual Fields Based-Method in Quasi-Static Ultrasound Elastography

Nowadays, detection and characterization of breast pathologies is an essential issue. Quasi-static ultrasound elastography have been proposed to provide information about the mechanical properties of tissues during the patient examination. However, reconstructing tissue properties is a challenging task as it requires to solve an ill-posed inverse problem, with generally no available boundary information and solely 2D estimated displacements, whereas the problem is inherently three-dimensional. In this paper, a Virtual fields based-method is investigated to reconstruct Young's modulus maps from the knowledge of internal displacements and the force applied. The media examined are assumed to be linear elastic and isotropic, and to overcome the lack of 3D data, the plane stress conditions are considered. The developed method is assessed with plane-stress and 3D simulations, as well as phantoms and patient data. For all the media examined, the reconstructed Young's modulus maps clearly reveal regions with different stiffnesses. The stiffness contrast between regions is accurately estimated for the different plane stress simulations, but underestimated for the 3D simulations. These results can be expected as plane stress conditions are no longer satisfied in the 3D simulations. On the other hand, for all these cases, the size and the position of the different regions are correctly estimated when the region is larger than a pixel. Finally, similar comments can be made for the experimental results. More especially for the in vivo results, the inclusion-to-background Young's modulus ratio is estimated in average around 6.61 for the carcinoma and 4.57 for the fibroedenoma, which is consistent with the literature.