Elastography Method to Identify Material Distribution in Two-Phase Nonlinear Media

Abstract

Many engineering and biological media can be described as the combination of several heterogeneous constituent phases. For instance, a tumor-containing organ can be approximated as two phases: tumor and tissue media. A nonlinear elastography method is developed in this paper to identify the distribution of mechanical properties in two-phase media, based solely on the measurement of displacements and forces on the external boundary. The two-phase distribution is approximated with a general continuous material parameter field, for which a designed grouping technique is applied to reduce the number of unknowns. The numerical efficiency of the minimization-based reconstruction is further enhanced by user-supplied gradients of the objective function, which are computed with minimal cost using a nonlinear adjoint method. Sample reconstruction is performed to identify two irregular inclusions in a two-dimensional nonlinear medium.