Imaging of elastic modulus of incompressible biological soft tissue from a knowledge of displacement measurements

A method is presented for the determination of the elasticity parameter of an isotropic, inhomogeneous, incompressible elastic medium subject to external mechanical forces. Given a knowledge of the displacements within the medium, a variational formulation is used to determine the shear modulus throughout the tissue. A finite-element based model for static deformation is proposed for solving the distribution of the relative shear modulus of the tissue. The feasibility of the proposed method is demonstrated using the simulated deformation data of the simple three-dimensional inclusion problem. The results show that the relative shear modulus may be reconstructed from the displacement data measured locally in the region of interest within an isotropic, incompressible medium, and that the relative shear modulus can be recovered to some degree of accuracy from only one-dimensional displacement data