Estimating elastic modulus of soft tissue from incomplete displacement measurement

Abstract

The determination of elasticity of living soft tissues is of interest in medical diagnostics since the tissue elasticity is usually related to some abnormal, pathological process. Internal tissue deformation induced by externally applied mechanical forces has been evaluated to characterize tissue elasticity. For a quantitative elasticity imaging, material parameter such as shear modulus must be reconstructed from the measurement of internal displacement. A method to estimate the elastic modulus of an isotropic, inhomogeneous, incompressible elastic medium using measured displacement data is formulated by inversely solving the forward problem for static deformation. A finite-element based model for static deformation is proposed and then rearranged for solving the distribution of the shear modulus of the soft tissue from a knowledge of the displacement within the tissue. When the force boundary condition is unknown, it reconstructs the relative value of the elastic modulus of the tissue. The feasibility of the proposed method is demonstrated and the performance of the algorithm with noise in the displacement data is tested using the simulated deformation data of the simple two-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, and that the relative shear modulus can be recovered to some degree of accuracy from only one-dimensional displacement data.