FORWARD AND INVERSE PROBLEMS IN ELASTICITY IMAGING OF SOFT-TISSUES

In elasticity imaging, a surface deformation is applied to an object u sing small pistons, and the resulting induced strains in the interior of the object are measured using ultrasonic imaging. Two important pro blems are considered: (1) the forward problem of determining the strai ns induced by a known deformation of an object with known elasticity; and (2) the inverse problem of reconstructing elasticity from measured strains and the equations of equilibrium. The method of finite differ ences is used to solve the forward problem for a given piston configur ation; some non-trivial issues arise in determining boundary condition s. The finite difference equations are then rearranged into a linear s ystem of equations which formulates the inverse problem; this system c an be solved for the unknown elasticities. This formulation of the inv erse problem is completely consistent with the forward problem; this i s useful for interative methods in which the deformation is adaptively changed. A comparison between simulated and actual measured results d emonstrate the feasibility of the proposed procedure.