Inverse and optimal drive problems in elasticity imaging of soft tissues

In elasticity imaging a surface deformation is applied to the object and the resulting induced strains in the interior of the object are measured using ultrasound. Two important problems are considered: (1) the inverse problem of determining the elasticity from the measured strains and the equations of equilibrium; and (2) the optimal drive problem of applying the optimum surface deformation that enables one to solve (1). The method of finite differences is used to solve (1) for a given piston configuration. The condition number of the matrix representing the resulting linear system of equations (Ax=b) is used as a criterion to solve (2). It appears from the authors´ simulations that this is a sufficient condition to enable reconstruction of the elasticity from strain measurements.