In recent years, imaging techniques have been adapted to indirectly measure stiffness of biological tissues, with the hope of using this information to aid in detecting and classifying pathological regions. Several methods have been developed to convert a sequence of strain images into a single elasticity image, but most are based on assumptions that limit the local variability of stiffness in the estimate. In this paper, two direct inversion methods are introduced. The novelty of these methods is that they concurrently solve a system of differential equations for the stiffness, allowing for strong local variations. Some ideas regarding uniqueness of solutions, an issue that is ignored in existing works, are also presented. Preliminary numerical results show that by keeping the differential terms in the tissue model, the new inversion methods can more accurately determine the tissue's stiffness distribution.