| It is well known that the mechanical properties of soft tissue can change with tissue pathology. For example, it is observed that the elastic (shear) modulus of malignant breast masses is typically an order of magnitude higher than the back ground of normal glandular tissue. In addition it is also known that with increasing applied strain the stiffness of cancerous soft tissues increases more rapidly than the background of non-malignant soft tissues.; Medical imaging techniques such as ultrasound imaging, combined with novel displacement estimation techniques enable the calculation of the displacement field in the interior of soft tissue. While many attempts have been made to use this information to map the linear elastic properties of soft tissue, relatively few attempts have been made that account for both large deformation and material non-linearity in reconstructing the elastic properties. In this dissertation, new algorithms are developed, implemented, and tested to reconstruct the material parameters in non-linear, large deformation hyperelastic tissue models.; The overall computational problem is formulated as a constrained minimization problem where the difference between a measured and a predicted displacement field is minimized. Upon discretization, the constraint takes the form of a finite element (FEN) model for the hyperelastic tissue response. In the forward FEM model, due consideration is given to issues of mesh locking which are avoided by the use of enhanced strain and higher order finite elements. The optimization problem is solved efficiently using a quasi-Newton method and adjoint gradient calculation, which significantly reduces the computational costs compared to more traditional approaches. A novel technique based on continuation in the material properties is used to further accelerate the inverse problem solution.; This algorithm is applied to problems of compressible hyperelasticity, incompressible plane stress hyperelasticity, and almost incompressible plane strain hyperelasticity. In each case an appropriate finite element method for solving the forward problem is identified and the effect of several variables on the reconstructed material property distributions is studied. These variables include the boundary conditions for the problem, the level of noise in the measurement, the choice of measurement norm and the regularization strategy. In addition, where appropriate, comparisons with linear elastic reconstructions are made to illustrate the effect of material and geometric nonlinearities. |
