Nonlinear elasticity imaging

We present the solution of the nonlinear inverse elasticity problem, wherein we image the linear and nonlinear hyperelastic properties of soft tissues in-vivo. For this, we solve a constrained optimization problem iteratively. The discrepancy between measured and predicted displacement fields is minimized in the objective function in the presence of regularization. The predicted displacement fields satisfy the equilibrium equations of elasticity from the current estimate of the elastic properties. The measured displacement fields are determined from a sequence of ultrasound radio frequency data while the tissue is slowly compressed. We model the tissue to have an exponential stress-stretch relation and capture its nonlinear response with a nonlinear parameter at large deformations.