Reconstructive elasticity imaging for large deformations

A method is presented to reconstruct the elastic modulus of soft tissue bas ed on ultrasonic displacement and strain images for comparatively large def ormations. If the average deformation is too large to be described with a l inear elastic model, nonlinear displacement-strain relations must be used a nd the mechanical equilibrium equations must include high order spatial der ivatives of the displacement. Numerical methods were developed to reduce er ror propagation in reconstruction algorithms, including these higher order derivatives. Problems arising with the methods, as well as results using ul trasound measurements on gel-based, tissue equivalent phantoms, are given. Comparison to reconstructions using a linear elastic model shows that equiv alent image quality can be produced with algorithms appropriate for finite amplitude deformations.