Nonlinear elastic behavior of phantom materials for elastography.

The development of phantom materials for elasticity imaging is reported in this paper. These materials were specifically designed to provide nonlinear stress/strain relationship that can be controlled independently of the small strain shear modulus of the material. The materials are mixtures of agar and gelatin gels. Oil droplet dispersions in these materials provide further control of the small strain shear modulus and the nonlinear parameter of the material. Since these materials are mostly water, they are assumed to be incompressible under typical experimental conditions in elasticity imaging. The Veronda-Westman model for strain energy density provided a good fit to all materials used in this study. Materials with a constant gelatin concentration (3.0% dry weight) but varying agar concentration (0.6-2.8% dry weight) demonstrated the same power law relationship between elastic modulus and agar concentration found for pure agar (1.89 +/- 0.02), consistent with percolation theory, and provided a consistent nonlinearity parameter of 4.5 +/- 0.3. The insights provided by this study will form the basis for stable elastography phantoms with stiffness and nonlinear stress/strain relationships in the background that differ from those in the target.