Viscoelastic characterization of an elliptic structure in dynamic elastography imaging using a semi-analytical shear wave scattering model

In the context of dynamic elastography, the quantitative estimation of elasticity usually relies on homogeneity, linearity and isotropy assumptions. However, the presence of confined mechanical heterogeneities such as tumors, make those assumptions coarse. In this study, a semi-analytical model of shear wave scattering by elliptical structures is proposed in order to take into account physical interactions due to the presence of a mechanical heterogeneity including viscous effects. The model was validated using the finite element method as a reference in a forward problem approach. Then, an inversion method based on a least-square optimization was applied to in-vitro results obtained on agar-gelatin phantoms. Finally, the robustness of the inversion procedure was assessed considering various signal-to-noise ratios. Theoretical results were found in good agreement with the forward problem formulation. The inverse problem allowed robust viscoelastic assessments of phantom materials without any assumption on their rheological behavior.