Three-dimensional transient and harmonic shear-wave scattering by a soft cylinder for dynamic vascular elastography.

With the objective of characterizing biological soft tissues with dynamic elastography, a three-dimensional (3D) analytical model is proposed to simulate the scattering of plane shear waves by a soft cylinder embedded in an infinite soft medium. The 3D problem of harmonic plane shear-wave scattering is first formulated and solved, and the monochromatic solution is employed to simulate transient wave scattering. Both harmonic and transient simulations are compared with experimental 3D acquisitions. The good agreements obtained between measured and calculated displacement fields allowed to conclude on the validity of the proposed 3D harmonic and transient models. The spatial distribution of displacements (diffraction lobes, displacement oscillations, wave diffraction angles, etc.) and their relative amplitudes in both inclusion and surrounding materials depended on the contrast between the viscoelastic properties of the different media. The possibility of solving an inverse problem to assess soft heterogeneous medium viscoelasticity is discussed and some future theoretical and experimental developments are proposed.