Reconstruction of tensile and shear elastic moduli in anisotropic nearly incompressible media using Rayleigh wave phase and group velocities

Dynamic optical coherence elastography can excite and detect propagating mechanical waves in soft tissue without physical contact and in near real time. However, most soft tissue is anisotropic, characterized by at least three independent elastic moduli. As a result, reconstructing these moduli from mechanical wave fields requires a complex procedure. We consider a nearly incompressible transverse isotropic (NITI) material, which has been shown to locally define the symmetry of many soft tissues such as muscle, tendon, skin, cornea, heart, and brain. Reconstruction of elastic moduli in the NITI medium using Rayleigh waves is addressed here. A method to accurately compute the angular dependence of Rayleigh wave phase velocity for the most common geometries (point-like and line sources) of mechanical wave excitation is described. When a line source is used to launch plane mechanical waves over the medium surface, the phase velocity of Rayleigh waves in the direction of propagation is directly accessible. For a point-like source, propagation of the energy flux is tracked (i.e., its group velocity), which cannot be directly used for moduli inversion. In this case, angular spectrum decomposition is used to access the phase velocity. Both numerical simulations in OnScale and experiments in a stretched PVA phantom were performed. We show that both methods (line source wave excitation and angular decomposition from a point-like source) produce similar results and accurately estimate the angular anisotropy of the Rayleigh wave phase velocity. We also explicitly show that a commonly used group velocity approach leads to inadequate moduli inversion and should not be used for reconstruction. We suggest that the line source is best when a surface area must be scanned, whereas the point-like source with the proposed phase velocity reconstruction is best for single-point moduli estimation or when tissue motion is a concern.