Quantifying the impact of shear wavelength and kernel size on shear wave speed estimation

Quantitative measurements of tissue stiffness can be obtained by measuring the speed of shear waves induced in tissue by acoustic radiation force. In homogeneous media, time-of-flight (TOF) measurements of shear wave speed (SWS) ideally are independent of the size of the region of interest (or reconstruction kernel). However, in heterogeneous media, shear wave morphology is altered by discontinuities in stiffness due to reflections or boundary conditions, which introduce error to the measured SWS. In addition, the size of the reconstruction kernel limits the spatial resolution, or ability to precisely localize changes in stiffness. This study investigated the impact of shear wavelength, and reconstruction kernel size on the accuracy and spatial resolution of TOF SWS reconstruction in heterogeneous media using finite element method (FEM) simulations. SWS estimation error was found to be most severe at locations where the shear wave travels through a stiff-to-soft interface, where reflections with the same polarity as the incident wave occur. The magnitude and spatial extent of errors near stiffness discontinuities in the direction of shear wave propagation increase as the shear wavelength increases, due to the larger size of the reflected wave. The SWS reconstruction error near stiffness discontinuities orthogonal to the direction of shear wave propagation was also found to be more severe for larger shear wavelengths. The ability of the shear wave to conform to discontinuities in stiffness in this orientation is limited by the boundary condition that the shear wave displacements must remain continuous. The spatial resolution of SWS estimates, as measured using edge widths at stiffness discontinuities, was found to be directly related to the reconstruction kernel size. Although SWS images represent quantitative measurements of stiffness, their spatial resolution is inherently inferior to ARFI images, since reconstruction kernels of finite spatial extent must always be used.