Ultrasound shear wave simulation of wave propagation at oblique angles

Shear wave elasticity imaging (SWEI) has been used to measure the local tissue elasticity. The local tissue shear modulus can be reconstructed from the displacement field of shear waves using an algebraic Helmholtz inversion (AHI) equation or a time-of-flight (TOF)-based algorithm. The shear waves, which are generated by successive focusing of ultrasonic beams at different depths, propagate at oblique angles rather than along the lateral position. The wave propagation at oblique angles can result in bias in shear modulus reconstruction using the AHI equation or the TOF-based algorithm. In this study, the effect of wave propagation at oblique angles on the tissue shear modulus reconstruction was investigated using in silico finite element (FE) simulation. An FE elastic tissue with a hard inclusion model was designed. The shear waves with propagation angles of 0 degrees, 5 degrees, and 10 degrees were applied to the model. The shear modulus and the percentage error in the model were computed using the AHI equation and the TOF-based algorithm at each propagation angle from 0 degrees to 10 degrees. For the AHI equation, the percentage error was 0% at propagation angles of 0 degrees and 5 degrees, and 1% at a propagation angle of 10 degrees in the inclusion. In the surrounding tissue, the percentage error was 0% at propagation angles of 0 degrees, 5 degrees, and 10 degrees. For the TOF-based algorithm, the percentage error was 0% at propagation angles of 0 degrees and 5 degrees, and 40% at a propagation angle of 10 degrees in the inclusion. In the surrounding tissue, the percentage error was 0% at propagation angles of 0 degrees and 5 degrees, and 35% at a propagation angle of 10 degrees in the inclusion. Therefore, whereas the TOF-based algorithm produced critical bias in shear modulus reconstruction by the shear wave propagation at oblique angles, the AHI equation was not affected by the propagation.