An in-silico study of travel time estimation using Eikonal equation with finite element method in ultrasound imaging

Estimating the travel time of ultrasound in an inhomogeneous medium is crucial for high-quality imaging, as with an accurate estimate of the distribution of speed of sound, phase aberration, which is normally viewed as one of the reasons for image degradation, can be corrected by multiple methods. In order to estimate the ultrasound travel time in an inhomogeneous medium, the approach using solutions to the eikonal equation is attractive, since it can be easily integrated into a conventional delay-and-sum beamformer. In our manuscript, we first propose employing the finite element method to solve the eikonal equation in ultrasound imaging, which is easy to extend to a high-order numerical scheme and potentially runs faster on GPU. Through a series of in-silicon experiments, our results are comparable to those of fast marching methods.