Robust estimation of time-of-flight shear wave speed using a radon sum transformation

Time-of-flight methods allow quantitative measurement of shear wave speed (SWS) from ultrasonically tracked displacements following impulsive excitation in tissue. However, application of these methods to in vivo data are challenging because of the presence of gross outlier data resulting from sources such as physiological motion or spatial inhomogeneities. This paper describes a new method for estimating SWS by considering a solution space of trajectories and evaluating each trajectory using a metric that characterizes wave motion along the entire trajectory. The metric used here is found by summing displacement data along the trajectory as in the calculation of projection data in the Radon transformation. The algorithm is evaluated using data acquired in calibrated phantoms and in vivo human liver. Results are compared with SWS estimates using a random sample consensus (RANSAC) algorithm described by Wang et al. Good agreement is found between the Radon sum and RANSAC SWS estimates with a correlation coefficient of greater than 0.99 for phantom data and 0.91 for in vivo liver data. The Radon sum transformation is suitable for use in situations requiring real-time feedback and is comparably robust to the RANSAC algorithm with respect to outlier data.