Comparing the Statistics of High-Resolution Time-of-Flight-Based Shear Wave Speed Estimation in the Presence of Speckle Bias Using Shear Wave Slowness or Velocity.

Ultrasound shear wave elasticity imaging (SWEI) quantifies the mechanical properties of soft tissue by relating measurements of shear wave speed (SWS) to a material model. Many SWEI algorithms estimate the time of flight (TOF) over some fixed distance along a given trajectory and calculate the wave velocity as the ratio of that distance to the TOF. To balance spatial resolution and SWS precision, most high-resolution 2D-SWEI algorithms average together multiple noisy velocity estimates to generate the final SWS. However, velocity calculated over a fixed distance with an estimated TOF can be prone to divide-by-near-zero (DBNZ) errors, especially as the true TOF approaches zero. The reciprocal of velocity, slowness, will never experience DBNZ errors as long as the fixed distance over which the TOF is estimated is greater than zero. In this work, we modify an existing 2D-SWEI algorithm to be based on point estimates of slowness. We propose a statistical model assuming normal TOF distributions and use it to evaluate the accuracy and the precision of the velocity- and slowness-based SWS algorithms in Monte Carlo simulations. We then extend our analysis of TOF data to empirically describe the bounds of the proposed model in the presence of speckle bias. Finally, we evaluate both algorithms in heterogeneous media and quantify the achievable lesion conspicuity across a range of shear wave SNR and SWS algorithm reconstruction parameters. We conclude that slowness-based SWS can achieve similar accuracy and precision as velocity-based SWS at less than one-tenth of the TOF SNR with no additional computational cost. For a fixed shear wave and TOF SNR in isotropic homogeneous media, we experimentally demonstrate a reduction in bias greater than 5% and a reduction in variability greater than 15%. We also demonstrate that the slowness-based approach achieves superior or equal lesion conspicuity as the velocity-based approach, regardless of imaging condition or algorithm parameters.