A Robust and Fast Method for 2-D Shear Wave Speed Calculation

We developed a new method, called the tangent plane method (TPM), for more efficiently and accurately estimating 2-D shear wave speed (SWS) from any direction of wave propagation. In this technique, we estimate SWS by solving the Eikonal equation because this approach is more robust to noise. To further enhance the performance, we computed the tangent plane of the arrival time surface. To evaluate the approach, we performed simulations and also conducted phantom studies. Simulation studies showed that TPM was more robust to noise than the conventional methods such as 2-D cross correlation (CC) and the distance method. The contrast/CNR for an inclusion (69 kPa; manufacturer provided stiffness) of a phantom is 0.54/4.17, 0.54/1.82, and 0.46/1.22. SWS results [mean and standard deviation (SD)] were 4.41 ± 0.49, 4.62 ± 0.85, and 3.66 ± 0.99 m/s, respectively, while the manufacturer's reported value (mean and range) is 4.81 ± 0.49 m/s. This shows that TPM has the higher CNR and lower SD than other methods. To increase the computation speed, an iterative version of TPM (ITPM) was also developed, which calculated the time-of-flight iteratively. ITPM reduced the computation time to 3.6%, i.e., from 748 to 27 s. In vivo case analysis demonstrated the feasibility of using the conventional ultrasound scanner for the proposed 2-D SWS algorithms.