# Shear Wave Velocity Estimation Using the Real-Time Curve Tracing Method in Ultrasound Elastography
## 3 Phantom Experiments
### Shear Wave Velocity Estimation  
In this paper, the real-time curve tracing is performed for the 10 th frame image of shear wave propagation in the targeted imaging area of Figure 1a. Figure 2a shows the original propagation trajectory of the shear wave. The shear wave front is obtained by the directional filter matrix, and then the central point of each transverse shear wave front is connected, as shown with the red curve of Figure 2b. Since the shear wave propagates in a homogeneous region, the tracing curve is close to a straight line with an inclination angle. Then, we do the same operation for the 30 th frame image of shear wave propagation in the targeted imaging area of Figure 1d. Similarly, Figure 2c shows the original propagation trajectory of the shear wave, and the tracing curve is shown with the red curve of Figure 2d. Owing to the deformation of the shear wave front at the inclusion, the tracing curve protrudes to the right, which is consistent with the expected result. Because the shear wave front cannot cover the whole longitudinal range, we set two transverse lines at the head and tail of the shear wave front. Figure 1: The selected experimental area in 040 GSE ultrasound phantom. (**a**) The selected experimental area of homogeneous region. (**b**) The selected experimental area containing a 10 kPa inclusion. (**c**) The selected experimental area containing a 40 kPa inclusion. (**d**) The selected experimental area containing a 60 kPa inclusion. Figure 2: Experimental results of real-time curve tracing. (**a**) The 10 th frame image of shear wave propagation in homogeneous region. (**b**) Tracing curve of (**a**). (**c**) The 30 th frame image of shear wave propagation in the region containing a 60 kPa inclusion. (**d**) Tracing curve of (**c**). Generally, the isotropic homogeneous region is used to analyze and evaluate the estimation method of shear wave velocity [33]. For the homogeneous region, the shear wave velocity can be quickly estimated by taking the lateral moving distance of several tracing curves in the same transverse direction as the shear wave displacement. With the real-time curve tracing method, the tracing curves of each frame of the high-frame rate shear wave propagation in the homogeneous region of Figure 1a can be obtained. Figure 3 lists the six tracing curves that are initially frame 4 and frame interval 5. Directly perceived from Figure 3, the shear wave tracing curve is an approximately inclined straight line, and the interval of each curve is roughly equal. On the one hand, these characteristics reflect the Mach cone shape of shear wave and, on the other hand, they reflect that the shear wave propagates at a uniform speed, which indicates that the targeted area is homogeneous. Since the longitudinal range of the data that can be used to calculate the wave velocity is different in each frame, the common part of these frames is selected to estimate the shear wave velocity (about 25 \(\lambda\) to 85 \(\lambda\)). A to F are the intersections of the tracing curves of the 4 th, 9 th, 14 th, 19 th, 24 th and 29 th frames at a depth of 55 \(\lambda\), respectively. By performing linear regression processing on the ordinates of these six intersections, the propagation velocity of the shear wave in the specified transverse direction can be estimated. Of course, one can choose the intersection point of any number of frames at a certain transverse position for linear regression to estimate the propagation velocity of the shear wave in the homogeneous region. The estimation error decreases with the increase in frame number. To verify and compare the performance of the proposed method, the time-to-peak and the lateral peak method are used to estimate the shear wave velocity in the homogeneous region under the same conditions, taking a homogeneous region with a Young's modulus of 30 kPa as an example.