## 3 Results  
### Results  
To validate the geometry of the fabricated stenotic phantom, the B-mode images of each phantom were coherently beamformed with a dynamic range of 45 dB, as shown in Figure 5a-d. It can be observed that the vessel wall is clearly visible, and the geometry of each flow phantom approximately follows the designed shape. There is a slight reduction in diameter in all four kinds of flow phantoms due to the slight shrinkage of the PVA-C vessel [42]. The diameters of the pre-stenotic region in four cases were measured as 5.7 mm, 5.7 mm, and 5.6 mm, respectively. The calculated acoustic properties, including the speed of sound and the attenuation of the agar tissue phantom and PVA-C vessel phantom, are shown below. The means and standard deviations (std) were calculated from five realisations of measurements. The measured acoustic speed and attenuation rate were (mean \(\pm\) std): 1548 \(\pm\) 34 m\(\cdot\)s\({}^{-1}\) and 0.46 \(\pm\) 005 dB\(\cdot\)cm\({}^{-1}\)-MHz\({}^{-1}\) for the PVA-C vessel and 1542 \(\pm\) 22 m\(\cdot\)s\({}^{-1}\) and 0.43 \(\pm\) 0.12 dB\(\cdot\)cm\({}^{-1}\).MHz\({}^{-1}\) for agar-TMM, respectively. The measured values show good agreement with previous work by our group [26]. The acoustic results mean that our fabricated flow phantoms have a good acoustic performance when used in ultrasound imaging. The accuracy of PW vector Doppler in estimating WSS was assessed in the synthetic vessel phantom created in Field II with a parabolic profile at centreline velocities of 0.2 m\(\cdot\)s\({}^{-1}\), 0.4 m\(\cdot\)s\({}^{-1}\), and 0.6 m\(\cdot\)s\({}^{-1}\). The WSS and velocity map from the simulation with a centreline velocity of 0.2 m\(\cdot\)s\({}^{-1}\) is presented in Figure 6. The direction and length of the arrows represent the velocity direction and magnitude, respectively. The colour-coded velocity and WSS maps represent the distribution of the velocity and WSS. Overall, it can be observed that the flow vectors visually present a parabolic shape in all cases, as expected. The NRMSE calculated from 10 realisations of estimations between the estimated WSS and the WSS reference were (mean \(\pm\) std) 9.4 \(\pm\) 0.3, 6.6 \(\pm\) 0.4, and 9.2 \(\pm\) 0.9. WSS measurements were conducted in the phantoms with a steady and pulsatile flow to investigate the relationship between WSS and the degree of stenosis. The vector maps and WSS maps of the four phantoms in the steady-flow experiment with a flow rate of 200 mL\(\cdot\)min\({}^{-1}\) are shown in Figure 7a-d. It can be observed that the flow scatterers accelerate when passing the stenotic region and move slower when the diameter increases. The central post-stenotic region has a higher velocity magnitude than the pre-stenotic region. The maximum WSS value was found around the stenotic regions. When the degree of stenosis increased, the separation regions located in the post-stenotic region expanded, where recirculation flow was observed. Figure 5: B-mode images of fabricated CA phantoms: (**a**) 0% stenosis, (**b**) 20% stenosis, (**c**) 40% stenosis, and (**d**) 60% stenosis. The scale bar on the right indicates the intensity (dB). Figure 8a-d show the mean WSS with variations in the degree of stenosis under different flow rates. For the stenotic vessel phantoms, the WSS was averaged along the vessel wall of stenotic regions. For the non-stenoic phantoms, the WSS was averaged along the vessel wall. The mean and std of WSS estimates were calculated from 10 consecutive realisations of WSS estimation. Each WSS estimation was performed in different frames of the acquired plane wave data. It can be seen that the mean WSS increased significantly with the degree of stenosis (\(p<0.01\)), except for the case between 0% and 20% (\(p=0.028\)). The WSS in the 60% stenotic region was significantly higher than in the 0% stenotic region (\(p<0.01\)), where the increases in WSS (in percentage) from are 226%, 381%, 367%, 341%, 403%, and 412% from 50 mL-min\({}^{-1}\) to 300 mL-min\({}^{-1}\), respectively.