## 3 Results
### Discussion  
The in silico experiments have demonstrated that WSS can be measured with an accuracy of less than 10% NRMSE. The flow phantom experiments have demonstrated that  
Figure 8: Mean WSS measured in stenotic regions with different degrees of stenosis under different flow rates: (**a–f**) 50 mL/min–300 mL/min. The vertical bar represents \(\pm 1\) standard deviation. Figure 10: The velocity vectors and WSS maps in the pulsatile flow experiment with 0% stenosis (**a**), 20% stenosis (**b**), 40% stenosis (**c**), and 60% stenosis (**d**). (**e**) WSS variations in the ROI (indicated by red circles in (**a–d**)) during the cardiac cycle. Figure 9: Maximum WSS in the flow phantoms with different degrees of stenosis under different flow rates. The vertical bar represents \(\pm 1\) standard deviation. the PW vector Doppler method can estimate the mean WSS, the maximum WSS increases with the degree of stenosis, and WSS can be measured as a function of time in the ROIs of vessels during the pulsatile cycle. This provides the necessary validation data to give confidence in WSS measurements in patients using the PW vector Doppler technique. This study adopted PW vector Doppler to measure WSS because it has a relatively low computational cost compared to other vector flow imaging methods, such as speckle tracking [41] and transverse oscillation [43]. For the development of a portable ultrasound device, a Doppler-based velocity estimator may be more suitable for the portable ultrasound system, most of which have a low computation ability and low power consumption. However, the estimated maximum velocity of the vector Doppler method is restricted by the pulse wavelength, leading to aliasing in the estimation of the high velocities present near the centre of the vessel. This may limit the use of PW vector Doppler in clinical practice for the measurement of the maximum velocity. For instance, for the experimental setup used in our study, the Nyquist velocity was 0.2 m\(\cdot\)s\({}^{-1}\). Because the overall velocity direction can be known in carotid arteries, the maximum measurable velocity is twice the Nyquist velocity, 0.4 m\(\cdot\)s\({}^{-1}\). Especially in multiple-transmission-angle Doppler schemes, the maximum measured velocity is reduced further. In some severely stenosed arteries, the flow velocity will be extremely high [44]. Thus, the aliasing problem will hinder the application of vector Doppler in the stenotic region. One straightforward way to tackle this problem is to use lower transmission angles to obtain a higher PRF at the cost of an increased estimation bias or apply an antialiasing algorithm in post-processing [45; 46]. However, there are still some limitations when applying anti-aliasing algorithms in applications. However, the measurement of WSS involves the measurement of low velocities near the vessel wall and hence is unaffected by issues of aliasing. The stenosis shape was an ideal cosine, which was originally used in the 1983 paper by [PERSON] and [PERSON] [30]. In practice, stenoses in patients will have a variety of shapes, including a steeper inlet region. However, the same overall flow patterns will be seen regardless of the exact shape; the blood velocity will increase, peaking just beyond the minimum lumen, and the WSS will peak at the minimum lumen. In this respect, the exact shape of the stenosis used in this work is representative of the wide variety of stenosis shapes in patients. As for the fabrication of the experimental flow phantoms, some had non-uniform wall thicknesses. This has been observed in other work [17; 21]. The vessel mould has two parts that need to be aligned together, and any bias may generate non-uniformity in the vessel mould. The variation in thickness will not invalidate measurements concerned with flow analysis and flow-derived parameters such as the WSR. More accurate flow phantom moulding must be considered when wall motion and pulse wave velocity are investigated.