## 3 Results
### Discussion
There is also a slight reduction in the diameter of the PVA-C vessels, typically by 2%, which has little influence on the estimation results. There are two key factors in the estimation of the WSR; one is the method by which the location of the wall is estimated, and the second is the method by which the velocity data are extrapolated to the location of the wall. In our phantom study, we used a wall detection method based on intensity differences, which has already been validated in [39; 47]. Compared to focused imaging, image quality based on plane wave ultrasound has a relatively low signal-to-noise ratio (SNR). If a high transmission frequency [48] or fewer pulse cycles are used to improve the image quality, due to the restriction of the Nyquist frequency, the maximum velocity and estimation accuracy would be influenced. Therefore, it needs a balance of parameters selected in the application. Moreover, the vessel wall is also in motion within cardiac cycles. These factors cause difficulties in accurately detecting the wall location. Especially if the imaging scenario is complex, such as in the carotid bifurcation, it is essential to seek a more robust wall segmentation method, for instance, deep learning [49] and adaptive wall tracking [50]. Moreover, clutter filtering is challenging when preserving the low-velocity components near the vessel wall. Designing a well-defined filter can help to remove the clutter as much as possible. However, the tissue velocity may overlap with the blood velocity. Very commonly used filters such as the finite impulse response (FIR) and infinite impulse response (IIR) may remove the blood flow vector within the stop band. In this work, we used an SVD filter to remove the clutter. The SVD filter is a spatiotemporal filter based on singular vector decomposition. The clutter removal is realised by rejecting the singular components belonging to tissue motion. The SVD filter performs better in separating the clutter and blood vector than traditional filter methods, such as the FIR and IIR filter methods [37]. To further increase the accuracy of estimated WSS, microbubble contrast agents may be used to increase the SNR of blood flow and the sensitivity of the imaging system [41, 51]. For the estimation of the wall shear rate, we regulated the velocity near the wall by using a Savitzky-Golay filter, which is commonly used, such as in [28, 41]. However, it requires the careful selection of the filter parameters. Some novel methods focusing on compensating the near-wall velocity or reconstructing the velocity profile near the wall also show promising results in estimating the near-wall velocity [11, 29]. The applicability of the results of the paper to the clinical scanning of patients will be considered. The phantoms are tissue-equivalent, and therefore, the images are comparable to those that would be obtained using a clinical ultrasound system on patients. The measured velocity vectors and WSS are able to give a detailed haemodynamic depiction of the region of interest. However, in the application of in vivo scanning, the image quality is likely to be poor, in association with shadowing arising from the calcified plaque. In this case, locating the vessel wall would be difficult, which will limit the accuracy of WSS estimation. It may be that adequate results could be obtained by choosing another image plane. A second issue concerns the fact that the fabricated phantoms are straight, whereas the carotid arteries are a 3D bifurcating structure. However, the entire 3D structure is not of interest in the current study. In ultrasound scanning, the operator chooses a longitudinal scan plane in which the stenosis is centrally placed, and the lumen is visualised for 2 cm or so on either side of the stenosis. In this respect, the straight-tube phantom could resemble situations in patients. It is noted that conventional ultrasound is a 2D technique; out-of-plane WSS components would require the use of a 3D technique, which is outside the scope of this study.