## 2 Materials and Methods
### The Customized Water Phantom  
Our research group designed several water phantoms customized to satisfy multiple factor settings in the [PERSON]'s analysis for various medical applications. These included line pair gauges [13; 19], a V-shaped line gauge [14; 15], and the latest water phantom [12] composed of two main compartments and several accessory components, as depicted in Figure 2A. This design satisfied the static [PERSON]'s analysis requirements and was found suitable for the dynamic one, as in [12]. Its first (left) compartment was the main water tank manufactured from stainless steel, and the second (right) one was a control box with a digital step motor-driven water pump for water flow control. The top device in Figure 2A was an electrical protractor with an adjustable clamp to turn sonography probes by the required inclination angle. The above phantom simulated the blood flow in the iliac artery. This study adopted a 90 cm/s flow rate controlled by a noninvasive flow rate meter. The latter operated as the central electronic device, monitoring the water flow in the silicon pipe for scanning. Figure 2B depicts the water tank inner space (L \(\times\) W \(\times\) H = 244 \(\times\) 194 \(\times\) 202 mm\({}^{3}\)), containing two silicon pipes with inner diameters of 19 and 10 mm and the wall thickness of 1 mm. Each pipe could be switched alternately by the external valve on the water tank bottom, marked in red in Figure 2A. As seen in Figure 2C, a 2 mm-thick silicon film shell of 175 mm in diameter was also used to simulate human skin: it was pressed tightly to the water surface. The water depth (preset at 45 mm) could be adjusted by the additional drain valve on the water tank bottom, marked in blue in Figure 2A. Since the pipe center was 20 mm from the bottom, the pipe top distance from the silicon film was 19 mm (45 \(-\) 20 \(-\) (10 + 1) = 14 mm) [12]. Figure 2D,E illustrate the adjustable clamp used to fix the required probe angle for scanning and an artificial stenosis analog model (silicon pipes of 50 mm in length and 8 or 4 mm inner diameter). These pipes simulated the stenosis by blocks with a tunnel cross-sectional area of 50.2 or 12.6 mm\({}^{2}\), respectively. The main advantage of the adopted phantom over other options was independent adjustability of each factor. Thus, flow rate, probe angle, and water depth were adjusted to the preset ultrasound scan protocol in order to arrange the L\({}_{18}\) orthogonal array for dynamic Taguchi's analysis. The particular settings are tabulated in Tables 1 and 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Factor**} & \multicolumn{3}{c}{**Levels**} \\ \cline{2-4}  & **1** & **2** & **3** \\ \hline (A) angle of probe (degree) & 30 & 0 & \\ (B) signal amplification gain (dB/cm) & 50 & 55 & 60 \\ (C) resolution vs. speed & R1 & RS & S1 \\ (D) dynamic range (dB) & 40 & 50 & 60 \\ (E) XRES (scenario) & 1 & 2 & 3 \\ (F) zoom & 0.8 & 1.0 & 1.2 \\ (G) time gain compensation & \(-\)1 & 0 & +1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Seven factors (each bearing two or three levels) used in the proposed ultrasound scan protocol, according to Taguchi’s settings in Table 1.  
Figure 2: **(A)**. The left part is the main water tank. The right part is the control box, whereas the central electronic device is a noninvasive flow rate meter. **(B)** The inner part of the water tank (L \(\times\) W \(\times\) H; 244 \(\times\) 194 \(\times\) 202 mm\({}^{3}\)). It includes two silicon pipes with inner diameters of 19 and 10 mm, and the 10 mm pipe is the target in this study; **(C)** 2 mm-thick silicon film 175 mm in diameter, simulating human skin, which could be pressed tightly over the water surface; **(D)** a close-up view of the adjustable clamp, which provides the required probe for scanning; and **(E)** the illustration of artificial stenosis made by silicon pipes similar to the pipe adopted in this work.