## 2 Materials and Methods  
To investigate the haemodynamics in the stenotic CA with different stenosis degrees, four flow phantoms were prepared from a polyvinyl alcohol cryogel (PVA-C) vessel and an agar tissue mimic (agar-TMM). Three-dimensional printing was used to produce the vessel mould and vessel core [21]. A cuboid phantom box was used to hold the fabricated vessel and tissue mimic, as shown in Figure 1. An acoustic absorber (AptFlex F28, Precision Acoustics Ltd., Dorset, UK) was placed on the bottom of the box to reduce the sound reflection from the box bottom. Two quick-fitting flow connectors were fixed and aligned by the bolts at the two opposite ends of the phantom box to be connected by the PVA-C vessel and outer C-flex connecting tubing. A series of stenotic vessel core models were first created in Solidworks (Dassault Systemes, Waltham, MA, USA). The stenosis was modelled at the middle of the vessel, and the degree of stenosis ranged from 0% to 60% with increments of 20%. The degree of stenosis \(P_{\text{stenosis}}\) is defined as a percentage using the following equation:  
\[P_{\text{stenosis}}=\frac{d_{\text{original}}-d_{\text{stenosis}}}{d_{ \text{original}}}, \tag{1}\]  
where \(d_{\text{original}}\) and \(d_{\text{stenosis}}\) are the vessel diameters before and at stenosis, respectively. The stenosis shape follows an ideal cosine function, as used in previous papers [25; 30; 31], and the length of stenosis is 12 mm, as shown in Figure 2. To help form the vessel wall, a detachable mould was 3D-printed. All vessel cores and moulds for fabricating flow phantoms were printed by a Stereolithography 3D printer Form 2 (Formlabs, Somerville, MA, USA) using white resin (Formlabs, Somerville, MA, USA), which has a resolution of 100 microns. The supports attached to the printing objects for facilitating the 3D printing process were removed by using sandpaper. The designed vessels have a diameter of 6 mm, a wall thickness of 1.5 mm in the non-stenotic part, and a total length of 180 mm. Polyvinyl alcohol (PVA) was used as the material to fabricate the vessel phantoms in this study. The fabrication of all PVA mixtures followed the fabrication procedure described by [PERSON] et al. [26]. In brief, a 10% (by weight) PVA mixture was mixed in 88.79% deionised (DI) water in a glass beaker to make the vessel mimic. Then, 0.75% silicon carbide was added as acoustic scatterers, and 0.46% benzalkonium chloride was added as an antibacterial agent to preserve the vessel. The PVA mixture was heated in a temperature-controlled water bath for around 2 h until a clear homogeneous gel was seen. Subsequently, the PVA mixture was degassed for 12 h after injecting the PVA mixture into the moulds. Vessel phantoms were put in a freezer for 14 h at a temperature of \(-20\,\mathrm{\SIUnitSymbolCelsius}\) and then kept at room temperature (22 \(\,\mathrm{\SIUnitSymbolCelsius}\)) for 10 h. This was repeated for a total of three freeze-thaw cycles. The vessel core was removed manually after completing freeze-thaw cycles. To simulate the surrounding human tissue, an agar-TMM was fabricated [26]. The agar-TMM consists of the following materials: (1) 3% (by weight) agar powder, (2) 82.4% DI water, (3) 3% silicon carbide, which was used as acoustic scatterers, (4) 11.32% glycerol, which was used to tune the sound speed, (5) 0.88% 0.3 \(\,\mathrm{\SIUnitSymbolMicro m}\) aluminium oxide powder and 0.94% 3 \(\,\mathrm{\SIUnitSymbolMicro m}\) aluminium oxide powder, which were used to tune the attenuation, and (6) 0.92% benzalkonium chloride, which served as the antibacterial agent. The mixture was heated in a water bath and mixed by a mechanical stirrer for 1.5 h. To prevent the collapse of the vessel, the PVA-C vessel was filled with water and sealed at both ends before pouring the agar-TMM solution into the phantom container. The acoustic properties of fabricated flow phantoms were measured by an in-house system using the time-of-flight method [32].