## 3 Results  
The total flow rate in the 5-Fr double-J stents was 23-63 mL/h in the 4.57-mm ureter and 43-147 mL/h in the 5.39-mm ureter, and in the 6-Fr double-J stents the flow rate was 20-47 mL/h in the 4.57-mm ureter and 36-116 mL/h in the 5.39-mm ureter (Figure 7). The total flow rate in the 7-Fr double-J stents was 17-35 mL/h in the 4.57-mm ureter and 29-92 mL/h in the 5.39-mm ureter, and in the 8-Fr double-J stents the flow rate was 16-26 mL/h in the 4.57-mm ureter and 26-71 mL/h in the 5.39-mm ureter.  
The total flow rate in the stented ureters with 5-Fr double-J stents was greater than that in the stented ureters with the other sizes of double-J stents.  
The total flow rate decreased with the increase in the size of the stents. The total flow rate in the stented ureters without any ureteral stenosis was greater than that in the stented ureters with ureteral stenosis. The total flow rate decreased with the increase in the severity of the stenosis. The 4.57-mm ureter with an 8-Fr double-J stent and 74% ureteral stenosis did not exhibit an extraluminal flow rate because of the lack of space between the inner ureter wall and the outer stent wall, that is, the absence of extraluminal space. In this case, the luminal flow rate was the total flow rate. The luminal flow rate around the ureteral stenosis in the mid-ureter was different from that in the proximal and distal ureter (Figures 8 and 9).  
The luminal flow formed through the fifth port in the renal pelvis and the first side hole in the proximal ureter was maintained in the proximal ureter. The luminal flow rate increased before the stenosis because of the increase in the luminal flow through the side holes before the stenosis.  
Figure 6: Flow in the stented ureter. Total flow consists of the luminal flow and the extraluminal flow.  
Then, it decreased after the stenosis because of the decrease in the luminal flow through the side holes after the stenosis. However, the luminal flow rate was maintained in the distal ureter.  
The luminal flow rate was greater when the size of the stent was larger. When a ureteral stenosis became more severe, the luminal flow rate in the proximal and distal ureter decreased and that in the mid-ureter increased. The luminal flow rate in the 5-Fr double-J stents reached 1.2 mL/h in the 4.57-mm ureter and 1.2 mL/h in the 5.39-mm ureter, and in the 6-Fr double-J stents the flow rate reached 5.9 mL/h in the 4.57-mm ureter and 6.1 mL/h in the 5.39-mm ureter. The luminal flow rate in the 7-Fr double-J stents reached 11.4 mL/h in the 4.57-mm ureter and 14.7 mL/h in the 5.39-mm ureter, and in the 8-Fr double-J stents the flow rate reached 16 mL/h in the 4.57-mm ureter and 24 mL/h in the 5.39-mm ureter.  
The extraluminal flow rate was greater than the luminal flow rate in the proximal and distal ureter (Figures 10 and 11). In the mid-ureter, the luminal flow rate was greater than the extraluminal flow rate when the ureteral stenosis was 74% and the size of the double-J stent was 8 Fr. However, in the remaining cases, the extraluminal flow rate was greater than the luminal flow rate.  
No significant flow into or out of the stent was found except for the first and last side holes in the proximal and distal ureter. The inflow and outflow to the stent were demonstrated before and after the stenosis. Around a ureteral stenosis, the flows into and out of a stent before and after the stenosis were shown.  
Figure 7: Total flow rate in the models of the 4.57 and 5.39 mm ureters (Cases 1–8 are defined in Table 3).  
Figure 8: Luminal flow rate in the models of the 4.57 mm ureter.  
Figure 9: Luminal flow rate in the models of the 5.39 mm ureter.  
Figure 10: Luminal, extraluminal, and total flow rates in the 5.39 mm ureter in Case 5 (1 cm side holes, 52% stenosis).  
Figure 11: Luminal, extraluminal, and total flow rates in the 5.39 mm ureter in Case 7 (1 cm side holes, 74% stenosis).