# Hemodynamic Interference of Serial Stenoses and Its Impact on FFR and iFR Measurements
## 3 Results
In 75% of diastole (2.4 s), it was clearly shown that vortex structures were significantly reduced throughout the serial stenoses, compared to those at 2.1 s.  
Figure 3: Pressure distributions in the case of the spacing ratio of 1, 3, 5, 7 and 10 at 2.1 s (**a**) and 2.4 s (**b**). Figure 4: Velocity streamlines at 2.1 s (**a**) and 2.4 s (**b**) and velocity plane profiles at 2.1 s (**c**) and 2.4 s (**d**) in the case of the spacing ratio of 1, 3, 5, 7 and 10. The role of the spacing ratio on Q-criterion in the artery at 2.1 s and 2.4 s is quantified in Figure 6. The Q-value represents the magnitude of Q-criterion. The locations of the maximum positive Q-value at 2.1 s are marked by the red-colored stars. These were located at 19.5 mm, 28.1 mm, 35.7 mm, 22.1 mm and 22.7 mm away from the inlet, respectively, in the case of the spacing ratio of 1, 3, 5, 7, and 10. The interesting observation was that the maximum positive Q-value at 2.1 s was located in the center of the second stenosis in the case of the spacing ratio of 1. Also, the location of the maximum positive Q-value moved toward the beginning of downstream of the second stenosis in the case of the spacing ratio of 3 and 5. However, in the case of the spacing ratio of 7 and 10, the maximum positive Q-values were located in the downstream of the first stenosis. Moreover, the averaged positive Q-values starting from the points 5.5D and 6.72D from the first stenosis to the end distal to first stenosis were 6.21 \(\times\) 10\({}^{5}\)\(s^{-2}\), and 2.18 \(\times\) 10\({}^{5}\)\(s^{-2}\) in the case of the spacing ratio of 7 and 10, respectively, which were less than 1% of the maximum Q-value. And the maximum Q-values at 2.1 s were likely to decrease as the spacing ratio increased. The positive maximum Q-value at 2.4 s showed a significant reduction, i.e., by 9423%, 6566%, 8471%, 5795%, and 5804%, in the positive Q-value compared to that at 2.1s in the case of the spacing ratio of 1, 3, 5, 7, and 10, respectively, which corresponded to the minimal pressure variations at 2.4s. Figure 7 shows the representative pressure distribution with vortex structures quantified by Q-criterion (20% of maximum) at 2.1 s in the case of the spacing ratio of 5. The pressure in the region where the vortex structures existed, 18.4 mm away from the inlet, was 23.1 kPa, while a pressure not in the vortex region, i.e., 19.3 mm away from the inlet, was 26.2 kPa. The difference between them was 13.2%. The pressure difference between two points at 25.5 mm and 25.9 mm, closer to the end distal to the first stenosis, was only 2.8%. The difference between them tended to be smaller as their locations became closer to the end distal to first stenosis. The same phenomenon was observed in other cases. Figure 5: Vortex structures, 20% of the maximum value of Q-criterion (8.531 \(\times\) 10\({}^{6}\) s\({}^{-2}\)) in the case of the spacing ratio of 1, 3, 5, 7 and 10 at 2.1 s (a) and 2.4 s (b). Figure 6: Q-values in the case of the spacing ratio of 1, 3, 5, 7 and 10 at 2.1 s (**a**) and at 2.4 (**b**). The red stars represent the locations of the maximum Q-value at 2.1 s.  
Table 1 shows the FFR and iFR measurements for the first and second lesions in the case of the spacing ratio of 1, 3, 5, 7, and 10. The pressures at three locations consistent with clinical settings [30] were extracted from the models, i.e., inlet, location \(\alpha\) and location \(\beta\). The pressure ratios across each stenosis for the FFR and iFR were then calculated. Specifically, for the case with a spacing ratio of 5, the systolic pressure at inlet, location \(\alpha\) and location \(\beta\) were 44.4 kPa, 25.6 KPa and 13.3 KPa, respectively. The corresponding pressure at 75% diastole were 15.7 kPa, 14.3 kPa, and 13.3 kPa, respectively. The FFR measurements, i.e., systolic pressure ratios across 1 st lesion and 2 nd lesion, were 0.577 and 0.520, respectively. The iFR measurements, i.e., the pressure ratios at 75% diastole were 0.911, and 0.930, respectively.