# Hemodynamic Interference of Serial Stenoses and Its Impact on FFR and iFR Measurements
## 3 Results  
Results were retrieved at 2.1 s (systole) and 2.4 s (75% of diastole). For simplicity, the pressure ratios across a stenosis at 2.1 s were assumed to be the FFR measurement under a hyperemic condition, since the influence of the systolic phase on the averaged measurement is much stronger than that of the rest of the cardiac cycle [29]. The results at 2.4 s literally represent the iFR measurement at 75% of diastole. The role of the spacing ratio on pressure distributions of the serial stenoses is depicted in Figure 3. Regardless of spacing ratios, two pressure valleys corresponding to the two narrowest sites were clearly observed. Following each stenosis, the local pressure fluctuation and the pressure recovery phenomenon were also observed. In systole, the pressure magnitude at the spacing ratio of 1 showed a sharp increase to 30.7 KPa at 17.8 mm away from the inlet due to the effect of high-inertia loads and the presence of a second stenosis. This sharpness was mitigated as the spacing ratio increased. This was due to the larger space between the two stenoses enabling the flow to decelerate more by the adverse pressure drop as the spacing ratio increased. It is interesting to observe that the pressure magnitude at 2.1 s in the case of the spacing ratio of 1, decreased sharply to 5.88 KPa in the center of the second stenosis. Also, the pressure variations were less than 1%, starting from 5.5D away from the first stenosis in the case of spacing ratio of 7. The same phenomenon was observed at 6.72D away from the first stenosis in the case of spacing ratio of 10. However, the pressure values fluctuated continuously from the downstream of the first stenosis to the downstream of the second stenosis in the case of the spacing ratio of 1, 3, and 5. The local pressure fluctuation became smaller distal to each of the two serial stenoses as the spacing ratio increased. The inlet pressure was elevated as the spacing ratio increased. This resulted in a larger pressure drop across the serial stenoses considering that the outlet pressure was prescribed as constant. Specifically, the inlet pressure in the systolic phase (2.1 s) was 41.8, 42.7, 44.4, 44.4 and 44.7 KPa for the spacing ratios of 1, 3, 5, 7, and 10, respectively, resulting in pressure drops across the first stenosis of 20.2, 21.2, 18.8, 17.8, and 17.6 KPa and across the second stenosis of 8.3, 8.2, 12.3, 13.3, and 13.8 KPa, as well as total pressure drops of 28.5, 29.4, 31.1, 31.1 and 31.4 KPa, respectively. The pressure distribution at 2.4 s also exhibited the effect of a high-inertia load at the end distal to the first stenosis, but the magnitude was significantly smaller than that at 2.1s. It is interesting to observe that the pressure variations following each stenosis at 2.4 s were less than 1%. The differences among the total pressure drops with different spacing ratios were also less than 1%. Figure 4 shows that the recirculation zone was formed following each stenosis. It is interesting to observe that the skewed velocity profiles were returned to be the normal ones in the vicinity at the end distal to the first stenosis in the case of a spacing ratio of 7 and 10. Figure 5 shows an instantaneous view of Q-criterion (8.531 \(\times\) 10\({}^{6}\) s\({}^{-2}\)) that corresponds to 20% of the maximum value of it. The grey-colored wormlike structures represent vortex structures. In systole (2.1 s), the distribution of the vortex structures were biased compared to those at the downstream of the second stenosis regardless of the spacing ratio. For the case of the spacing ratio of 1, 3 and 5, the vortex structures were continuously distributed from the downstream of the first stenosis to the distal to the second stenosis. However, in the case of the spacing ratio of 7 and 10, the vortex structures were not captured in vicinity at the end distal to the first stenosis, which corresponded to the locations where the pressure variations were minimal.