# Hemodynamic Interference of Serial Stenoses and Its Impact on FFR and iFR Measurements
## 4 Discussions  
The goal of this work is to quantify the hemodynamic interference in serial stenoses with different spacing ratios and its influence on the pressure measurement technique. Specifically, we examined whether the hemodynamic interference at 75% of diastole is negligible to identify the feasibility of iFR technique in serial stenoses. The velocity streamline plot, as shown in Figure 4, enabled the qualitative identification of the hemodynamic interference, such as flow recirculation and/or the shape of velocity profile. This has been illustrated in an early numerical study [14]. However, it was unable to evaluate the impact of the hemodynamic interference on the pressure measurement without quantitative results. Therefore, we proposed to use Q-criterion for quantitatively defining the existence of vortex structures, and then \begin{table}
\begin{tabular}{c c c} \hline \hline
**Spacing Ratio (L/D)** & **FFR (1 st Lesion/2 nd Lesion)** & **iFR (1 st Lesion/2 nd Lesion)** \\ \hline
1 & 0.517/0.618 & 0.904/0.943 \\
3 & 0.503/0.618 & 0.910/0.936 \\
5 & 0.577/0.520 & 0.911/0.930 \\
7 & 0.599/0.500 & 0.911/0.930 \\
10 & 0.606/0.490 & 0.917/0.923 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: FFR, and iFR for 1 st lesion and 2 nd lesion in the case of the spacing ratio of 1, 3, 5, 7, and 10. Figure 7: 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.  
therther than the lower thermodynamic interference in serial stenoses. The region with less than 1% of the maximum Q-value was considered as the inference-free zone. To the best of our knowledge, this is the first quantitative study in stenoses to use Q-criterion. Local pressure fluctuation and recovery are essential for accurate pressure measurement. They were interrelated to the vortex structures, as quantified by Q-criterion in this work, as shown in Figure 7. Pressure in the vortex region was lower than those in the surrounding areas, which induces the local pressure fluctuation. This pressure variation diminished with a longer distance away from the stenosis. This is due to the pressure recovery, i.e., adverse pressure drop, associated with the flow deceleration, during which the kinetic energy was converted to the potential energy [31]. In the FFR measurements represented by systolic phase at 2.1 s, both the pressure variations and averaged Q-values had minimal changes starting from 5.5D and 6.72D downstream of the 1 st stenosis in the case of spacing ratio of 7 and 10, respectively. This was considered as interference-free, which was supposed to be a pressure sensor location of FFR [30]. This interference-free zone indicated that the pressure recovery had been completed and the local pressure fluctuation by the vortex structures vanished. A smaller spacing ratio induced a higher positive Q-value, i.e., a larger hemodynamic interference. This, in turn, causes larger errors in FFR measurements, which is consistent with current clinical speculation [11]. It is worth noting that the peak Q-values in the case of the spacing ratios of 1, 3, and 5 were located at the center of the second stenosis or further downstream, rather than the downstream of the first stenosis. This could explain that, in the case of the spacing ratio of 1, the pressure magnitude at 2.1 s decreased sharply to 5.88 KPa at the center of the second stenosis. It indicated that the pressure recovery has not been completed due to the limited spacing distance and time. The kinetic energy was only partially converted to the potential energy. Therefore, the location and distribution of the Q-value should be considered simultaneously to estimate the hemodynamic interference as well as the associated error in FFR measurements. The FFR measurements for both the first and second lesions should be similar due to the same stenosis degree of 72%. However, the differences of the FFR measurements between the first and second lesions were greater than 19%, even in the case of the spacing ratio of 7.