# Hemodynamic Interference of Serial Stenoses and Its Impact on FFR and iFR Measurements
## 4 Discussions
This is because the increased flow under hyperemia was not transmitted uniformly over the two serial stenoses [13]. A larger amount of kinetic and potential energy was converted to thermal energy by friction and viscosity when passing through the first stenosis compared to the second stenosis [32]. For example, in the case of spacing ratio of 7, the pressure drop across the first stenosis was 33.83% higher than that across 2 nd stenosis, as shown in Figure 3a. This caused the underestimation of the first stenosis and overestimation of the second stenosis; this is evident in the FFR calculation (Table 1), as 0.599 and 0.500 across the first and second stenosis, respectively. This implied that, under the condition of serial stenoses, no hemodynamic interference still led to inevitable errors in FFR measurements due to the nature of the hyperemia. In the iFR measurements, i.e., diastolic phase (2.4 s), the pressure variations distal to each stenosis were less than 1%, regardless of the spacing ratios. Even in the case of the spacing ratio of 1, the high-inertia load effect caused a difference of only 1.4% in the pressure magnitude. The hemodynamic interference, associated with the local pressure fluctuation influenced by the vortex structures, was minimal. Specifically, the maximum positive Q-value at 2.4 s was decreased by 9423% compared to that at 2.1 s. This indicated that the hemodynamic interference is negligible at 75% of diastole, which is consistent with the current clinical speculation [13]. The iFR measurements for both the first and second lesion is similar, with a difference less than 5% regardless of spacing ratios. The differences in the total pressure drop were also less than 2.2%. The differences of iFR measurements among various spacing ratios were less than 1.54%. This implied that the iFR measurement overcame the disadvantage of the FFR measurement, in which the increased flow under the hyperemic condition was not transmitted uniformly over the serial stenoses, and the hemodynamic interference was significantly amplified under hyperemia [13; 33]. In the present work, the straight artery with generalized stenoses were modeled. More realistic models considering patient-specific stenoses, artery curvature, and the sequence of stenoses could be obtained from OCT (optical coherence tomography), CT (Computed Tomography) and/or MRI (Magnetic Resonance Imaging) scans. The lesions were assumed to be rigid, although they have been shown to be anisotropic, heterogeneous, and viscoelastic [34]. These simplifications might alter the magnitude of our results [35; 36]. In addition, the impeded flow from guiding catheter might also alter velocity and pressure fields [30]. The dynamic outlet boundary condition will be more appropriate [37] for quantifying the hemodynamic interference and its clinical measurements. Despite these simplifications, the present work demonstrated a novel way to define the hemodynamic interference and to evaluate the measurement accuracy of both FFR and iFR, which may have significant clinical implications for diagnosis and treatment decisions of serial stenosis. In addition, although this work illustrated the feasibility of iFR measurement, it needs be further tested in clinical studies. One potential challenge could lie in the measurement resolution and the iFR threshold [38; 39].