## 3 Results
_Role of microvascular disease in the modelled FFR:_ The average flow (flow), maximum flow, and FFR values of simultaneous focal stenosis and microvascular disease are shown in Figure 5. Microvascular disease was simulated by varying the daughter vessel's radius taper exponent \(\epsilon\) (Equation (1)) from 2.76 (0% microvascular disease, control) to 2.33 (100% microvascular disease) which represents turbulent flow [22]. At diameter reductions below 70%, the flow in each blood vessel (Figure 5, top row) is significantly restricted by up to half of the control flow with the increase in severity of microvascular disease. At similar diameter reductions in the LAD and LCX however, the peak reduction in max flow values (near 0.5 of the control values) occur at 50% microvascular disease and returns to near control values at maximal microvascular disease. At diameter reductions above 80%, microvascular exacerbates the effect of the stenosis on FFR values. However, an almost unique value of diameter reduction for each, LAD, LCX, and RCA, was observed to characterize a clinically significant FFR transition to below 0.8 in the presence of an arbitrarily severe microvascular disease. While the diameter reduction was 0.7 for LAD and LCX, it was seen to be a much lower 0.55 in the case of RCA. Figure 3: Flow profiles in the LAD (column **A**), LCX (column **B**), and RCA (column **C**). In all columns, top row shows non-stenosed (control) model flow, second row shows flow under focal stenosis (\(\alpha=90\%\)) and the third row shows the flow under microvascular disease in the absence of focal stenosis (\(\alpha=100\%\); \(\epsilon=2.33\)). _Sensitivity analysis to stratify FFR impacting parameters_: The results of the sensitivity analysis are shown in Figures 6 and 7. The histograms of FFR values obtained during the PRCC calculation are shown in Figure 6. As can be seen, the model did not produce any instances with FFR less than 0.3 due to the ranges of parameters considered. The model appears to produce FFR values centered around 0.54. Further, in all three coronaries, the FFR values appear to be distributed in a left-skewed Gaussian manner. Figure 4: Dependence of flow rate (top row), maximum flow (middle row), and mean FFR (bottom row) on stenosis length (vertical axis, all panels) and vessel diameter (horizontal axis, all panels). Columns (**A–C**) show LAD, LCX, and RCA results, respectively. The black line in the bottom row demarcates the FFR = 0.8 threshold. Figure 5: Dependence of flow rate (top row), maximum flow (middle row), and mean FFR (bottom row) on microvascular resistance increase ( microvascular disease, vertical axis in all panels) and vessel diameter (horizontal axis, all panels). Columns (**A–C**) show LAD, LCX, and RCA results, respectively. The black line in the bottom row demarcates the FFR = 0.8 threshold. Figure 6: Histograms of FFR obtained from PRCC simulations (see Figure 7). Panel (**A**) shows the data for LAD, panel (**B**) for LCX, and panel (**C**) for RCA. Figure 7: PRCC sensitivity of FFR to model control parameters. In all panels, the sensitivity of FFR to the six most relevant parameters are shown. Panel (**A**) shows the PRCC for LAD, panel (**B**) for the LCX, and panel (**C**) for the RCA. In all panels, HR: heart rate; fs: focal stenosis; ds: diffuse stenosis; \(r_{0}\): root radius of microvascular bed; \(Z_{i}\): microvascular impedance; \(\varepsilon\): microvasculature taper exponent; and \(\mathrm{E_{sys,rv}}\): systolic elastance of the right ventricle. The sensitivity analysis generated PRCC coefficients are shown in Figure 7. Heart rate (HR) is the most impactful model parameter regulating the FFR. Consistently, focal stenosis (fs) is also a significant regulator of PRCC. Both HR and fs negatively regulate FFR. Diffuse stenosis (ds) and the right ventricular systolic elastance (E\({}_{\text{sys,rv}}\)) also negatively regulate FFR.