# Fractional Flow Reserve (FFR) Estimation from OCT-Based CFD Simulations: Role of Side Branches
## 3 Results and Discussion  
### FFR and Flow Distribution in Idealized Artery Models  
CFD simulations were performed in three idealized artery models, namely, model 1 (without side branch), model 2 (with one side branch located at the upstream of the stenosis), and model 3 (with one side branch located at the downstream of the stenosis). The pressure and velocity distributions in the three idealized artery models are shown in Figure 4a-c. A significant pressure drop was observed as the flow passed through the stenosis. The lowest pressure was seen at the stenosis region due to a high velocity at the narrow section. As the flow traveled further downstream, the pressure slightly increased due to pressure recovery with velocity reduction. A more axial symmetric velocity distribution was observed in model 1 (without side branches) compared with the other two models (with a side branch). The blood flow was redistributed to maintain the same inlet aortic pressure, as depicted in Figure 4d. Models 2 and 3 showed a higher inlet flowrate than model 1. This indicated that the inclusion of the side branch requires more blood flow intake. Models 1 and 2 had a similar outlet flowrate from the main vessel (outlet1), i.e., <0.01% difference. It suggested a minimal alteration in the flowrate through the stenosis when the side branch is located before the stenosis region. In contrast, the outlet flowrate of the main vessel in model 3 was 15% lower than the other models. It should be noted that the flowrate through the stenosis was the same as the inlet in model 3, and as the outlet1 in the other models. This means that blood flow through the stenosis in model 3 (inlet) was 27% higher than the other models (outlet1). The alterations in the velocity distributions caused by side branches can lead to changes in local hemodynamics parameters, such as wall shear stress (WSS), and further induce remodeling of the vessel wall. Previous studies [26; 27] have revealed the importance of the inclusion of side branches when assessing the risk of atherosclerosis development in relation to WSS distribution. Figure 4: CFD-derived pressure and velocity distributions in an idealized artery model: (**a**) model 1: without side branch; (**b**) model 2: with side branch located at the upstream; (**c**) model 3: with a side branch located at the downstream. Comparison of (**d**) flowrate into side branches and (**e**) CFD-derived FFR between the three models. FFR was determined as the ratio between the outlet pressure and the inlet pressure of the main vessel, as shown in Figure 4e. The estimated FFR of model 2 was slightly less than model 1 (with a difference of 0.002). This insignificant change in FFR is also in accordance with the similar flowrate observed through the stenosed region of these models. The estimated FFR in model 3 was significantly smaller, which was 15.5% lower compared to the other two models, suggesting that the side branch located at the downstream has a significant impact on FFR estimation. The influence of the side branches on the FFR value can be further illustrated with electrical circuit models (Figure 5). Here, the variables, in terms of voltage and resistance, are analogous to the pressure and flow resistance in the fluid domain, respectively. V and V1 denote the voltage (analogous to the pressure) at the main vessel inlet and outlet, respectively. R1 and R2 denote the distal microvascular resistances of the main vessel and side branch, respectively. R(q) denotes the flow resistance induced by the stenosis region. Flow resistances of the healthy segments of the arteries are assumed to be negligible compared to the stenosis region and distal microvascular resistances. The pressure drop (\(dP\)) across the stenosis can be described by a nonlinear function of the flowrate (\(q\)) as,  
\[dP=C_{1}q+C_{2}q^{2} \tag{11}\]  
where the first term and the second term of the Equation (11) represent the viscous pressure drop and expansion pressure drop across the stenosis, respectively.