## 2 Materials and Methods
Hence, element numbers of the artery with an inflated two-stent model were approximately 3,938,265 to obtain the convergence criterion. The convergence elements were applied and meshed for whole arterial models of the CFD simulation. All stenting bifurcation models were performed in the CFD analysis using the CFX module of the ANSYS Workbench 16 (ANSYS Inc., Canonsburg, PA, USA). The non-Newtonian Casson model was selected to describe the blood's shear-thinning behavior [28]. The blood density and the dynamic viscosity of the blood were assumed at 1060 kg/m\({}^{3}\) and 0.0035 Pa\(\cdot\)s, respectively [29]. The pulsatile flow rate was applied as an inlet boundary condition at the left main coronary artery (Figure 4) [30]. A constant zero pressure boundary condition was applied at the outlet. Moreover, both the arterial wall and stent were rigid with a no-slip boundary condition. The hemodynamic evaluations of the CFD analysis included flow velocity (FV), time-averaged wall shear stress (_TAWSS_), and oscillatory shear index (_OSI_). Wall shear stress (_WSS_) is used to associate dynamic behaviors of blood flow with potential clinical outcomes. The instantaneous _WSS_ is defined as  
\[WSS=\mathcal{T}_{t}-(\mathcal{T}_{t}\cdot n)n. \tag{1}\]  
Figure 4: The definition of the pulsatile flow rate. Cardiac pulsatile velocity was selected for computational fluid dynamic simulation of the left coronary bifurcation artery in this study. Figure 3: The models of post-stenting. The three stenting techniques models of the T-stenting, Culotte, and Kissing were selected in the bifurcation angles with 80\({}^{\circ}\), 113\({}^{\circ}\), and 142\({}^{\circ}\) from left to right in the artery A and the artery B; (**a**) Type of artery A; (**b**) Type of artery B. The _WSS_ can be further calculated as a time-averaged index over a cardiac cycle. The formula is defined as  
\[TAWSS=\frac{1}{T}\int_{0}^{T}\lvert WSS\rvert dt \tag{2}\]  
where \(T\) is the period of one cardiac cycle. In vitro studies have demonstrated that low _TAWSS_ (<0.5 Pa) is associated with promoting endothelial cell proliferation and plaque growth [31]. The OSI is a non-dimensional scalar variable; it represents the change of direction of the _WSS_ vector from a predominant blood flow direction during the cardiac cycle. The value of the OSI distribution is computed from 0 to 0.5; both values 0 and 0.5 represent a region of unidirectional flow and full-oscillatory flow, respectively. The high OSI (>0.2) has been considered to increase endothelin cell proliferation and to cause higher vessel wall permeability [32]. The formula of the \(OSI\) is defined as below  
Figure 1.0  
The four consecutive cardiac cycles were simulated for investigating the stenting restenosis with different stenting techniques by the CFD simulation. Moreover, final results were taken from the fourth cycle for comparing the effects of stenting restenosis with different stenting techniques. This determination of cardiac cycles was cited as a reference from [PERSON] et al. in 2016 [33]. Hence, this study set four cardiac cycles to perform simulation to provide the results of the _TAWSS_ and _OSI_ values.