## 6 Discussion  
The current study demonstrates the impact of stenosis located at multiple positions within the left coronary artery (LCA), on hemodynamic indicators. The simulation was performed in a patient specific left coronary artery model while considering the walls to be rigid and flexible in nature, through establishing a two-way FSI approach. A multiphase blood model incorporating a mixture of RBC and plasma is further considered. The results obtained within a rigid walled is compared against a FSI model and has not been previously studied. Left anterior descending (LAD) exhibits a stenosis of 70% and 80% while left circumflex (LCx) encounters a 90% occlusion. The local hemodynamic parameters such as WSS play a significant role in damaging the endothelial cells located on the inner side of the arteries. The WSS and another hemodynamic variable cannot be determined non-invasively. In the past few years, advances in medical imaging techniques such as MRI, CTA, and IVUS have made it possible to differentiate between the wall of the coronary artery and the undesirable deposition but are limited to find the disturbed flow region and oscillatory shear stress regions. The variation in the normal physiologic value of WSS leads to determining the progression and development of atherosclerosis. The simulated results showed that WSS was significantly higher than the physiological value (50 Pa) in the presence of stenosis, and the disturbed flow region was noted across the bifurcations and post-stenotic regions. The maximum WSS was found across the 90% AS, which was consistent with the previously published literature. The pressure drop increased across the higher degree of stenosis as noted in the previous studies. Bifurcation and post-stenotic regions encounter lower pressure as demonstrated in Figure 6, these are primarily the areas associated with progression and development of stenosis [27, 41]. A notable accumulation of RBC at the pre stenosed region was demonstrated by current results in Figure 10, consistent with the previously published literature [13, 14] and in turn, essentially contributes to thrombosis [22, 42]. The discrepancies of rigid model results are due to overlooking the wall motion that subsequently generates pulse that travels within the flexible model (FSI) which, however, in rigid model is suppressed. Additionally, the contours obtained for pressure, velocity and WSS are qualitatively similar, across rigid and FSI models. However, quantitatively; along the throat of 90% occlusion these are different compared to rigid in the following aspects: (a) the FSI model encounters higher flow velocities during the diastolic portion of the cycle. At systolic phase a 2% decrease in the velocity is encountered while along the diastolic phase, a 3.5% increase in velocity is achieved. (b) The overall pressures based on the average quantity are lower by 5.7% in FSI models due to wall deformations. (c) Along the stenosis, the WSS values are suppressed by 6.5% in flexible models (d) Recirculation regions along the post-stenotic region are smaller in FSI models. The competence of calculating the hemodynamic parameters non-invasively is not only important for the diagnosis of diseases, but also significant for the development of a patient's specific devices to improve the quality of treatment procedure. There are some limitations of this study that should be addressed in future. Firstly, the wall of the artery was modeled with the uniform thickness, which is a common assumption reasoned by previous studies. Secondly, the flow waveform at the model inlet has been adopted from literature studies [14, 20, 43] while the outlets are assigned an outflow condition, thus the simulated results do not reflect the actual physiological condition. Therefore, the flow and pressure waveforms should be used for that individual patient through a medical hospital to obtain more realistic and precise physiological conditions.