## 4 Discussion
### Modeling Simplifications  
Constrained by the computational resource, capability of the numerical algorithm as well as the availability of data, several simplifications have been made in the current study.  
First of all, only steady-state CFD analyses were performed in this study. In the numerical investigations of prosthetic aortic valves, the use of FEM, CFD and fluid-structure interaction (FSI) techniques have been reported. Among these, FSI simulations are advanced in providing the valvular hemodynamics characteristics and strain/stress on leaflets simultaneously, and have started to merge in recent years [37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58]. The most popular FSI algorithms for valvular simulations are arbitrary Lagrangian-Eulerian (ALE) [59], immersed boundary (IB) [60] and smoothed particle hydrodynamics (SPH) [61]. However, the extremely computation-intensive nature of the FSI method has constrained its application in dealing with large-scale models, which would take weeks to months to solve [62; 63; 64]. Compared with FSI simulation, the steady-state CFD simulation is advanced in providing a fast prediction of non-temporal flow characteristics with ease and has been widely used in the studies of valvular and aortic hemodynamics [65; 66; 67; 68; 69; 70; 71; 72]. Despite the fact that the blood flow in the vascular system was pulsatile under physiological conditions, several numerical [73; 74] and in vitro [75; 76; 77] studies have suggested that steady-state simulation can predict the non-temporal related flow characteristics at the corresponding point of the pulsatile flow profile. In addition, it has been reported that the WSS distribution patterns derived from the steady flow simulations are similar to the time-averaged WSS (TAWSS) from the unsteady analyses [78; 79; 67].  
Secondly, the volumetric flow rates were imposed at the inlet and mapped onto the inlet plane by using an idealized parabolic velocity profile [28]. [PERSON] et al. concluded that the inlet boundary condition profile could drastically affect the helical flow pattern in the aorta and suggested imposing an in vivo velocity profile at the inlet to accurately predict the individual flow phenomena in patient-specific analyses [80]. This observation was further supported by the study of [PERSON] et al. [81]. Nevertheless, the idealized inlet profiles, such as parabolic and plug, are still commonly used in the related studies [82; 83; 84] due to the limited availability of in vivo data. As the scope of this preliminary study is not to predict the patient-specific hemodynamics metrics, but to compare the impacts of valve structures on aortic flow, the use of the same idealized inlet flow profile among the cases at each time point could be a reasonable baseline.  
Moreover, the laminar flow condition was assumed in this study due to the constriction of the solver. Although the laminar assumption has been widely used in the flow simulations in the aortic valve and aorta [85; 86; 42; 80; 52], its inaccurate estimation of flow parameters within the transitional and turbulent flow regime region should be noted in the individualized evaluations [87].