A stenosed model of three-dimensional geometry ( Figure 1 ) for 45%, 60%, and 75% stenoses has been considered here to investigate the pulsatile atherosclerotic hemodynamics in mimics blood flow. The directions of the horizontal and vertical axes are shown by the coordinates X and Y. The length of pre-stenosis is 3D and the post-stenosis is 10D. The parameter D indicates the artery diameter. The laminar and incompressible flow is assumed for the investigated trapezium model of stenosis.

The fluid flow simulations are governed by the continuity and Navier-Stokes equations, as given in the following way:

The general continuity equation’s form for fluid flow is

$\nabla \cdot v=0$ (1)

The Navier-Stokes equations’ form is

$\rho \left(\frac{\partial v}{\partial t}+\left(\nabla \cdot v\right)v\right)=\nabla \cdot \sigma$ (2)

where $v$ is the velocity vector, t is the time, $\rho$ indicates the density of the fluid, and p is the fluid pressure. The Cauchy stress tensor $\sigma$ can be given as follows:

$-PI+\mu \left(\nabla v+{\left(\nabla v\right)}^{\text{T}}\right)$

where $\mu$ presents the dynamic viscosity of the fluid, and $I$ is the identity matrix. The non-Newtonian Carreau model is as follows:

$\mu ={\mu }_{\inf }+\left({\mu }_0-{\mu }_{\inf }\right){\left[1+{\left(\lambda \frac{\partial \gamma }{\partial t}\right)}^2\right]}^{\frac{n-1}{2}}$

where infinite shear rate ${\mu }_{\inf }=0.00345$, zero shear rate ${\mu }_0=0.056$, time constant $\lambda =3.313$, and index n = 0.3568. The pulse given in Figure 2 presents the

inlet flowrate pulse for the present computational fluid model [28] . A no-slip boundary condition is applied at the wall, while the outlet pressure remains static. The pulsatile flow exhibits a waveform of 4.3 ± 2.6 ml with a duration of 0.345 s, produced by a frequency of 2.9 Hz. The fluid has a density of 755 kg/m³ and a viscosity of 0.00143 N∙s/m². The inlet pulse is a sinusoidal wave with an average Reynolds number of 575 and a peak value of 930 [29] .

Newtonian and non-Newtonian rheological models have been assumed for incompressible, laminar and time-dependent flow. The finite element approach in the COMSOL Multiphysics software has been activated for numerical computational techniques. Time-dependent solver takes the fully coupled, advanced and iterative approach for the execution of pulsatile blood flow simulation. Different mesh densities, namely 36,405, 80,542, 107,835, 206,940, and 307,560, have been selected to decide the appropriate mesh for the prediction of outcomes. The mesh elements of 206,940 are appropriate to acquire the results because the last two elements, 206,940 and 307,560, carry approximately the same TAWSS magnitudes. Figure 3(a) shows the grid, and Figure 3(b) presents the grid test in TAWSS. In unsteady flow, the second cycle has been taken to get the simulated results.

In the present research, axial velocity through the radial direction is employed to contrast the results with those of Lee et al. , aiming to verify and affirm the precision and reliability of the computational evaluation. The axial velocity is taken as a post-stenotic distance of 21.5 mm at t = 0.1725 sec. Moreover, as shown in Figure 4 , the comparison of the currently predicted axial velocity results with those obtained by Lee et al. demonstrates significant agreement.

WSS is the key hemodynamic factor that signifies the level of risk for patients. Elevated WSS is associated with the development of susceptible plaques, whereas diminished WSS may result in intimal thickening. Figure 5 illustrates the distributions of WSS with noticeable variations of Newtonian and non-Newtonian fluids at various significant time points (t = 0.08623 s, t = 0.1725 s, t = 0.25875 s, t = 0.345 s). Since the flow directly affects the stenosis’s inlet region, the WSS peaks there, WSS then abruptly increases, remains somewhat elevated throughout the constricted region, and then decreases from the terminating regions. While both fluids result in elevated WSS close to the narrowed portion, the rheological non-Newtonian model generates a greater WSS at every site except the closely post-stenotic part. The Newtonian fluid exhibits a higher recirculation in the area immediately downstream of the blockage than the rheological fluid. The arterial wall displays time-averaged markers such as TAWSS, OSI, and RRT, serving as indicators of endothelial deterioration ( Figures 6(a)-(c) ). The top values of OSI and RRT signify the reattachment locations, which align with zero for TAWSS, and Newtonian fluid gives a more disturbed flow area.

Without a doubt, the intensity or size significantly influences the flow area of the narrowed channels of blockage. To examine the impact of stenosis intensity, three

distinct sizes, specifically 45%, 60%, and 75% ( Figure 7(a) ), have been analyzed in terms of WSS. As the severity of the blockage deepens, the flow field diminishes, resulting in an increase in velocity, which significantly affects the WSS, leading to a peak in the WSS due to the acceleration of flow. The TAWSS for 75% stenosis rises by 54.84% and 37.18% compared to 45% and 60% stenoses, respectively. Finally, it may be concluded that the more vascular injury generates the more WSS. Figure 7(b) presents the contours of WSS distributions for the various sizes of blockage severity. At the stenosis location, the flow area is reduced and experiences a maximum shearing stress. The higher blockage (75%) attains a maximum value of WSS compared to the lower blockages.

Pressure distributions for Newtonian and rheological models may vary greatly because of their different viscosities and responses to shear stress. The comparison of pressure contours between the two aforementioned models reveals a significant difference in Figure 8 , in which the non-Newtonian model generates greater pressure. The artery’s initial higher pressure drops sharply at the blockage’s midpoint, followed by a gradual rise until the artery’s end, indicating a slight variation between the fluids. The lowest pressure is observed just downstream of the blockage, suggesting a condition favorable to the development of atherosclerosis.