## 3 Results and Discussion  
We tested the validity of the model developed for the current study on the topics covered in the research publications listed below. We want to confirm the areas with aberrant velocity, pressure, and WSS readings. For validating the model considered in the present study, we enlisted assistance from the previously published articles [40; 47]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Study Combinations**} & \multicolumn{1}{c}{**Healthy**} & \multicolumn{1}{c}{**Stensored**} & \multicolumn{1}{c}{**Aneurysmic**} \\ \hline \multicolumn{2}{c}{**Sl.No.**} & \multicolumn{1}{c}{**Mesh entities**} & & \\ \hline
1 & Triangular elements & 12,636 & 12,230 & 6565 \\ \hline
2 & Quadrilateral elements & 1428 & 1458 & 999 \\ \hline
3 & Edge elements & 600 & 606 & 437 \\ \hline
4 & Vertex elements & 8 & 13 & 8 \\ \hline \multicolumn{2}{c}{**Domain element statistics**} & & & \\ \hline
5 & Total number of elements & 14,064 & 13,688 & 7564 \\ \hline
6 & Minimum element quality & 0.2539 & 0.2388 & 0.1078 \\ \hline
7 & Average element quality & 0.8725 & 0.8683 & 0.832 \\ \hline
8 & Element area ratio & 0.05841 & 0.0737 & 0.04112 \\ \hline
9 & Mesh area & 0.6 mm\({}^{2}\) & 0.5817 mm\({}^{2}\) & 0.6258 mm\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mesh details. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Parameters**} & \multicolumn{1}{c}{**Values**} & \multicolumn{1}{c}{**Source**} \\ \hline \multicolumn{2}{c}{Fluid properties: Blood} & \\ \hline Blood density, \(\rho\) & 1050 kg/m\({}^{3}\) & & [39; 40] \\ \hline Blood viscosity, \(\mu\) & 0.0035 Pa.s & & \\ \hline \multicolumn{2}{c}{Fluid properties: Water} & & \\ \hline Water density, \(\rho\) & 1000 kg/m\({}^{3}\) & & [44] \\ \hline Water viscosity, \(\mu\) & \(8.9\times 10^{-4}\) Pa.s & & \\ \hline \multicolumn{2}{c}{Solid properties: Graphene} & & \\ \hline Graphene density & 2.26 g/cm\({}^{3}\) & & [45] \\ \hline Permeability & 0.001 m\({}^{2}\) & & \\ \hline \multicolumn{2}{c}{**Initial and Boundary Conditions**} & \\ \hline Initial pressure of the blood & 10,000 Pa & & \\ \hline Inlet velocity of blood & 0.6 m/s & & [38; 46] \\ \hline Outlet pressure of blood & Null pressure & & \\ \hline Arteriole wall & No slip condition & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical and physical parameter values. It has been noted that the results of validation obtained are in agreement with that of these articles. We intended to explore the flow domain initially by excluding the graphene layer. Figures 14-19 represent the flow and pressure profiles for the case of blood flow across an arteriole segment without the graphene layer. The results obtained were in good agreement with the various studies conducted previously on the blood flow across an arterial segment [39; 40; 41]. On comparing the velocity vector profiles of the cases without graphene and with graphene, it can be noted that inclusion of the graphene layer significantly changes the flow profile. In the case of the healthy arteriole segment, a linear flow of blood is seen, as in Figure 16. The pressure is uniformly distributed across the flow domain with the exclusion of the graphene layer in the healthy vessel, as shown in Figure 17. The inclusion of the graphene layer induces a zone of higher velocity neighboring the foot of the graphene layer (evident from Figures 20-32). Figures 16 and 18 depict the velocity profiles of blood flow in stenosed and aneurysm segments, respectively. A similar zonal separation is seen due to the insertion of the graphene layer. Figures 17 and 19 represent the pressure distribution without the graphene layer. As shown in Figures 33-45, the pressure distribution also is majorly affected by insertion of the graphene layer. The discussion on the advantages and disadvantages of the insertion of this chemical layer is articulated in the upcoming sections of the manuscript. Figure 16: Blood flow across stenosed arteriole segment without graphene layer.