## 4 Discussion  
This study employed a hybrid approach, using both Autodesk CFD and MATLAB, to investigate the effects of fatty streaks on the endothelial shear stress distribution in a simplified model of the aorta. This hybrid approach allowed us to leverage the strengths of both software tools, thereby overcoming the weaknesses inherent in each when used independently. Autodesk CFD facilitated comprehensive and accurate simulation of blood flow dynamics, while MATLAB enabled detailed numerical analysis of the simulation results. The choice of the Petrov-Galerkin model for our simulation was primarily motivated by its ability to enhance the accuracy of the computational fluid dynamics simulation. The Petrov-Galerkin model employs a method of error minimization that provides a more accurate representation of the endothelial shear stress distribution in the aorta, thereby enhancing the reliability of our simulation results. The presence of fatty streaks in the aorta presents a significant challenge in terms of the complexity of calculations for endothelial shear stress. This is particularly true when considering the dynamic nature of blood flow in the arteries. However, the use of CFD simulation and numerical analysis in tandem greatly simplifies this task, making it a viable approach for studying the effects of fatty streaks on endothelial shear stress. Our results revealed that the presence of fatty streaks leads to significant alterations in the ESS distribution. This alteration can be viewed from three main angles. Firstly, a higher standard deviation (SD) in ESS distribution in the presence of FS at low blood velocity compared to high blood velocity indicates oscillations in ESS, which are believed to be an important factor in disease development. Secondly, there is an 80% increase in regions with ESS less than 4.5 (Figure 3) at lower blood velocities. This observation is crucial because plaque typically occurs in regions with lower ESS [10]. Finally, as the plaque progresses, the area that remains stable in terms of ESS extends longitudinally (Figure 5), which suggests that the presence of fatty streaks can lead to a 'dam-like' effect, potentially trapping lipids and other inflammatory cells within the arterial wall. This dam-like effect, coupled with the increased permeability associated with elevated ESS, as shown in previous studies [11],  
Figure 5: The impact of the increase in the thickness of the aortic wall on ESS distribution. The difference in ESS increases from 2.58 Pa in the original model to 8.48 Pa in a model with a 3 mm thickness increase. The stable area length in terms of ESS increases from \(\sim\)0.2 cm to \(\sim\)0.8 cm. may serve as an entry point for these elements, thereby contributing to the progression of atherosclerosis. These findings underscore the potential of early intervention strategies to mitigate the progression of atherosclerosis by controlling the factors influencing ESS and endothelial permeability. This ESS change not only pushes LDL and other lipids into these spaces [12], but it can also stimulate inflammatory reactions, starting to propagate macrophage recruitment, which is one of the major contributing factors to the development of atherosclerotic plaques [13]. Furthermore, our results align with the study \"Acute and chronic exposure to shear stress have opposite effects on endothelial permeability to macromolecules\", suggesting that an increase in blood flow could potentially counteract the increase in permeability, thereby acting as a preventative measure against atherosclerosis progression [14]. While acknowledging the limitations of our study, it is important to highlight that our findings regarding the effects of fatty streaks on endothelial shear stress distribution are not solely dependent on the simplified model of the aorta. The observed phenomenon, where areas of high ESS join with increased blood flow, is fundamentally related to the hill-like shape of the fatty streaks and the nature of the ESS function.