**Abstract**

Cardiovascular diseases are amongst the main causes of death worldwide, and the main underlying pathological process is atherosclerosis. Over the years, fatty materials are accumulated in the arterial which consequently hinders the blood flow. Due to the great mortality rate of this disease, hemodynamic studies within stenotic arteries have been of great clinical interest, and computational methods have played an important role. Commonly, computational fluid dynamics methods, where only the blood flow behavior is considered, however, the study of both blood and artery walls' interaction is of foremost importance. In this regard, in the present study, both computational fluid dynamics and fluid-structure interaction modeling analysis were performed in order to evaluate if the arterial wall compliance affects considerably the hemodynamic results obtained in idealized stenotic coronary models. From the overall results, it was observed that the influence of wall compliance was noteworthy on wall shear stress distribution, but its effect on the time-averaged wall shear stress and on the oscillatory shear index was minor.

**Keywords:** atherosclerosis, blood flow, coronary arteries, fluid-structure interaction, computational fluid dynamics

## **1. Introduction**

Over the last year, COVID-19 has been the most widely spoken and researched disease worldwide and, inevitably, other existing pathologies were moved to the background. Amongst these, cardiovascular diseases (CVDs) should be highlighted because they still are by far the major contributor to global mortality [1]. CVDs are mainly caused by a blockage that prevents blood from flowing properly, known as atherosclerosis [2, 3]. This is a complex disease that affects medium and large size arteries and consists of a build-up of fatty deposits on the inner walls of the blood vessels, hampering the blood flow through the body [4]. The effect of atherosclerosis can be exacerbated by other diseases that affect blood circulation. Particularly, it has been shown that patients with COVID-19 are prone to develop blood clots on both arteries and veins [5], and thus atherosclerosis may be an even more important factor to global mortality.

Given the prevalence of this disease, atherosclerosis has been intensely studied through both cardiovascular modeling and experimental procedures, as reviewed

elsewhere [6–9]. Nevertheless, with the growing trend of greater computer power, computational approaches have become a valuable, cheaper, and efficient alternative for numerous researchers to predict blood flow behavior [10–13].

There are two main approaches for simulating blood flow, computational fluid dynamics (CFD) and fluid-structure interaction (FSI). In the first one, the arterial wall is assumed as rigid, while in the second one, arteries are considered elastic and the interaction between the blood and the arterial walls are included in the simulation [14]. Although CFD has been widely applied in the study of blood flow under pathological conditions in virtue of lower computational cost [15–20], since FSI provides a more realistic simulation of the human vasculature behavior, it has received increasing interest [21, 22]. Nonetheless, this approach requires significantly more computational effort, and the foremost difficulty is stability and convergence [23, 24].

In order to evaluate if the differences between CFD and FSI results are significant, some researchers have investigated and compared both. A commonly mentioned work was developed by Torii et al. [25]. The authors studied the effects of wall compliance on a stenotic patient-specific coronary artery and found noticeable differences in the instantaneous wall shear stress (WSS) produced by the FSI and rigid wall models. However, the effects of wall compliance on time-averaged WSS (TAWSS) and oscillatory shear index (OSI) were negligible. Malvè et al. [26] performed a similar study in the left coronary artery bifurcation and the conclusions regarding the WSS agreed with the previous study, but they observed significant differences in the TAWSS, especially on its spatial distribution. More recently, another similar study was performed on carotid bifurcation [10]. The authors found that the rigid model overestimates the flow velocity and WSS, but its influence on the TAWSS is minimal.

The differences between the CFD and FSI simulations have thus been the subject of several studies, however, as demonstrated, there is still a debate as to whether it is really necessary to use the most realistic approach, namely in computing WSS dependent variables, and sometimes the findings are contradictory. In this regard, this work presents the comparison of the results of both CFD and FSI simulations in an idealized stenotic coronary artery, with a degree of stenosis of 50%.
