I. Introduction

In this paper the concept and the modeling of the 5D cardiac system was described (3D model + temporal dimension functional dimension of the flow) detailed in our research work mentioned in (Sakly et al., 2019) and (Sakly et al., 2020). This strategy consists in the reconstructing of a 3D geometry of the descending aorta and diffuse a 2D viscous laminar fluid to detect the zones of narrowing. Blood flow is impeded at the site of the stenosis in the narrowed aorta, which hampers the transport of blood cells and subsequently causes turbulence of the wall of the internal aorta. However, the behavior of blood flow depends on various other parameters, including thermo-physical properties such as viscosity, surface tension, and wettability(Sikarwar et al., 2016). Different mathematical models of blood rheology have been studied over the last decades and on the basis of these studies, various hidden characteristics are discovered such as the behavior of the fluid and the nature of the flow.(Roy et al., 2017). Therefore, defining the value of wall pressure and tension stress of the wall in the arteries is a vital issue for medical experts. Many researchers have reported pulsed flow behavior and its fluctuations are continuously damped, which can be attributed to the elasticity of the blood arteries. Blood-artery disease plays an important role in hemodynamics because it disrupts the flow pattern that causes a change in wall pressure and shear stress in the arteries (Cebral et al., 2011). Previously, a large part of published studies (Thomas & Sumam, 2016) focused on the physiological causes of blood-related disease. However, a very small number is an incredible step to understand the underlying physics of the disease in order to understand the cause and thus pave the way for less invasive and more sustainable techniques for their processing. Current imaging techniques do not allow doctors to know the parietal pressure and the parietal stress exerted by the blood on the inner periphery of the artery. The revolutionary development of physiological modeling of pathology and cardiovascular physiology paves the way for bridging the gap. Recent developments in the field of Computational Fluid Dynamics (CFD) have the ability to simulate blood flow in a geometry of the heart structure. It is a less invasive method; a computer can show you the flow pattern of blood for a different disease artery. As a result, CFD has now become a clinical diagnostic tool for the medical practitioner in the field of congenital heart valve, coronary, myocardial and peripheral vascular diseases.(Xiong et al., 2011). However, the CFD module relies on the precise definition of geometric and flow boundary conditions and requires non-clinical expertise, engineering tools, powerful computer systems and a large number of calculations. Because of these requirements and limitations, it is difficult to include CFDs in routine clinical practices. Alternatively, the viscous dissipation can be calculated using the viscous term of the Navier-Stokes equation (Cibis et al., 2015). This approach bypasses the need for pressure and requires only the blood flow velocities inside, which can be obtained noninvasively in 4D flow MRI.
Our main contribution is to present a numerical simulation of a laminar blood flow in 3D aortic modeling in the presence of a left subclavian aortic coarctation as well as an analytical study is explained to study the impact of a solver of dynamic fluid on the detection of aortic stenosis.