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.