Simulation and Analyses of Turbulent Flow in Different Phases of Stenosed Renal Artery

. This study concerns the two-dimensional structure computational results of renal artery stenosis. In this paper, the turbulent flow of the stenosed vessel is stimulated and correlates the different stages of stenosis with each other. As we know that the blood flow in most blood vessels is laminar, but in case of stenosed vessel, the blood flow becomes turbulent; this is due to the blockage that blood does not flow linearly and produces chaos. Several liquid parameters are analyzed, such as pressure, velocity, turbulence kinetic energy, density, and shear rate. The inlet and outlet flow are especially concerning. For this purpose, we explored the stenosed behavior by the software COMSOL Multiphysics which provided us with a complete examination of the Computational fluid dynamics. With an increase in renal artery stenosis, there is a decrease in the blood flow which will automatically affect the pressure of the blood and can cause serious kidney diseases and, in some cases, permanent damage to the kidney sometimes. This paper highlights the early stages of renal artery stenosis, which are likely to be cured. Also, it shows the behavior of the severe late stages, which we consider nearly impossible to cure. The result explains that how different parameters vary according to stated cases .


Introduction
According to the WORLD HEALTH ORGANIZATION, in 2008 statistics were about 17000000 people passed away due to cardiovascular diseases, accounting for 30% of the worldwide. Renal artery blockage, also referred Atherosclerosis, is one of the major issues of the stenosed artery. The plaques are formed by aggregation of lipids in the artery. Blood is a multiplex blend of cells, lipoproteins, proteins, and ions by which wastes and nutrients are delivered. As red blood cells are diminutive semisolid fragments, they are basically higher in blood viscosity and influence the conduct of the liquid. Blood is around four spans denser than water as blood does not indicate an invariant consistency at all flow rates and is particularly non-Newtonian. The stenosis can initiate turbulence and lowers the flow employing vicious head losses and obstruction in flow. Spotting and analysis of stenosis provide support for surgical intervention. Stenotic flows have been well-identified in numerous studies. secondary reason for Hypertension, but it does not imply causation. People who were about age 77 years, renal duplex screening showed stenosis greater than 60% in 6.8%. In an autopsy series, stenosis was found in 27% of patients 50 years, increasing to 53% if there was a record of intense diastolic Hypertension greater than 100 mm Hg. [1] Among patients starting dialysis treatment, 10% to 15% will have Atherosclerotic renal artery stenosis, with around 25% of aged patients with chronic kidney disease discovered to have unsuspected atherosclerotic renal artery stenosis. [2] As we hypothesized here, a consideration geometry that is a circle or an oval. The plaque shape, sizes, and site are rudimentary to analyzing the affected flow field.Fluid analysis is done by Software COMSOL. We have compared various stages of stenosis. Parameters like velocity, pressure, and a few more fluid parameters are analyzed in this study's helps us to analyze the fluid flow, and it is important for us to analyze the flow at different diameters as we are focusing on different stages, which include the early stages of stenosis and the late-stage stenosis. [3]

Methods
The COMSOL Multiphysics is used for the modelling and simulation of renal artery, mainly there is an analysis of stenosed stages. Different Stages of stenosis will explain the early detection and the late stages. This is done by giving different stenosis to the artery i.e., giving different diameters to the renal artery, the diameter is given in mm. there are five different conditions given. COMSOL Multiphysics is a convenient, effective CFD program that proposes its users' many alternatives. Nevertheless, computational resource need is elevated. The user is now exposed to the relevant fields, which becomes vital. COMSOL Multiphysics is essential to pick the effects of some parameters proposed by this program. [4] Microsoft excel is used in examining the parameters value, different graphs are displayed which shows the increasing decreasing pressure, velocity, turbulence kinetic energy, and density. Mathematical equations are also made by using these graphical values, it will help to give a clearer understanding of the parameters. [5]

PHYSICS USED IN COMSOL
When we are doing the simulation of anything in COMSOL, adding the conditions is the most important step Fluid flow physics is used. It will help to add constraints which will help to give appropriate parameters for simulation and modelling .This physics provides fluid analyses which include internal, external flow, compressible or incompressible fluid, single phase Multiphysics flow and free and porous media flow. Multiphysics tendencies are numerous. [6]

MICROSOFT EXCEL ANALYSIS
Data of different parameters in excel spreadsheets are organized in rows and columns to model, store and manipulate .This helped us by giving us graphs of all parameters that we were focusing on along the x-axis and y-axis.

SIMULATION METHADOLOGY
The geometry in the examination is carried as an equal-sided, which is the two-dimensional arrangement of the artery wall. Its elevation is kept at 6mm, which is close to the renal artery, which we are focusing on, denoted by D The measurements were obtained through a literature review because we wanted to be as close as possible to the original artery. [7] The flow is created through the entire geometry. The left flank is an outpour inlet, and the right side is an outlet, whereas the top and bottom are a wall. Different diameters are applied to see the effect of stenosis, which includes the initial stage of stenosis and the closure-stage stenosis.This is designed on the software COMSOL Multiphysics which has several option for a number of parametrs. Fig 1 shows the depiction of renal artery stenosis that we are focusing.

Fig.1. General representation of stenosis
The Comsol Multiphysics explains the fluid in words of the Navier-stroke equation which recounts the activity of liquids and has also been taken as newton's second law for fluids. [8] is the fluid velocity, Where p is the fluid pressure μ is the dynamic fluid viscosity and ρ is the fluid density, In the analysis renal artery stenosis using COMSOL Multiphysics, the equation 1 [9]. Navier Strokes are used to describe the flow of blood through the stenotic artery. This equation provide a mathematical representation of the velocity, pressure, density, and temperature changes that occur in response to external forces, such as pressure gradients and shear stresses.Specifically, in the case of renal artery stenosis, the Navier-Stokes equations are used to simulate the flow of blood through the narrowed artery, taking into account the geometry of the stenosis and the surrounding tissue. By solving these equations numerically using COMSOL Multiphysics, researchers can study how the stenosis affects blood flow and pressure, as well as other fluid dynamics phenomena such as turbulence and viscosity.The simulation results obtained from COMSOL Multiphysics can provide valuable insights into the impact of renal artery stenosis on kidney function and overall cardiovascular health.Overall, the Navier-Stokes equations are an essential tool for modeling fluid dynamics problems such as renal artery stenosis in COMSOL Multiphysics.These equations that fundamentally explain how a fluid flows through its domain. Biomedical researcher workers make use of equations to model how blood flows via the body. [10] The table shows the blood properties incoparated in COMSOL Multiphysics.

Results
The renal arteries stenosis is done explaining different stages of stenosis. Different parameter analyses are done using the stenosis vessel, several parameters are examined such as velocity, pressure, turbulence kinetic energy, density, and shear rate is analyzed.

VELOCITY
The outcomes of different stages of the shape of stenosis, radius of artery, and other conducts of blood fluid are scrutinized in the outpour of blood velocity in the artery. [11] The analysis exhibited that the flow disruption and extreme velocity typically rely on plaque formation and altitude, though the disparities were lowest in diastole. Due to the limited void, velocity is heightened, mainly at systolic and diastolic flow. [12] The effect of different stenosis with different radii is measured to determine the stages of renal artery stenosis. The velocity is the major parameter in the analyses of stenosis it tells the amount of blood going to the kidney by decreasing the artery radius the maximum velocity is increased. We analyzed 0.4mm, 0.3mm, 0.2mm,9.5mm, and 1mm diameter of arterial stenosis. Any sort of stenosis rate is studied by three separate portions in the graph it signifies how integral is the arterial stenosis is there: The three distinct zones are as follows: I. The systolic peak velocity: which is the most elevated systolic velocity inside the stenosis. II.
The diastolic end velocity: which is most elevated end-diastolic velocity. III.
The systolic velocity ratio: in which there is the comparison of the peak of systole within the stenosis with peak systole proximal to the stenosis. The x-axis generally designates time, with an individual point on the graph illustrating a distinct moment in time. The y-axis illustrates blood flow velocity, with the height of each point on the graph showing the velocity of blood flow at that distinct moment in time.  The standards for choosing the most appropriate approach for interpreting patients with dread of Renal Artery Stenosis still need to be described in context of needed spatial resolution and detection of velocity understanding for computation of geometry and depiction of the blood flow. When there is stenosis in the renal artery, blood flow is held back, and the velocity of blood in the restricted site is higher. This raised velocity is due to the constriction of the artery, which compels the blood to flow through a more small space, directing to higher flow speeds.This increased velocity can be detected using Doppler ultrasound, a non-invasive imaging approach that estimates the velocity of blood flow in the renal artery. Doppler ultrasound detects the presence of renal artery stenosis and deliver knowledge about the degree of stenosis and its place. [13] The effect of improved velocity on renal function is complicated and can rely on different factors, such as the harshness and duration of the stenosis, the location of the stenosis, and the presence of other constitutions like a person having one or more diseases. In general, raised velocity due to renal artery stenosis can direct to reduced kidney function, which may result in symptoms such as high blood pressure, fluid retention, and reduced urine outcome.All the graphs from smaller diameter to larger diameter shows as the stenois is increasesig the peak systolic velocity is increasing with the decrease in end diastolic. As we can see in the Figure 2 we have the peak systolic velocity and end diastolic velocity. As we move further there is more rise in systolic peak velocity and decrease in the end diastolic velocity due to severe renal artery stenoisis that we have represented Figure 4.

PRESSURE
Renal Artery Stenosis of less than 50% can be related to a gradient of 15 mm Hg. These data only add to the anticipation, and hence a sensible approach would be to believe revascularization in Renal Artery Stenosis is greater than 60%, dependent upon the clinical presentation. [14] Three parts of stenosis are covered: Proximal stenosis: Renal artery nearest to the aorta. Mid-artery stenosis: Middle part of artery, away from both the aorta and the kidney. Mid-artery stenosis may also be induced by atherosclerosis, or it may be the outcome of fibromuscular dysplasia, a condition in which the walls of the artery become condensed and restricted. Distal stenosis: Renal artery closest to the kidney. The relation between these three zones of stenosis is that they can all contribute to reduced flow of blood to the kidney and may cause symptoms of renal artery stenosis, such as high blood pressure or decreased kidney function. Also, treating one site of stenosis may not completely fix the problem if other zones of stenosis are present. Therefore, an assessment of the renal arteries is crucial in specifying the best cure policy for renal artery stenosis. [15]  To study the effect of pressure in renal artery stenosis using COMSOL Multiphysics, we created a model of the stenosed artery and simulated the flow of blood through it. The model we considered i.e., artery geometry, the properties of the blood, and the pressure and flow conditions at the outlet and inlet of the artery.

SHEAR RATE
The shear rate can have both useful and detrimental impacts on the arterial wall. On one side, shear stress can produce the endothelial cells lining the artery to free nitric oxide and other vasodilators, which enable it to enhance blood flow and decrease the chance of thrombosis. Extreme shear stress can hurt the endothelial cells and generate hives and oxidative stress, which can lead to the advance of stenosis and the growth of atherosclerosis. [16] 8 In a stenosed artery with a diameter of 1mm, if the stenosis decreases the diameter to 0.5mm, the shear rate will rise by a factor of four, considering that the velocity of blood flow remains unchanging. due to the same volume of blood being pushed to flow through a more diminutive cross-sectional area, boosting the velocity of blood flow and, thus, an increase in shear rate. In a shear rate graph, the peaks define areas of most elevated shear rate, which coordinate with the most limited part of the artery where there is the presence of stenosis.

TURBULENCE KINETIC ENERGY
The Kinetic Energy of turbulence is associated with fluid turbulence, which is due to the presence of blocks or kinks in flowing direction. In the circumstance of artery stenosis, the narrowing of the artery can induce turbulence in the blood flow, directing to an upsurge in Turbulence Kinetic Energy. [17]  The growth in TKE can result in raised shear stresses and endothelial damage, which can further aggravate the stenosis and increase the chance of thrombosis or embolism. Further, the increase in TKE can lead to increased energy overindulgence, which elevates the blood temperature and the surrounding tissues. Thus, the presence of renal artery stenosis can result in raised turbulence kinetic energy in the blood flow, effects on healthiness. [18] As the diameter of an artery reduces due to stenosis, the TKE of the blood is anticipated to rise. This is due to the decrease in the diameter of the artery compels the blood flow to evolve more turbulent, resulting in more elevated levels of Turbulence Kinetic Energy. The peaks illustrate areas of high turbulence kinetic energy, which correspond to the place of the stenosis. Existence of stenosis compels the blood flow to become turbulent, which directs to more elevated Turbulence Kinetic Energy levels in these regions. The extent of its peak can be used to evaluate the stringency of the stenosis and its conceivable impact on blood flow. On the other hand, the flat response regions in the TKE graph describe regions of lower turbulence kinetic energy, which approximate areas of normal blood flow. These regions have slick blood flow with low turbulence, resulting in more downward TKE levels. The flat response regions can be used as a regard to approximate the TKE levels in the stenotic area. [19] Figure.10.Turbulence kinetic energy when stenosis is 1mm in diameter.
The two extremes in the turbulence Kinetic Energy graph generally happen in the pre-and post-stenotic areas. [12] The crest in the pre-stenotic area illustrates high level turbulence induced by the narrowing of the artery, while the crest in post-stenotic region may be due to the re-circulation of blood flow caused by the obstacle. The flat part in the middle of the Turbulence Kinetic Energy graph illustrates a transition from turbulent to laminar flow as the blood passes via the stenosis. The height and form of this flat region can deliver facts about the stringency and area of the stenosis. Prevailing, the two peaks and one flat part in the middle of the Turbulence Kinetic Energy graph can deliver useful details about the blood flow ways in the stenotic region and can help in the diagnosis and management of RAS.

DENSITY
The stenosis commonly does not impact the blood density. The density is determined by its composition, which possesses red and white blood cells, plasma, and other details such as lipids, proteins, and electrolytes. The existence of stenosis in an artery can influence the flow of blood and may guide modifications in blood velocity, pressure, and turbulence, but it does not change the density of the blood itself. As Figure 11 shows the COMSOL Multiphysics simulation and it proves that the blood is not affected by any kind of renal artery stenosis. However, many other parameters are affected which are already discussed above.