Abstract
Although stenosis is crucial in diagnosing health conditions that result from the constriction of an artery in time, a few studied have been conducted to investigate the characteristics of the unsteady flow of blood. The research focuses on examining the attributes of wobbly flow of blood in arteries with a period of dependent stenosis. The researchers have used the Power-law fluid framework. The model has been chosen because of its usefulness in determining dynamic velocity. In this framework, it is assumed that the governing equation for the flow of blood in the axisymmetric shape. This mode is held to be effective because it simulates the movement of blood in the artery. To establish the factors that influence the flow of blood in an artery, the researchers have employed two models, which are mathematical and computational approaches. The models have been used to determine aspects, such as the velocity of the flow, the variation in pressure, which is also called stress gradient, impedance, and stress that results from shearing of wall. The factors tested are for the throat and essential height of the stenosis.
Moreover, the scholars concentrated on assessing how the quantities depend on each other on following and spatial variables. Apart from the above investigations, the regularity of flow of vacillation in time and the principal aspects of the flow structure has been investigated. Based on the mentioned evaluation, writers of the article have drawn several conclusions. First, they discovered that as the rate of abnormal narrowing augmented with instance and rate, other factors also increased. Values that increased are the scale of the axial speed and the pressure that resulted from shear of the wall. Moreover, they have also discovered that the enormities of the values under study are higher when Newtonian fluid is used compared with when non-Newtonian fluid is employed.
Introduction
Heart attacks and strokes are held to be the leading causes of several deaths globally. The conditions are associated with many causes, which include deposition of cholesterol, consuming food that contains a lot of fat, cellular waste products, among others [1]. Evidently, the causes are many, and the constriction that develops in artery makes important alterations in the flow of blood. However, a few studies have been conducted to investigate the flow pattern of blood flow in an artery that has stenosis, implying that there is no evidence to inform people how blood flows. What is explicit is that there are various patterns of flow for diverse shapes of stenosis. The reason the paper is interested in the flow that takes place through stenosed vessel is that it would be critical for diagnosing the diseases when they have not advanced [1]. When a condition is discovered in early stages, treatment is possible and efficient even when stenosis is becoming a medical issue. Based on the fact that understanding flow in stenosis is essential for early treatment, it is critical to understand how hemodynamic aspects lead to the pathology to the development of the disease. Notably, some researchers speculate that wall shear stress leads to the thinning of luminal and facilitates the rupture of plaque. There are several questions concerning if hemodynamic shear can interrupt a stenotic plaque and whether the stresses are smaller than the mechanical one. There has not been an exact approximation of reduction of flow that is caused by the shear wall. Some other scholars have also argued that blood flow can be illustrated using Power-Law framework [1]. Using the model, they have revealed that axial velocity decreases as the radial variables augment. As a result, many of them have advocated the use of this model because it provides credible and valid results. It is important to state that understanding physical features of the flow of blood in arteries with time is determined by many factors, which many of authors have not investigated. Unless these aspects are examined, people may continue losing lives because it is not possible to diagnose heart attacks and strokes in time.
There are many studies that have been conducted with the aim of linking the fluid dynamically that is induced by stress with the development of stenosis in the blood circulatory system. The article has acknowledged the findings of Texon, who revealed that hydrodynamic factors contribute significantly to the development of stenosis. Additionally, pieces of research that have carried out by several researchers, such as Young, Tsai, Morgan, and McDonald have provided some features of blood flow in arteries by factoring how it flows in Newtonian fluid [1]. The research conducted by Taylor has demonstrated that at escalated cut off speed, blood indicates Newtonian features in a big artery. The tentative investigations that have been carried out have revealed that in the environs of blood abnormal narrowing, the magnitude of shave in fluid is less, demonstrating that the non-Newtonian character of fluid in area is outstanding [1]
According to the writers, many scholars hold that blood flow behaves the same manner like a non-Newtonian fluid inside a compressed artery. They researchers have given various findings regarding the flow of blood. Some of the results from the early scholars include, non-Newtonian fluid, blood flows at a low magnitude and the flow of blood is not more than 20 s-1 rate of shear in limited thickness. Others have shown that Power-law framework displays various behaviors than the other two models, although variations were minimal. In fact, most of the studies that have conducted have advocated the use of Power-law approach.
Problem Statement
The current studies that focus on arteries concentrate on employing the mathematical frameworks, which represent non-Newtonian flow of fluid through an abnormally narrowed artery. Although a lot of work has been done regarding the topic under study, some of them do not use the methods that would yield the best results. It is important to state that scholars have investigated the characteristics of tremulous movement cases [1]. However, the article has recognized the works that focused on examining the characteristics of the flow of blood utilizing the various shapes stenoses as critical to the current study. The researchers who examined the aspects observed that the flow of blood encountered more resistance with a cosine shaped stenosis that the ones that were regular and asymmetrical [1]. Based on the fact that characteristics of blood flow have not been investigated, it is important to carry out investigation and shed light concerning them.
The authors of this article consider the issue of wobbly flow of blood through an artery with new complex sine figured abnormal narrowing that depends on time and find out its attributes utilizing Power-Law fluid approach. The writers have introduced the new model that is advantageous because it takes into account into time that is determined by composite stenosis as well as the wobbly flow of blood in arteries [1]. In this study, the dependent variable has the capacity to oscillate in time, while at the same uphold a nonzero firm state of average. The authors have considered various factors, such as the flow of blood in arteries, force, and radial flow to be composed of unique stable elements as well as unusual constituents. They have utilized various factors to analyze the tremulous movement of blood in artery employing a volume that is prescribed, contrary to other works that use laid down pressure gradients. The elements are compared and presented in Newtonian and non-Newton circumstances.
- R. Roy, D. N. Riahi, and N. Carrasquero, “Mathematical Modeling of Blood Flow in an Artery with an Unsteady Stenosis using Power-Law Fluid Model”. Sop Transactions on Applied Mathematics., Vol. 1, pp. 88-103. Jul. 2014.
