Background and objective: This study aims to investigate the haemodynamical factors with the motive to spell out some useful information for better interpretation and treatment of cardiovascular diseases. Numerous researchers theoretically investigated the movement of blood in the vascular system, treating blood as either single-layered or two-layered fluid representation. In this contemporary study, a four-layered fluid model is developed to analyse the rheological elements of blood when it flows via constricted arteries with slight constriction and the arterial wall is considered as porous medium.

Methods: The momentum and constitutive equations are solved together with the suitable boundary conditions in an attempt to get the results on the distribution of velocity, volumetric flow rate, pressure gradient, shear stresses at the wall and resistive impedance to flow in which methods of integration and perturbation are utilized. The analytical/numerical solutions and graphical results are obtained by the extensive use of MATLAB software.

Results: It is of importance to state that the magnitude of the shear stresses on the wall reduces with the rise of Darcy number, Weissenberg number and power law index. Velocity of blood however, rises with the upsurge in Darcy slip parameter, Weissenberg number and power law index. It is pertinent to record that when the stenosis depth rises from 0 to 0.15, the ratio of increase in the mean velocity of healthy, anemic and diabetic subjects are recorded as 4.58, 2.62 and 22.44 respectively. It is also found that the ratio of increase in the wall shear stress in the aforementioned states of blood are found to be 4.7, 4.27 and 3.62 respectively when the stenosis depth rises from 0 to 0.15.

Conclusion: The nature of increased flow resistance in all three different situations such as anemic, healthy, and diabetic shows that the larger the constriction in the artery, the less amount of blood is transported to crucial organs which results in the sudden death of subjects. It is hoped that the outcomes of this study would be useful to medical practitioners and bio-medical engineers in predicting the behavior of blood flow in narrowed blood vessels for a more probable treatment modalities.

背景与目的：本研究旨在调查血液动力学因素，以期阐明一些有用的信息，以更好地解释和治疗心血管疾病。从理论上讲，许多研究人员研究了血液在血管系统中的运动，将血液视为单层或两层流体表示。在这项当代研究中，开发了一种四层流体模型来分析血液流经具有轻微收缩的狭窄动脉并将动脉壁视为多孔介质时的流变学要素。

方法：将动量和本构方程与合适的边界条件一起求解，以求得速度，体积流量，压力梯度，壁上的剪应力和流动阻力的结果，其中积分方法和摄动被利用。通过广泛使用MATLAB软件可以获得解析/数值解和图形结果。

结果：必须指出的是，随着达西数，魏森伯格数和幂律指数的增加，墙体上的剪应力的大小会减小。然而，血液速度随着达西滑移参数，魏森伯格数和幂律指数的增加而上升。有必要记录一下，当狭窄深度从0增加到0.15时，健康，贫血和糖尿病患者平均速度的增加比率分别记录为4.58、2.62和22.44。还发现，当狭窄深度从0增加到0.15时，在上述血液状态下壁剪切应力的增加比率分别为4.7、4.27和3.62。

结论：在贫血，健康和糖尿病这三种不同情况下，血流阻力增加的性质表明，动脉的收缩越大，输送至关键器官的血液越少，这导致受试者猝死。希望这项研究的结果对医疗从业者和生物医学工程师在预测狭窄血管中的血流行为以更可能的治疗方式方面有所帮助。