Applied Mathematics and Economics Programme Area, School of Applied Sciences and Mathematics, Universiti Teknologi Brunei, Jalan Tungku Link, Gadong BE1410 Bandar Seri Begawan, Brunei Darussalam.
Comput Methods Programs Biomed. 2021 Feb;199:105907. doi: 10.1016/j.cmpb.2020.105907. Epub 2020 Dec 22.
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.
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.
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.
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.
本研究旨在探讨血流动力学因素，以期为心血管疾病的更好解释和治疗提供有用信息。许多研究人员从理论上研究了血液在血管系统中的流动，将血液视为单层或双层流体。在本当代研究中，开发了一个四层流体模型来分析血液在轻微狭窄的动脉中流动时的流变学元素，并且将动脉壁视为多孔介质。
动量和本构方程与合适的边界条件一起求解，试图通过积分和摄动方法获得速度分布、体积流量、压力梯度、壁剪切应力和流动阻力的结果。通过广泛使用 MATLAB 软件获得分析/数值解和图形结果。
值得指出的是，壁剪切应力的大小随着达西数、魏森贝格数和幂律指数的增加而减小。然而，血液速度随着达西滑移参数、魏森贝格数和幂律指数的增加而增加。需要记录的是，当狭窄深度从 0 增加到 0.15 时，健康、贫血和糖尿病患者的平均速度增加比例分别记录为 4.58、2.62 和 22.44。还发现，当狭窄深度从 0 增加到 0.15 时，上述三种血液状态下壁剪切应力的增加比例分别为 4.7、4.27 和 3.62。
在所有三种不同情况下（贫血、健康和糖尿病）增加的流动阻力的性质表明，动脉中的狭窄越大，输送到关键器官的血液量就越少，这会导致患者突然死亡。希望本研究的结果能为医生和生物医学工程师预测狭窄血管中血液流动的行为提供有用的信息，以实现更可能的治疗方式。
