Ponalagusamy R, Priyadharshini S
Department of Mathematics, National Institute of Technology, Tiruchirappalli, India.
Comput Methods Programs Biomed. 2017 Apr;142:31-41. doi: 10.1016/j.cmpb.2017.02.014. Epub 2017 Feb 16.
Background and Objective: The motivation of cardiovascular modeling is to understand the haemodynamic and mechanical factors in the diagnosis and treatment of cardiovascular diseases. Several investigations have been carried out by many authors to understand the flow properties of blood in modelling blood flows in the circulatory system. In the present article, the pulsatile flow of Herschel-Bulkley fluid through a bifurcated arterial stenosis in a porous medium with magnetic field and periodic body acceleration has been investigated in view of understanding the role of rheological behaviour of blood, stenotic height, bifurcation angle, magnetic field and porosity of wall in the initiation and proliferation of cardiovascular diseases.
The governing equations involving shear stress are solved numerically using finite difference schemes and the shear stress values in parent and daughter arteries are obtained using MATLAB software. The constitutive equation of Herschel-Bulkley fluid is highly nonlinear and using the equation, velocity distribution has been obtained. From the obtained velocity distribution, the numerical solutions of wall shear stress and flow resistance are found.
The plug core radius is, for the first time, computed for various stenotic heights and it is found that the magnetic field and porosity increase the plug core radius. The wall shear stress and flow resistance increase as stenotic height, yield stress, power law index, consistency and Hartmann number increase and decrease with increase in Darcy number and half of the bifurcation angle. It is significant to note that when the value of yield stress is increased from 0.1 to 0.2, the plug core radius is increased by 7.3%. In the presence of yield stress in blood, the applied magnetic field causes 33.87% increase in the plug core radius.
The mathematical model clearly shows that the increase in wall shear stress affects the aggregation of human platelets and rearranging the alignment of endothelial cells near the arterial wall. This implies that the wall shear stress is to be brought down below its critical level by increasing the values of Darcy number and half of the bifurcation angle. Further, the nature of increased flow resistance reduces the amount of blood supply to the vital organs which ultimately leads to a sudden death. This information is useful for bio-medical engineering in developing bio-medical instruments for a great potential treatment modalities inturn, prevent the causes of stroke, heart attack and renal failure.
心血管建模的目的是了解心血管疾病诊断和治疗中的血流动力学和力学因素。许多作者已经进行了多项研究，以了解在循环系统血流建模中血液的流动特性。在本文中，考虑到血液流变行为、狭窄高度、分叉角度、磁场和壁孔隙率在心血管疾病发生和发展中的作用，研究了赫谢尔-布勒流体在多孔介质中带有磁场和周期性身体加速度的分叉动脉狭窄处的脉动流。
使用有限差分格式对涉及剪应力的控制方程进行数值求解，并使用MATLAB软件获得母动脉和子动脉中的剪应力值。赫谢尔-布勒流体的本构方程是高度非线性的，利用该方程得到了速度分布。从得到的速度分布中，求出了壁面剪应力和流动阻力的数值解。
首次计算了不同狭窄高度下的栓塞核心半径，发现磁场和孔隙率会增加栓塞核心半径。壁面剪应力和流动阻力随着狭窄高度、屈服应力、幂律指数、稠度和哈特曼数的增加而增加，随着达西数和分叉角度一半的增加而减小。值得注意的是，当屈服应力值从0.1增加到0.2时，栓塞核心半径增加了7.3%。在血液存在屈服应力的情况下，施加的磁场使栓塞核心半径增加了33.87%。
数学模型清楚地表明，壁面剪应力的增加会影响人体血小板的聚集，并重新排列动脉壁附近内皮细胞的排列。这意味着通过增加达西数和分叉角度的一半，可将壁面剪应力降低到其临界水平以下。此外，流动阻力增加的性质会减少对重要器官的血液供应量，最终导致猝死。这些信息对于生物医学工程开发具有巨大潜在治疗方式的生物医学仪器很有用，进而预防中风、心脏病发作和肾衰竭的病因。
