Nonlinear model on pulsatile flow of blood through a porous bifurcated arterial stenosis in the presence of magnetic field and periodic body acceleration

Abstract

Background and objectiveBackground 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. MethodsThe 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. ResultsThe 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. ConclusionThe 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.