Mathematical modeling of a complex system in hemodynamics

The branch of complex system spans over a wide range of areas from physical and technological systems to social and biological systems. Hemodynamics is a branch of physiology and is a complex system which deals with the study of blood flow in arteries. Being a complex physical system, blood flow in a narrow stenosed artery is modeled as a two-phase fluid flow with the inner phase consisting of all the erythrocytes being represented by Herschel-Bulkey fluid model and the outer phase composed of only plasma being treated as Newtonian fluid. Perturbation method is employed to obtain an asymptotic solution to the resulting system of nonlinear partial differential equations. The expressions for the physiologically important flow quantities such as shear stress, velocity, plug core radius, flow rate and longitudinal impedance to flow are obtained. It is found that the velocity increases with the increase of the body acceleration, pressure gradient and the width of the peripheral layer thickness and the reverse behavior is noticed when the yield stress and depth of the stenosis increase. It is also observed that the flow rate decreases with the increase of the stenosis shape parameter, power law index and yield stress. Also, it is noted that the presence of body acceleration and peripheral layer influences the mean velocity by increasing its magnitude significantly in the arteries of different radii.