Oscillatory Viscoelastic Model of Blood Flow in Stenotic Artery
Pramod Kumar Yadav, Bhupesh Dutt Sharma, А. Н. Филиппов
Abstract
An analytic solution for the two-layered model of pulsatile blood flow in stenotic arteries is discussed. The blood flow in narrow arteries is assumed to obey the two-fluid model: non-Newtonian viscoelastic as Jeffrey fluid in core region, and Newtonian as plasma fluid in peripheral region. The present study is aimed to develop an oscillatory viscoelastic model of blood flow and obtain the analytic expressions for velocity of pulsatile blood flow in a stenotic artery. The velocity of pulsatile blood flow is used to discuss the wall shear stress and volume flow rate through stenotic artery and to relate relaxation time, retardation time, height of the stenosis with the velocity, volume flow rate and wall shear stress. The solution of the model boundary value problem is obtained by the method of special functions under the assumption of steady oscillations. It is found that the velocity is directly proportional to relaxation time and on the other hand retardation time is inversely proportional. For non-zero time period, the wall shear stress increases as relaxation time increases and decreases as retardation time increases. It reveals a significant influence of relaxation and retardation time on oscillatory blood flow in stenotic artery under the pathological state of cardiovascular disease.