A Mathematical modeling for the study of blood flow as a cross fluid through a tapered artery

Subject Areas : Statistics

A.R.  haghighi ¹ (Associate Professor, Department of mathematics, Technical and Vocational University, Tehran, Iran)
N.  Pirhadi ² (MSc, Department of mathematics, Urmia University of Technology, Urmia, Iran)
M.  Shahbazi Asl ³ (Ph.D, Department of mathematics, University of Tabriz, Tabriz, Iran)

Received: 2017-06-12 Accepted : 2019-04-27 Published : 2019-10-23

Keywords: روش تفاضلات متناهی, جریان خون پالسی, رگ مخروطی, گرفتگی نامتقارن, سیال کراس,

Abstract :

In this research, a two-dimensional model of pulsatile blood flow through a tapered artery with a non-symmetric stenosis is simulated. The blood flow as a cross fluid is modeled in an elastic cylindrical tube with an axially non-symmetric stenosis and a time-dependent geometry. The velocity of blood flow is compared within an elastic artery and an inelastic artery. Mild stenosis approximation is applied to simplify the governing equations. By applying an appropriate coordinate transformation, a cosine elastic artery turns into a rectangular and rigid artery. Using the finite difference method the Navier-Stokes equations governing the dynamics of the blood flow are numerically solved for velocity field. The correctness of the proposed model is proved through a comparison between the obtained results the present study and the previously obtained ones by others. The blood flow characteristics including resistive impedances, volumetric flow rate, and wall shear stress are obtained via the axial velocity profile. Various Two-dimensional diagrams for different parameters of the velocity distribution are also provided.

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