A 3-D numerical simulation of non-Newtonian blood flow through femoral artery bifurcation with a moderate arteriosclerosis: investigating Newtonian/non-Newtonian flow and its effects on elastic vessel walls

  • Mohammad Hassan Amiri
  • Ahmad Keshavarzi
  • Arash Karimipour
  • Mehdi Bahiraei
  • Marjan GoodarziEmail author
  • J. A. Esfahani


In this study, a fluid-structure interaction (FSI) simulation of the blood flow in the femoral artery with a small occlusion is presented. For a more accurate simulation of the real conditions, computerized tomography (CT) scan was used to obtain a 3-D model of leg blood vessels, while the vessel was modeled as an isotropic elastic wall. By assuming a heartbeat period of 0.5 s, the inlet condition was considered as a time-dependent pulse using a non-Newtonian flow model. Blood flow was assumed nonlinear and incompressible, and Carreau model was used for blood rheological model.

By considering unstable blood flow at the inlet, the involved hemodynamic parameters are velocity profile, vortices shapes, pressure drop, and streamlines. Furthermore, to determine the relationship between flow geometry and the vascular wall, wall shear stress (WSS) was calculated.

By taking the real geometry of the vessel and fluidity of blood into account, comparison of computational results indicated a significant difference in velocity distribution and shear stress depending on whether the fluid-structure interaction is considered Newtonian or non-Newtonian. The results showed that employing Newtonian models for the blood flow does not lead to promising results at occluded areas and beyond them.


X, Y, Z



Velocity vector (m/s)


Blood density (kg/m3)


Stress tensor


Blood pressure (Pa)


Identity matrix

\( {\eta}_f\left(\dot{\gamma}\right) \)

Blood viscosity (Ns/m2)

\( \dot{\gamma} \)

Shear strain

η0 f

Zero strain viscosity (Pa. s)


Infinite strain viscosity (Pa. s)


Empirical exponent


Time constant (s)


Young module (N/m2)


Poisson ratio


Artery density (kg/m3)


Artery wall displacement (m)

\( {d}_i^f \)

Fluid displacement at FSI (m)

\( {d}_i^s \)

Artery displacement at FSI (m)


Normal vector at FSI


Time (s)


Compliance with ethical standards

Conflicts of interest

The authors declare that there is no conflict of interest or funding resource regarding the publication of this paper.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Khomeinishahr BranchIslamic Azad UniversityKhomeinishahrIran
  2. 2.Department of Mechanical Engineering, Najafabad BranchIslamic Azad UniversityNajafabadIran
  3. 3.Department of Mechanical EngineeringKermanshah University of TechnologyKermanshahIran
  4. 4.Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour SafetyTon Duc Thang UniversityHo Chi Minh CityVietnam
  5. 5.Department of Mechanical Engineering, Faculty of EngineeringFerdowsi University of MashhadMashhadIran

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