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Fluid–structure interaction analysis of non-Newtonian Herschel–Bulkley fluid viscosity model for pulsating flow of blood in ω-shaped stenosed arteries

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Abstract

The present study investigated the transient pulsatile blood flow of Herschel–Bulkley fluid through tapered arteries with overlapping stenosis and hyperelastic wall material by employing fully coupled fluid–structure interaction technique. 3D ω-shaped tapered arteries with hyperelastic wall material were ideally modelled with different aspect ratios (ARs), stenosis severities (SSs) and tapering angles (\(\xi \)). The effects of non-Newtonian Herschel–Bulkley fluid model on various parameters, such as \(\xi \), length of stenosed region (\({\overline{L} }_{0}\)) and SS, were explored for converging, diverging and normal arteries in terms of induced wall stresses, flow patterns and wall displacements. The differences in wall stress, flow streamlines, velocity and pressure contours were also highlighted. Wall pressure increases as SS increases; however, wall pressure suddenly decreases with the decrease in AR. The increase in SS in greater wall deformation with higher pressure gradients can be used as a remarkable indicator of hypertension. Higher average wall shear stress (AWSS) values were observed at the regions of high contact areas of stenosis to the fluid. The sudden fall in pressure can cause the stenosed vessel to collapse under the influence of low-pressure gradients. AR and \({\overline{L} }_{0}\) can be considered important parameters to predict hypertension in overlapping stenosed arteries. The contact region of stenosed arteries should be kept under observation to reduce the further development of atherosclerosis. Higher AWSS values may help in reducing the risk of thrombosis after the stenosed region in converging tapering arteries.

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Abbreviations

AR:

Aspect ratio

CVD:

Cardiovascular disease

\(\overline{d }\) :

Location of stenotic region

\(D\) :

Deformation tensor

E :

Young’s modulus

FSI:

Fluid–structure interaction

I :

Identity matrix

\(k\) :

Consistency index

\({\overline{L} }_{0}\) :

Stenotic segment length

\(p\left(t\right)\) :

Exit pressure (Pa)

\({\overline{R} }_{0}\) :

Radius of normal artery

\(\overline{R }(\overline{z })\) :

Stenotic region radius

SS:

Stenosis severity

VMS:

Von Mises stress

WSS:

Wall shear stress

\(\phi \) :

Tapering angle

\(\rho \) :

Density (kg m−3)

\({\tau }_{0}\) :

Yield stress

\(\tau \) :

Stress tensor

\(\overrightarrow{\nu }\) :

Fluid velocity vector

\(\dot{\gamma }\) :

Shear rate (s−1)

\(\eta \) :

Dynamic viscosity (Pa s)

\({\sigma }_{nn}\) :

Traction parallel to normal vector n̂

\(\overline{\epsilon }\) :

Critical stenotic height

\(\overline{\xi }\) :

Slope of tapering artery

\(\nu \) :

Poisson’s ratio

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Acknowledgements

This study was supported by the National Research Foundation of Korea and funded by the Korean government (MSIP Grant Nos. 2020R1A2B5B02002512 and 2020R1A4A1018652).

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  1. School of Mechanical Engineering, Kyungpook National University, 80 Daehakro, Bukgu, Daegu, 41566, Korea

    Fahmida Ashraf & Cheol Woo Park

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Ashraf, F., Park, C.W. Fluid–structure interaction analysis of non-Newtonian Herschel–Bulkley fluid viscosity model for pulsating flow of blood in ω-shaped stenosed arteries. Korea-Aust. Rheol. J. 34, 51–67 (2022). https://doi.org/10.1007/s13367-022-00025-y

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