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Local hemodynamic analysis after coronary stent implantation based on Euler-Lagrange method

Abstract

Coronary stents are deployed to treat the coronary artery disease (CAD) by reopening stenotic regions in arteries to restore blood flow, but the risk of the in-stent restenosis (ISR) is high after stent implantation. One of the reasons is that stent implantation induces changes in local hemodynamic environment, so it is of vital importance to study the blood flow in stented arteries. Based on regarding the red blood cell (RBC) as a rigid solid particle and regarding the blood (including RBCs and plasma) as particle suspensions, a non-Newtonian particle suspensions model is proposed to simulate the realistic blood flow in this work. It considers the blood’s flow pattern and non-Newtonian characteristic, the blood cell-cell interactions, and the additional effects owing to the bi-concave shape and rotation of the RBC. Then, it is compared with other four common hemodynamic models (Newtonian single-phase flow model, Newtonian Eulerian two-phase flow model, non-Newtonian single-phase flow model, non-Newtonian Eulerian two-phase flow model), and the comparison results indicate that the models with the non-Newtonian characteristic are more suitable to describe the realistic blood flow. Afterwards, based on the non-Newtonian particle suspensions model, the local hemodynamic environment in stented arteries is investigated. The result shows that the stent strut protrusion into the flow stream would be likely to produce the flow stagnation zone. And the stent implantation can make the pressure gradient distribution uneven. Besides, the wall shear stress (WSS) of the region adjacent to every stent strut is lower than 0.5 Pa, and along the flow direction, the low-WSS zone near the strut behind is larger than that near the front strut. What’s more, in the regions near the struts in the proximal of the stent, the RBC particle stagnation zone is easy to be formed, and the erosion and deposition of RBCs are prone to occur. These hemodynamic analyses illustrate that the risk of ISR is high in the regions adjacent to the struts in the proximal and the distal ends of the stent when compared with struts in other positions of the stent. So the research can provide a suggestion on the stent design, which indicates that the strut structure in these positions of a stent should be optimized further.

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Abbreviations

τ :

Shear stress (F·m−2)

μ :

Dynamic viscosity of fluid (Pa·s)

u :

Velocity (m·s−1)

ρ mix :

Density of blood fluid (kg·m−3)

ρ plasma :

Density of plasma fluid (kg·m−3)

ρ RBC :

Density of red blood cell fluid (kg·m−3)

ε plasma :

Volume fraction of plasma

ε RBC :

Volume fraction of RBCs

η mix :

Kinematic viscosity of blood fluid (kg·m−1·s−1)

η plasma :

Kinematic viscosity of plasma fluid (kg·m−1·s−1)

η RBC :

Kinematic viscosity of RBC fluid (kg·m−1·s−1)

β kl :

Momentum exchange coefficient

C d :

Drag coefficient

Re:

Reynolds number

d RBC :

Diameter of the RBCs (m)

ϕ :

Shape factor

a :

Carreau-Yasuda fluid parameter

γ :

Scalar measure of rate deformation (s−1)

λ :

Relaxation time (s)

\( \overset{\rightharpoonup }{F} \) :

Additional acceleration term (m·s−2)

τ r :

Relaxation time (s)

α :

Impact angle of particle path and wall

μ :

Infinite shear rate viscosity (Pa·s)

μ 0 :

Zero shear rate viscosity (Pa·s)

K :

Spring constant (n·m−1)

f loss :

Loss factor

F friction :

Tangential force between particles (N)

F normal :

Normal force between particles (N)

μ(v r):

Friction coefficient

μ stick :

Sticking friction coefficient

μ glide :

Gliding friction coefficient

μ limit :

High-velocity limit friction coefficient

C w :

Rotational drag coefficient

C D :

Non-spherical drag coefficient

A face :

Unit surface area on wall (m2)

ν :

Relative particle velocity (m·s−1)

R erosion :

Erosion rate (kg·m2·s−1)

R accresion :

Deposition rate (kg·m2·s−1)

CAD:

Coronary artery disease

ISR:

In-stent restenosis

WSS:

Wall shear stress

NT:

Neointimal thickness

CFD:

Computational fluid dynamics

RBC:

Red blood cell

LBM:

Lattice Boltzmann method

IBM:

Immersed boundary method

DPM:

Discrete phase model

DEM:

Discrete element method

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Funding

This work was financially supported by the National Natural Science Foundation of China under Grant No. 81672187 and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China under Grant No. 51721004.

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Correspondence to Min Zeng.

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Highlights

1. A non-Newtonian particle suspensions model is proposed to investigate blood flow at stented areas.

2. The hemodynamic model with the non-Newtonian characteristic is more suitable to describe the realistic blood flow.

3. The risk of the in-stent restenosis is high in the regions adjacent to the struts in the proximal and the distal ends of the stent.

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Wang, Y., Zhan, J., Bian, W. et al. Local hemodynamic analysis after coronary stent implantation based on Euler-Lagrange method. J Biol Phys 47, 143–170 (2021). https://doi.org/10.1007/s10867-021-09571-y

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Keywords

  • Blood flow
  • Red blood cells
  • Coronary stent
  • Non-Newtonian fluid
  • In-stent restenosis