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Effects of shear-dependent transport properties on lumen surface concentration of LDL particles in stenosed carotid artery

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Abstract

Growth of stenosis is mainly due to the high concentration of plasma lipoprotein such as low density lipoprotein (LDL) near the art ery walls. Accurate prediction of LDL concentration especially near the stenosis and where the shear stress is low, can help to predict the plaque growth. In this paper, a novel model is introduced to predict the LDL concentration near a plaque. This model is based on variable diffusion coefficient of LDL due to the non-Newtonian behavior of the blood flow in low shear stress regions such as flow around plaques. The new model for diffusion coefficient consists of two parts: the stationary and the shear- induced particle diffusivity due to rotation of red blood cells. The results show that the new model predicts the LDL concentration well and unlike the constant diffusion coefficient which is used by others, produces more physical and meaningful results.

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Abbreviations

a :

Radius of the red blood cells (4 μm)

C :

Concentration of LDL particles (kg/m3)

C 0 :

Inlet concentration of LDL particles (kg/m3)

C w :

Wall concentration of LDL particles (kg/m3)

D :

Diffusion coefficient of LDL particles (m2/s)

D e :

Effective diffusion coefficient of particles (m2/s)

D P :

Shear-induced particle diffusivity (m2/s)

D s :

Brownian molecular diffusion coefficient (m2/s)

l :

Length of the artery (m)

L i :

Upstream length of the arterial stenosis (m)

L o :

Downstream length of the arterial stenosis (m)

m :

Shear rate modifier

P :

Pressure (Pa)

r :

Radial coordinate

R 0 :

Radius of vessel (3.5 mm)

Re :

Mean inlet Reynolds number

Sc :

Schmidt number (Sc = ν/D)

u :

Velocity vector (m/s)

u r :

Velocity component in radial direction (m/s)

u z :

Velocity component in axial direction (m/s)

U 0 :

Inlet average velocity (m/s)

V w :

Filtration velocity (4 × 10−8 m/s)

WSS :

Wall Shear Stress (Pa)

z :

Axial coordinate

λ :

Constant parameter for stenosis severity

ρ :

Blood density (1,050 kg/m3)

µ:

Blood viscosity (0.0035 kg/m.s)

µ c :

Limiting high shear rate Newtonian viscosity (kg/m.s)

ν :

Kinematic viscosity (m2/s)

τ y :

Blood yield stress (Pa)

ϕ P :

Hematocrit

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Acknowledgments

We thank Department of Mechanical Engineering in Isfahan University of Technology of Iran for their supports.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada

    Ali Nematollahi

  2. Department of Mechanical Engineering, Foolad Institute of Technology (FIT), Fooladshahr, 84916-63763, Isfahan, Iran

    Ebrahim Shirani

  3. Department of Biomedical Engineering, University of Isfahan, 81746-73441, Isfahan, Iran

    Mahmood Reza Sadeghi

  4. Department of Mechanical Engineering, Urmia University of Technology, 419-57155, Urmia, Iran

    Iraj Mirzaee

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  1. Ali Nematollahi
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Correspondence to Ebrahim Shirani.

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Nematollahi, A., Shirani, E., Sadeghi, M.R. et al. Effects of shear-dependent transport properties on lumen surface concentration of LDL particles in stenosed carotid artery. Meccanica 50, 1733–1746 (2015). https://doi.org/10.1007/s11012-015-0120-5

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