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Analysis of Low Density Lipoprotein (LDL) Transport Within a Curved Artery

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Abstract

To elucidate the mechanism of the effect of LDL concentration on the thickening of intima in a curved artery, LDL transport in each layer of the curved arterial wall is studied analytically. A comprehensive concentration distribution expression of LDL in each layer of the curved artery wall is presented along with the characterization and estimation of the effect of curvature on the growth of atherosclerosis within the arterial wall. The effect of curvature on species concentration distribution is analyzed and the results are thoroughly benchmarked against prior pertinent works. The concentration at the interface of lumen and endothelium will directly affect the concentration profile inside the arterial wall layers. The results show that the average concentration in the circumferential direction is actually decreasing in the axial direction for a curved artery compared with a straight artery. Small radius ratio and Reynolds number will augment the LDL accumulation at the lumen endothelium interface. The increase in concentration at the lumen/endothelium interface in the axial direction has a minor effect on the concentration profile at the other wall interface layers.

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Abbreviations

c :

LDL concentration

Dn :

Dean number \( {\text{Dn}} = 2\sqrt \lambda \text{Re} \)

Re:

Reynolds number Re = ρv2r0/μ

D :

LDL diffusivity

De :

Effective LDL diffusivity

F:

Dimensionless inertia coefficient

λ :

Ratio of artery radius to curvature radius r 0/R

V :

Velocity vector

p :

Hydraulic pressure

ρ :

Fluid density

δ :

Porosity

μ :

Dynamic viscosity

L :

Length of the artery

R :

Radius of the curvature

σ :

Reflection coefficient

y :

y = r 0 − r

r 0 :

Radius of the lumen domain

k :

Reaction coefficient

r :

Radial coordinate

K :

Permeability

E :

De/r 20

Δ:

Thickness of concentration boundary layer

〈〉:

Local volume average

F :

Fluid

I :

i = 0, 1, 2, 3 and 4 representing lumen, endothelium, intima, IEL, and media, respectively

70 mmHg:

Refers to properties with a gauge pressure of 70 mmHg

eff, e :

Refers to an effective property

end:

Refers to the endothelium layer

w :

Wall

+:

Non-dimensional parameter

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There is no conflict of interest. This manuscript has not been submitted to anywhere else.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of California, Riverside, CA, 92521, USA

    Shujuan Wang & Kambiz Vafai

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  1. Shujuan Wang
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  2. Kambiz Vafai
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Correspondence to Kambiz Vafai.

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Associate Editor Gerhard A. Holzapfel oversaw the review of this article.

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Wang, S., Vafai, K. Analysis of Low Density Lipoprotein (LDL) Transport Within a Curved Artery. Ann Biomed Eng 43, 1571–1584 (2015). https://doi.org/10.1007/s10439-014-1219-x

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  • DOI: https://doi.org/10.1007/s10439-014-1219-x

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