Numerical simulations of a 3D fluid-structure interaction model for blood flow in an atherosclerotic artery

Oualid Kafi; Nader El Khatib; Jorge Tiago; Adélia Sequeira

doi:10.3934/mbe.2017012

Article Contents

2017, Volume 14, Issue 1: 179-193. Doi: 10.3934/mbe.2017012

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Numerical simulations of a 3D fluid-structure interaction model for blood flow in an atherosclerotic artery

1.
Dept. Math., IST, Univ. Lisboa and CEMAT, Av. Rovisco Pais, 1049-001, Lisboa, Portugal
2.
Dept. of CS. and Math., LAU, P-36, Byblos, Lebanon

Author Bio: E-mail address: majc@st-andrews.ac.uk; E-mail address: oualid.kafi@tecnico.ulisboa.pt; E-mail address: nader.elkhatib@lau.edu.lb; E-mail address: adelia.sequeira@math.tecnico.ulisboa.pt
* Corresponding author: oualid.kafi@tecnico.ulisboa.pt
* Corresponding author: oualid.kafi@tecnico.ulisboa.pt

Received: November 30, 2015

Accepted: May 03, 2016

Published: September 2017

The first author is supported by PHYSIOMATH project EXCL/MAT-NAN/0114/2012.

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Abstract

The inflammatory process of atherosclerosis leads to the formation of an atheromatous plaque in the intima of the blood vessel. The plaque rupture may result from the interaction between the blood and the plaque. In each cardiac cycle, blood interacts with the vessel, considered as a compliant nonlinear hyperelastic. A three dimensional idealized fluid-structure interaction (FSI) model is constructed to perform the blood-plaque and blood-vessel wall interaction studies. An absorbing boundary condition (BC) is imposed directly on the outflow in order to cope with the spurious reflexions due to the truncation of the computational domain. The difference between the Newtonian and non-Newtonian effects is highlighted. It is shown that the von Mises and wall shear stresses are significantly affected according to the rigidity of the wall. The numerical results have shown that the risk of plaque rupture is higher in the case of a moving wall, while in the case of a fixed wall the risk of progression of the atheromatous plaque is higher.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. 3D computational domain of the idealized stenosed artery model composed of fibrous cap, lipid pool and vascular wall

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Figure 2. Inlet pressure waveform.

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Figure 3. Sagittal cut of 3D meshed geometry. The mesh is more refined in the stenosed region (1) and less refined far from the stenosis (parts 2, 3 and 4)

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Figure 4. Extra meshes for convergence study. Detail of regions 1, 2 and 3 (see Figure 3) representing the lumen, fibrous cap and lipid pool. The total number of DOF for the coarse mesh (left) is 359 231 and for the fine mesh (right) is 780 283

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Figure 5. Comparison between the maximal values of WSS in the stenosed region (1) (left) and the total displacement values of the fibrous cap (right) in a coarse, intermediate size and fine mesh

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Figure 6. Total volume displacement of the fibrous cap at the peak of the pressure (t = 0:22 s). The upper figures, left and right, represent the case of a fixed wall where blood is modeled as a New tonian fluid and a shear-thinning non-Newtonian fluid using the Carreau-Yasuda viscosity model, respectively. The representation for the same models in the case of a moving wall is in the lower figures

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Figure 7. Average variation of the WSS at the interface of the volume shown in Figure 6

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Figure 9. The von Mises stress distribution on the fibrous cap at the peak of the pressure (t = 0:22 s). upstream the stenosis for fixed and moving walls (top left and right, respectively) and downstream the stenosis (down left and right, respectively)

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Figure 8. Average variation of the von Mises stress at the inter face of the volume shown in Figure 6

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Figure 10. The WSS distribution on the fibrous cap at the peak of the pressure (t = 0:22 s). upstream the stenosis for fixed and moving walls (top left and right, respectively) and downstream the stenosis (down left and right, respectively)

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Figure 11. Average variation of the WSS at the interface of the volume shown in Figure 6

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Table 1. Parameters used for the plaque components

Plaque components	C₁₀ (N.m^-2)	C₀₁ (N.m^-2)	κ (MPa)	Density (kg.m^-3)
Fibrous cap	9200	0	3000	1000
Lipid pool	500	0	200	1000

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