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Research Papers

Numerical Modeling of Stress in Stenotic Arteries With Microcalcifications: A Micromechanical Approximation

[+] Author and Article Information
Jonathan F. Wenk1

Department of Mechanical Engineering, University of California, Berkeley, 6141 Etcheverry Hall, Mail Code 1740, Berkeley, CA 94720-1740jwenk1@me.berkeley.edu

Panayiotis Papadopoulos, Tarek I. Zohdi

Department of Mechanical Engineering, University of California, Berkeley, 6141 Etcheverry Hall, Mail Code 1740, Berkeley, CA 94720-1740

Effective material responses have been used in the modeling of various biological materials, see Refs. 34-35.

1

Corresponding author.

J Biomech Eng 132(9), 091011 (Sep 01, 2010) (11 pages) doi:10.1115/1.4001351 History: Received October 30, 2009; Revised January 24, 2010; Posted February 25, 2010; Published September 01, 2010; Online September 01, 2010

Most finite element models of atherosclerotic arteries do not account for the heterogeneity of the plaque constituents at the microscale. Failure of plaque lesions has been shown to be a local event, linked to stress concentrations caused by cap thinning, inflammation, macroscopic heterogeneity, and recently, the presence of microcalcifications. There is growing evidence that microcalcifications exist in the fibrous cap of plaque lesions. However, their role is not yet fully understood. The goal of the present work is to investigate the effects of localized regions of microcalcifications on the stress field of atherosclerotic plaque caps in a section of carotid artery. This is achieved by performing finite element simulations of three-dimensional fluid-structure interaction models. The material response in the region of microcalcification is modeled using a combination of finite elements, homogenization theory, and a stress concentration function that approximates the average local stresses in the fibrous tissue and microcalcification phases. The results indicate that the circumferential stress in the fibrous tissue phase increases as the volume fraction of microcalcifications is increased, and that the stress exceeds a critical threshold when the fibrous cap thickness is decreased. Furthermore, the presence of the microcalcifications significantly influences the distribution of stress by shifting the maximum circumferential stress away from the cap shoulders, where failure is most common when the effective region of microcalcification is located at the center of the cap. This is a possible explanation of why 40% of plaque ruptures occur away from the shoulder region of the cap.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Three-dimensional view of the full section of stenotic artery with a close-up view of the effective region of microcalcification and lipid pool, which are outlined and indicated with the arrows

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Figure 2

Circumferential cross-section view of the stenosis with: (a) center region of microcalcification and (b) shoulder region of microcalcification. Asterisk indicates the region of microcalcification.

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Figure 3

Close-up view of the longitudinal cross-section of the stenosis. Asterisk indicates the region of microcalcification.

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Figure 4

(a) Cylinder intersecting with thin plate and (b) final intersection region embedded in the middle of the thin plate

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Figure 5

Spatial distribution of the volume fraction vpo within the effective region of the cap for a peak volume fraction of 0.03

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Figure 6

Far field loading of a single inclusion with an initial debonded region at the pole

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Figure 7

Close-up view of the fluid solution in the lumen for (a) the pressure field (Pa) and (b) the velocity field (m/s). The length of the velocity vectors are proportional to the magnitude and are not color coded.

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Figure 8

Circumferential cross-section view of the circumferential stress distribution, cap thickness of 150 μm and vp=0.0. The arrow indicates the point, where the maximum circumferential stress occurs.

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Figure 9

Circumferential stress (Pa) distribution when the region of microcalcification is located at the center of the cap with a thickness of 150 μm and a volume fraction of 0.03: (a) full three-dimensional view of the artery model, (b) close-up three-dimensional view of the stenosis, (c) longitudinal cross-section view of the stenosis, (d) full circumferential cross-section view through the point of maximum stress, and (e) close-up circumferential view. The arrows indicate the point, where the maximum circumferential stress occurs.

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Figure 10

Circumferential stress (Pa) distribution when the region of microcalcification is located at the shoulder of the cap with a thickness of 150 μm and a volume fraction of 0.03: (a) full three-dimensional view of the artery model, (b) close-up three-dimensional view of the stenosis, (c) longitudinal cross-section view of the stenosis, (d) full circumferential cross-section view through the point of maximum stress, and (e) close-up circumferential view. The arrows indicate the point, where the maximum circumferential stress occurs.

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