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Technical Briefs

# Lumen Irregularity Dominates the Relationship Between Mechanical Stress Condition, Fibrous-Cap Thickness, and Lumen Curvature in Carotid Atherosclerotic Plaque

[+] Author and Article Information
Zhongzhao Teng1

Department of Radiology, University of Cambridge, Cambridge, CB2 0QQ, UKzt215@cam.ac.uk

Umar Sadat, Chengcheng Zhu, Victoria E. Young, Martin J. Graves, Jonathan H. Gillard

Department of Radiology, University of Cambridge, Cambridge, CB2 0QQ, UK

Guangyu Ji

Division of Cardiothoracic Surgery, Changhai Hospital, Second Military Medical University, Shanghai, 200433, China

1

Corresponding author. Present address: Level 5, P.O. Box 218, Addenbrooke’s Hospital, Hills Road, Cambridge CB2 0QQ, UK.

J Biomech Eng 133(3), 034501 (Feb 04, 2011) (4 pages) doi:10.1115/1.4003439 History: Received September 16, 2010; Revised December 29, 2010; Posted January 14, 2011; Published February 04, 2011; Online February 04, 2011

## Abstract

High mechanical stress condition over the fibrous cap (FC) has been widely accepted as a contributor to plaque rupture. The relationships between the stress, lumen curvature, and FC thickness have not been explored in detail. In this study, we investigate lumen irregularity-dependent relationships between mechanical stress conditions, local FC thickness $(LTFC)$, and lumen curvature $(LClumen)$. Magnetic resonance imaging slices of carotid plaque from 100 patients with delineated atherosclerotic components were used. Two-dimensional structure-only finite element simulations were performed for the mechanical analysis, and maximum principal stress (stress-$P1$) at all integral nodes along the lumen was obtained. $LTFC$ and $LClumen$ were computed using the segmented contour. The lumen irregularity $(L-δir)$ was defined as the difference between the largest and the smallest lumen curvature. The results indicated that the relationship between stress-$P1$, $LTFC$, and $LClumen$ is largely dependent on $L-δir$. When $L-δir≥1.31$ (irregular lumen), stress-$P1$ strongly correlated with lumen curvature and had a weak/no correlation with local FC thickness, and in 73.4% of magnetic resonance (MR) slices, the critical stress (maximum of stress-$P1$ over the diseased region) was found at the site where the lumen curvature was large. When $L-δir≤0.28$ (relatively round lumen), stress-$P1$ showed a strong correlation with local FC thickness but weak/no correlation with lumen curvature, and in 71.7% of MR slices, the critical stress was located at the site of minimum FC thickness. Using lumen irregularity as a method of identifying vulnerable plaque sites by referring to the lumen shape is a novel and simple method, which can be used for mechanics-based plaque vulnerability assessment.

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## Figures

Figure 1

(a) Multisequence high-resolution in vivo MRI: lipid pool (marked by white arrow), lumen (marked by asterisk), and fibrous wall; (b) segmented plaque contour showing lipid core (dashed line); (c) schematic drawing for computing the local FC thickness (LTFC) and local maximum lumen curvature (LClumen). The circle is determined by three adjacent points and used to compute the curvature, and the length of the line with double arrows is the measurement of local FC thickness.

Figure 2

The relationships between stress-P1, LClumen, and LTFC largely depend on the lumen irregularity. (a) In a slice with a round lumen contour, stress-P1 has a strong negative correlation with LTFC and no correlation with LClumen. Critical stress appears at the location with minimum FC thickness; (b) when the lumen is irregular, stress-P1 has a weak correlation with LTFC and a strong positive correlation with LClumen. Critical stress appears at the location with the largest lumen curvature.

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