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Research Papers

# Matrix Metalloproteinase-2 and -9 Are Associated With High Stresses Predicted Using a Nonlinear Heterogeneous Model of Arteries

[+] Author and Article Information
Yu Shin Kim

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, IBB Room 2117, 315 Ferst Drive, Atlanta, GA 30332yushin.kim@gatech.edu

Zorina S. Galis

Eli Lilly and Co., Lilly Corporate Center, Drop Code 0520, Indianapolis, IN 46285galis̱zorina@lilly.com

Alexander Rachev

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, IBB Room 3306, 315 Ferst Drive, Atlanta, GA 30332alexander.rachev@me.gatech.edu

Hai-Chao Han

Department of Mechanical Engineering, University of Texas at San Antonio, 6900 North Loop, 1604 West, San Antonio, TX 78249haichao.han@utsa.edu

Raymond P. Vito

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, IBB Room 2308, 315 Ferst Drive, Atlanta, GA 30332raymond.vito@me.gatech.edu

J Biomech Eng 131(1), 011009 (Nov 21, 2008) (10 pages) doi:10.1115/1.3005163 History: Received September 17, 2007; Revised August 05, 2008; Published November 21, 2008

## Abstract

Arteries adapt to their mechanical environment by undergoing remodeling of the structural scaffold via the action of matrix metalloproteinases (MMPs). Cell culture studies have shown that stretching vascular smooth muscle cells (VSMCs) positively correlates to the production of MMP-2 and -9. In tissue level studies, the expressions and activations of MMP-2 and -9 are generally higher in the outer media. However, homogeneous mechanical models of arteries predict lower stress and strain in the outer media, which appear inconsistent with experimental findings. The effects of heterogeneity may be important to our understanding of VSMC function since arteries exhibit structural heterogeneity across the wall. We hypothesized that local stresses, computed using a heterogeneous mechanical model of arteries, positively correlate to the levels of MMP-2 and -9 in situ. We developed a model of the arterial wall accounting for nonlinearity, residual strain, anisotropy, and structural heterogeneity. The distributions of elastin and collagen fibers in situ, measured in the media of porcine carotid arteries, showed significant nonuniformities. Anisotropy was represented by the direction of collagen fibers measured by the helical angle of VSMC nuclei. The points at which the collagen fibers became load bearing were computed, assuming a uniform fiber strain and orientation under physiological loading conditions, an assumption motivated by morphological measurements. The distributions of circumferential stresses, computed using both heterogeneous and homogeneous models, were correlated to the distributions of expressions and activations of MMP-2 and -9 in porcine common carotid arteries incubated in an ex vivo perfusion organ culture system under physiological conditions for $48h$. While strains computed using incompressibility were identical in both models, the heterogeneous model, unlike the homogeneous model, predicted higher circumferential stresses in the outer layer correlated to the expressions and activations of MMP-2 and -9. This implies that localized remodeling occurs in the areas of high stress and agrees with results from cell culture studies. The results support the role of mechanical stress in vascular remodeling and the importance of structural heterogeneity in understanding mechanobiological responses.

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Copyright © 2009 by American Society of Mechanical Engineers
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## Figures

Figure 1

(a) The configuration of an artery at the zero stress state and (b) the loaded state. An arbitrary point (R,Θ,Z) in the zero stress configuration is mapped to a point (r,θ,z) in the loaded configuration.

Figure 2

(a) Schematic of collagen fiber arrangements in the model. Collagen fibers were modeled as helices at an angle of ±θh. (b) The configurations of a collagen fiber at the zero stress state, recruiting point, and loaded state, where λh is the stretch ratio of the arterial tissue in the direction of fibers and λRP is the stretch ratio along the helix at a recruiting point.

Figure 3

(a) A representative image of elastin structure taken from arteries fixed at 100mmHg and in vivo stretch (λ=1.5). An arrow indicates one normalized thickness. Bar=50μm. (b) The average intensity of pixels due to elastin autofluorescence in each layer was plotted against the normalized thickness as mean (●) ± SD (+) (n=5).

Figure 4

(a) A representative image of collagen structure taken from arteries fixed at 100mmHg and in vivo stretch (λ=1.5). An arrow indicates one normalized thickness. Bar=50μm. (b) The average intensity of pixels due to collagen birefringence in each layer was plotted against the normalized thickness as mean (●) ± SD (+) (n=5).

Figure 5

(a) The distribution of circumferential stress computed using the heterogeneous model. The circumferential stress in each layer computed using the heterogeneous model was plotted against the normalized thickness as mean (●) ± SD (+) (n=5). (b) The distribution of circumferential stress computed using the homogeneous model (solid line). It is plotted with the circumferential stress distribution in the heterogeneous model.

Figure 6

(a) A representative image of the immunostaining for MMP-2. Areas positively stained for MMP-2 appear to be dark gray-black. Negative control is shown together in a small window. An arrow indicates one normalized thickness. Bar=100μm. (b) The average area fraction of pixels positively stained for MMP-2 in each layer was plotted against the normalized thickness as mean (●) ± SD (+) (n=5).

Figure 7

(a) A representative image of the immunostaining for MMP-9. Areas positively stained for MMP-9 appear to be dark gray-black. Negative control is shown together in a small window. An arrow indicates one normalized thickness. Bar=100μm. (b) The average area fraction of pixels positively stained for MMP-9 in each layer was plotted against the normalized thickness as mean (●) ± SD (+) (n=5).

Figure 8

(a) A representative image of in situ zymography. Dark regions indicate localized gelatinolytic activities. An arrow indicates one normalized thickness. Bar=100μm. (b) The average area fraction of gelatinolytic activities in each layer was plotted against the normalized thickness as mean (●) ± SD (+) (n=5).

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