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Research Papers

A New Observation on the Stress Distribution in the Coronary Artery Wall

[+] Author and Article Information
Chong Wang

Robert M. Berne Cardiovascular Research Center, University of Virginia, Charlottesville, VA 22908

Xiaomei Guo

Department of Biomedical Engineering, IUPUI, Indianapolis, IN 46202

Ghassan S. Kassab1

Department of Biomedical Engineering, Department of Surgery, and Department of Cellular and Integrative Physiology, IUPUI, Indianapolis, IN 46202; Indiana Center for Vascular Biology and Medicine, IUPUI, Indianapolis, IN 46202gkassab@iupui.edu

1

Corresponding author.

J Biomech Eng 131(11), 111011 (Oct 26, 2009) (5 pages) doi:10.1115/1.4000106 History: Received March 20, 2008; Revised June 17, 2009; Posted September 01, 2009; Published October 26, 2009

The stress distribution in the vessel wall has an important bearing on vascular function in health and disease. We studied the relationship between the transmural stress distribution and the opening angle (OA) to determine the stress gradient. The simulation of wall stress was based on transmural measurements of strain and material properties of coronary arteries in reference to the zero-stress state. A one-layer model with material constants of the intact vessel was used to calculate the circumferential stress distribution. A sensitivity analysis using both one- and two-layer models (intima-media and adventitia layers) was carried out to study the effect of the OA on the circumferential stress distribution and average circumferential stress. A larger OA always shifts the circumferential stress from the intima-media to the adventitia layer. We report a new observation that the circumferential stress at the adventitia may exceed that at the intima at physiological loading due to the larger OA in the porcine coronary artery. This has important implications for growth and remodeling, where an increase in opening angle may shift excessive stress from the inner layer to the outer layer.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Relation between average circumferential stress σθ,AVG and OA from experimental measurements of the swine left anterior descending artery (15). Data can be fitted with a linear equation as σθ,AVG=0.115OA+124.5, R2=0.32, and p-value <0.0001. (b) Relation between stress distribution factor (σθ,e/σθ,i) and OA, based on experimental measurements of the swine left anterior descending artery (15). Data can be fitted with a linear equation as σθ,e/σθ,i=0.0278OA−2.56, R2=0.84, and p-value <0.000001.

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Figure 2

Numerical sensitivity analysis of the dependence of the circumferential stress (σθ,AVG) on the OA. Opening angle changes due to (a) inner circumference, (b) outer circumference, and (c) wall area in zero-stress state. Opening angle varies from 75 deg to 250 deg in Figs.  22, and from 120 deg to 170 deg in Fig. 2. Ci varies from 6.45 mm to 8.5 mm. Co varies from 6.67 mm to 8.67 mm. A varies from 0.75 mm2 to 4 mm2.

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Figure 3

Numerical sensitivity analysis of the dependence of the outer-to-inner circumferential stress ratio (stress distribution factor) on an OA. Internal pressure is 100 mmHg for all curves. Opening angle changes due to (a) inner circumference, (b) outer circumference, and (c) area change in zero-stress state. Opening angle varies from 75 deg to 250 deg in Figs  33, and from 120 deg to 170 deg in Fig. 3. Ci varies from 6.45 mm to 8.5 mm. Co varies from 6.67 mm to 8.67 mm. A varies from 0.75 mm2 to 4 mm2.

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Figure 4

Effect of transmural pressure on the stress distribution factor. Triangles represent internal pressure increase with zero external pressure. Round dots represent the same interpressure pattern with 30 mmHg external pressure. Ci, Co, and A are constants. (a) Ci=7.58 mm, Co=7.78 mm, and A=2.57 mm2, OA=162 deg; (b) Ci=7.58 mm, Co=8.12 mm, and A=2.57 mm2, OA=132 deg.

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Figure 5

Numerical sensitivity analysis of the dependence of stress distribution in the two-layer model on the OA. Pressure is 100 mmHg for all curves. OA change due to (a) inner circumference, (b) outer circumference, and (c) area change in zero-stress state.

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