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Research Papers

# 3D MRI-Based Anisotropic FSI Models With Cyclic Bending for Human Coronary Atherosclerotic Plaque Mechanical Analysis

[+] Author and Article Information
Dalin Tang1

Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609dtang@wpi.edu

Chun Yang

Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609; School of Mathematical Sciences, Beijing Normal University, Beijing, China

Shunichi Kobayashi

Division of Creative Engineering, Shinshu University, Ueda, Nagano, Japan

Jie Zheng, Pamela K. Woodard

Zhongzhao Teng

Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609

Kristen Billiar

Department of Biomedical Engineering, Worcester Polytechnic Institute, Worcester, MA 01609

Richard Bach

Division of Cardiovascular Diseases, Washington University, St. Louis, MO 63110

David N. Ku

School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332

1

Corresponding author.

J Biomech Eng 131(6), 061010 (May 05, 2009) (11 pages) doi:10.1115/1.3127253 History: Received August 23, 2008; Revised January 21, 2009; Published May 05, 2009

## Abstract

Heart attack and stroke are often caused by atherosclerotic plaque rupture, which happens without warning most of the time. Magnetic resonance imaging (MRI)-based atherosclerotic plaque models with fluid-structure interactions (FSIs) have been introduced to perform flow and stress/strain analysis and identify possible mechanical and morphological indices for accurate plaque vulnerability assessment. For coronary arteries, cyclic bending associated with heart motion and anisotropy of the vessel walls may have significant influence on flow and stress/strain distributions in the plaque. FSI models with cyclic bending and anisotropic vessel properties for coronary plaques are lacking in the current literature. In this paper, cyclic bending and anisotropic vessel properties were added to 3D FSI coronary plaque models so that the models would be more realistic for more accurate computational flow and stress/strain predictions. Six computational models using one ex vivo MRI human coronary plaque specimen data were constructed to assess the effects of cyclic bending, anisotropic vessel properties, pulsating pressure, plaque structure, and axial stretch on plaque stress/strain distributions. Our results indicate that cyclic bending and anisotropic properties may cause 50–800% increase in maximum principal stress $(Stress-P1)$ values at selected locations. The stress increase varies with location and is higher when bending is coupled with axial stretch, nonsmooth plaque structure, and resonant pressure conditions (zero phase angle shift). Effects of cyclic bending on flow behaviors are more modest (9.8% decrease in maximum velocity, 2.5% decrease in flow rate, 15% increase in maximum flow shear stress). Inclusion of cyclic bending, anisotropic vessel material properties, accurate plaque structure, and axial stretch in computational FSI models should lead to a considerable improvement of accuracy of computational stress/strain predictions for coronary plaque vulnerability assessment. Further studies incorporating additional mechanical property data and in vivo MRI data are needed to obtain more complete and accurate knowledge about flow and stress/strain behaviors in coronary plaques and to identify critical indicators for better plaque assessment and possible rupture predictions.

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## Figures

Figure 1

A human coronary atherosclerotic plaque sample: multicontract MR images and reconstructed 3D geometry. (a)-(c) MR images with T1, middle-T2, and T2-weighted images. (d) Contour plot of the segmented image using a multicontrast algorithm; (e) histological data. The location and shape of each major plaque component correlated very well with histological data; (f) 3D plaque geometry reconstructed from a 36-slice ex vivo MRI data set.

Figure 2

The component-fitting mesh generation process. ((a) and (b)) Two slices with a lipid core inclusion (yellow) and numerically-generated component-fitting curves and “surfaces” to form “volumes;” (c) component-fitting volumes formed by connection corresponding areas from stacking adjacent slices. Distance between the two slices was enlarged fro better viewing.

Figure 3

Prescribed pressure conditions for the baseline model and corresponding flow rates. (a) A simplified pressure profile for human coronary artery was scaled to 70–130 mm Hg and used as the upstream pressure (pin). Downstream pressure was chosen so that flow rate was within physiological range; (b) flow rate corresponding to the prescribed pressure conditions with and without cyclic bending. Cyclic bending reduced max flow rate by about 2.5%.

Figure 4

Material stress-stretch curves and imposed curvature conditions. (a) Axial and circumferential stress-stretch data (marked by x) measured from a human coronary specimen and stress-stretch matching curves derived from the modified anisotropic Mooney–Rivlin models for fibrous tissue (vessel). Stress-stretch curves for lipid pool and calcification models were also included. Parameter values are given in the main text; (b) imposed curvature conditions based on human coronary curvature variation data (36).

Figure 5

Cyclic bending leads to large stress/strain variations: Stress-P1/Strain-P1 distributions from Model 1 (with cyclic bending) corresponding to maximum and minimum curvature conditions. Position of the cut-surface is shown.

Figure 6

Stress-P1/Strain-P1 distributions from Model 2 (no cyclic bending) show only modest variations caused by imposed pulsating pressure conditions

Figure 7

Comparison of FMSS and velocity plots from Models 1 (with bending) and 2 (no bending) shows that cyclic bending has modest effects (<15%) on flow velocity and maximum shear stress

Figure 8

Combined effects of plaque components, pressure/curvature phase angle, and axial stretch with cyclic bending on stress/strain distributions

Figure 9

Stress/strain plots from the isotropic model (Model 6) with cyclic bending showing different stress/strain distribution patterns

Figure 10

Local Stress-P1 variations tracked at four selected locations from four models showing cyclic bending causes large stress variations in the coronary plaque. TP1: a location where global maximum Stress-P1 was found; TP2: calcification plaque cap (thinnest site); TP3: a location on the bending side with a large local curvature; and TP4: lipid pool plaque cap.

## Errata

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