Research Papers

A Methodology to Analyze Changes in Lipid Core and Calcification Onto Fibrous Cap Vulnerability: The Human Atherosclerotic Carotid Bifurcation as an Illustratory Example

[+] Author and Article Information
Dimitrios E. Kiousis, Stephan F. Rubinigg

Institute of Biomechanics, Center of Biomedical Engineering, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria

Martin Auer

Department of Solid Mechanics, School of Engineering Sciences, Royal Institute of Technology (KTH), 10044 Stockholm, Sweden

Gerhard A. Holzapfel1

Institute of Biomechanics, Center of Biomedical Engineering, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria; Department of Solid Mechanics, School of Engineering Sciences, Royal Institute of Technology (KTH), 10044 Stockholm, Swedenholzapfel@tugraz.at

The abbreviation “nos” stands for n ot o therwise s pecified. In the context of the present study it means “no appreciable disease” or, more precisely, “nonatherosclerotic.”


Corresponding author.

J Biomech Eng 131(12), 121002 (Oct 29, 2009) (9 pages) doi:10.1115/1.4000078 History: Received August 25, 2008; Revised February 19, 2009; Posted September 01, 2009; Published October 29, 2009

A lipid core that occupies a high proportion of the plaque volume in addition to a thin fibrous cap is a predominant indicator of plaque vulnerability. Nowadays, noninvasive imaging modalities can identify such structural components, however, morphological criteria alone cannot reliably identify high-risk plaques. Information, such as stresses in the lesion’s components, seems to be essential. This work presents a methodology able to analyze the effect of changes in the lipid core and calcification on the wall stresses, in particular, on the fibrous cap vulnerability. Using high-resolution magnetic resonance imaging and histology of an ex vivo human atherosclerotic carotid bifurcation, a patient-specific three-dimensional geometric model, consisting of four tissue components, is generated. The adopted constitutive model accounts for the nonlinear and anisotropic tissue behavior incorporating the collagen fiber orientation by means of a novel and robust algorithm. The material parameters are identified from experimental data. A novel stress-based computational cap vulnerability index is proposed to assess quantitatively the rupture-risk of fibrous caps. Nonlinear finite element analyses identify that the highest stress regions are located at the vicinity of the shoulders of the fibrous cap and in the stiff calcified tissue. A parametric analysis reveals a positive correlation between the increase in lipid core portion and the mechanical stress in the fibrous cap and, hence, the risk for cap rupture. The highest values of the vulnerability index, which correlate to more vulnerable caps, are obtained for morphologies for which the lipid cores were severe; heavily loaded fibrous caps were thus detected. The proposed multidisciplinary methodology is able to investigate quantitatively the mechanical behavior of atherosclerotic plaques in patient-specific stenoses. The introduced vulnerability index may serve as a more quantitative tool for diagnosis, treatment and prevention.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Representative T1-weighted MR images (slice thickness of 0.8 mm and in plane resolution of 0.15 mm) showing different sections of the excised human carotid bifurcation, with z referring to the coordinate system, as introduced in Fig. 2

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Figure 2

3D geometric model of a stenotic human carotid bifurcation (atherosclerotic lesion of type V (35)) based on in vitro MRI (Fig. 1) reconstructed using NURBS. Four arterial tissues are considered: nondiseased wall (W-nos), calcification (I-c), lipid core (I-lp), and fibrous cap (I-fc). Two characteristic cross sections are shown at axial planes z=53.6 mm (Section A) and z=64.0 mm (Section B).

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Figure 3

Transverse (a) and longitudinal (b) sections of the carotid bifurcation model. Every point P is projected onto its corresponding tangential planes Ω1 and Ω2. 3D view of the computed fiber direction vectors M and M′ at the center of the superficial finite elements of the carotid bifurcation wall (c).

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Figure 4

Maximum principal Cauchy stress at the deformed configuration of the cross sections A, at z=53.6 mm, and B, at z=64.0 mm (for the geometrical situation see Fig. 2) for (a) model RM (VI-lp=25%, VI-c=75%) and (b) model M2 (VI-lp=75%, VI-c=25%). Stress difference between models M2 and RM at the unloaded configuration of the considered cross sections (c). For the sake of clearness, the boundaries of fibrous cap, lipid core, and calcification are shown.

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Figure 5

Maximum principal Cauchy stress in the fibrous cap I-fc for the four models (Table 2). The ranges of stress are plotted with respect to the volume of I-fc. As the tissue composition becomes richer in lipid higher stresses are identified in the fibrous cap.

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Figure 6

Maximum principal Cauchy stress σI-fc in the finite elements of the fibrous cap I-fc for model M2 (75% I-lp). At several locations the stresses in I-fc exceed the allowable stress σallow=50 kPa. For scalar D1, i.e., Eq. 9, the maximum stress max(σI-fc) at i=12 (symbol ⋆) is relevant, while for scalar D2, i.e., Eq. 10, every finite element in which the stress is above σallow is considered.

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Figure 7

Vulnerability index ξ, i.e., Eq. 8, for the four models (Table 2) with w1=w2=0.5. Model M1 has no lipid core while VI-lp=100% in model M3. For models M2 and M3 the vulnerability index is more than 50% higher in comparison to reference model RM.



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