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Research Papers

Influence of Medial Collagen Organization and Axial In Situ Stretch on Saccular Cerebral Aneurysm Growth

[+] Author and Article Information
Thomas Eriksson

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), 100 44 Stockholm, Sweden

Martin Kroon

Department of Solid Mechanics, School of Engineering Sciences, Royal Institute of Technology (KTH), 100 44 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), 100 44 Stockholm, Swedenholzapfel@tugraz.at

1

Corresponding author.

J Biomech Eng 131(10), 101010 (Sep 04, 2009) (7 pages) doi:10.1115/1.3200911 History: Received November 24, 2008; Revised July 08, 2009; Published September 04, 2009

A model for saccular cerebral aneurysm growth, proposed by Kroon and Holzapfel (2007, “A Model for Saccular Cerebral Aneurysm Growth in a Human Middle Cerebral Artery,” J. Theor. Biol., 247, pp. 775–787; 2008, “Modeling of Saccular Aneurysm Growth in a Human Middle Cerebral Artery,” ASME J. Biomech. Eng., 130, p. 051012), is further investigated. A human middle cerebral artery is modeled as a two-layer cylinder where the layers correspond to the media and the adventitia. The immediate loss of media in the location of the aneurysm is taken to be responsible for the initiation of the aneurysm growth. The aneurysm is regarded as a development of the adventitia, which is composed of several distinct layers of collagen fibers perfectly aligned in specified directions. The collagen fibers are the only load-bearing constituent in the aneurysm wall; their production and degradation depend on the stretch of the wall and are responsible for the aneurysm growth. The anisotropy of the surrounding media was modeled using the strain-energy function proposed by Holzapfel (2000, “A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models,” J. Elast., 61, pp. 1–48), which is valid for an elastic material with two families of fibers. It was shown that the inclusion of fibers in the media reduced the maximum principal Cauchy stress and the maximum shear stress in the aneurysm wall. The thickness increase in the aneurysm wall due to material growth was also decreased. Varying the fiber angle in the media from a circumferential direction to a deviation of 10 deg from the circumferential direction did, however, only show a little effect. Altering the axial in situ stretch of the artery had a much larger effect in terms of the steady-state shape of the aneurysm and the resulting stresses in the aneurysm wall. The peak values of the maximum principal stress and the thickness increase both became significantly higher for larger axial stretches.

FIGURES IN THIS ARTICLE
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Copyright © 2009 by American Society of Mechanical Engineers
Topics: Fibers , Stress , Aneurysms
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Figures

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Figure 1

Middle cerebral artery modeled as a two-layer cylinder (media and adventitia). The cylindrical structure (top right figure) constitutes the reference configuration of the posed problem.

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Figure 2

Uniform fiber distribution in the aneurysm wall shown for eight layers. The coordinate system ζ1-ζ2 corresponds to the tangential and axial directions, as shown in Fig. 1.

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Figure 3

Orientations a01 and a02 of two families of fibers in the media symmetrically disposed with respect to the cylinder axis. The parameter β is the angle between the collagen fiber and the circumferential direction ζ1.

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Figure 4

Distributions of maximum principal Cauchy stress σ1∗ (axial in situ stretch λL=1.2). The fiber angle of the medial collagen varies according to (a) β=0 deg, (b) 5 deg, and (c) 10 deg; in (d) no collagen fiber is included in the media and the related aneurysm size is noticeably larger. Including collagen fibers in the media decreases the peak stress by 7.2%. The peak values are at the fundus.

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Figure 5

Distributions of the thickness increase λ3 (axial in situ stretch λL=1.2), i.e., according to Eq. 14. The fiber angle varies at (a) β=0 deg, (b) 5 deg, and (c) 10 deg; in (d) no fiber is included in the media. The largest thickness increases occur at the fundus, which is 4.34 for (a)–(c) and 4.56 for (d).

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Figure 6

Distributions of maximum in-plane Cauchy shear stress τ (axial in situ stretch λL=1.2). The fiber angle varies at (a) β=0 deg, (b) 5 deg, and (c) 10 deg; in (d) no fiber is included in the media. The peak values are located close to the neck at the long side of the aneurysm (0.093 MPa, 0.094 MPa, and 0.095 MPa for (a)–(c), respectively, and 0.102 MPa for (d)). The minimum values are located between the fundus and the neck in the plane X2=0.

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Figure 7

Distributions of maximum principal Cauchy stress σ1∗ (fiber angle β=0 deg). The axial stretch varies at (a) λL=1.0, (b) 1.2, and (c) 1.4. The peak values are at the fundus. No axial stretch results in a more spherical shape, whereas an axial stretch of 1.4 results in a more elliptic shape.

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Figure 8

Distributions of the thickness increase λ3 (fiber angle β=0 deg). The axial stretch varies at (a) λL=1.0, (b) 1.2, and (c) 1.4. The increase in λ3 is not always at the fundus. For λL=1.4, the maximum value of λ3 is located in the intact artery close to the neck of the aneurysm, with a value of 5.64.

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Figure 9

Distributions of maximum in-plane Cauchy shear stress τ (fiber angle β=0 deg). The axial stretch varies at (a) λL=1.0, (b) 1.2, and (c) 1.4. The maximum value is lowest for λL=1.2, whereas the peak values are almost identical for λL=1.0 and 1.4. The location of the maximum values for λL=1.0 and 1.2 is at the long side of the aneurysm and on the short side for 1.4.

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