Research Papers

Modeling of Saccular Aneurysm Growth in a Human Middle Cerebral Artery

[+] Author and Article Information
Martin Kroon

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

Gerhard A. Holzapfel1

School of Engineering Sciences, Department of Solid Mechanics, Royal Institute of Technology (KTH), 10044 Stockholm, Sweden; Institute of Biomechanics, Graz University of Technology, 8010 Graz, Austriaholzapfel@tugraz.at


Corresponding author.

J Biomech Eng 130(5), 051012 (Sep 10, 2008) (10 pages) doi:10.1115/1.2965597 History: Received May 15, 2007; Revised September 03, 2007; Published September 10, 2008

Saccular aneurysm growth in a human middle cerebral artery is modeled. The aneurysm growth model was presented in a companion paper by Kroon and Holzapfel (“A Model for Saccular Cerebral Aneurysm Growth by Collagen Fibre Remodelling  ,” J. Theor. Biol., in press) and was assessed there for axisymmetric growth. The aneurysm growth model is now evaluated for a more realistic setting. The middle cerebral artery is modeled as a two-layered cylinder, where the layers correspond to the media and the adventitia. An instant loss of the media in a region of the artery wall initiates the growth of the saccular aneurysm. The aneurysm wall is assumed to be a development of the adventitia of the original healthy artery, and collagen is assumed to be the only load-bearing constituent in the adventitia and in the aneurysm wall. The collagen is organized in a number of distinct layers where fibers in a specific layer are perfectly aligned in a certain fiber direction. The production of new collagen is taken to depend on the stretching of the aneurysm wall, and the continuous remodeling of the collagen fibers is responsible for the aneurysm growth. The general behavior of the growth model is investigated and also the influence of the structural organization of the collagen fabric. The analysis underlines the fact that the material behavior of aneurysmal tissue cannot be expected to be isotropic. The model predictions agree well with clinical and experimental results, for example, in terms of aneurysm size and shape, wall stress levels, and wall thickness.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Middle cerebral artery modeled as a two-layer cylinder

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Figure 2

Three fiber distributions used in the present study (n=8): (a) uniform (ξ=1); (b) anisotropic (ξ=0.765); (c) anisotropic (ξ=1.262). The coordinate system ζ1-ζ2 is with respect to Fig. 1.

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Figure 3

Mesh of 13,093 finite elements used throughout the present study

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Figure 4

Developing aneurysm at four time stages

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Figure 5

Stress and stretch fields of the aneurysm wall at steady state: (a) corotated maximum principal Cauchy-like stress σ1⋆; (b) maximum shear stress τmax⋆; (c) and (d) maximum principal in-plane stretch λ1 and corresponding distribution of thickness change λ3, respectively

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Figure 11

Corotated deformed fiber distribution (dotted lines) and reference fiber distribution (solid lines) at the evaluation point at steady state. The reference distribution is isotropic (ξ=1)

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Figure 10

Distributions of the principal stretch λ1 at steady state for n=4 and n=32

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Figure 9

Initial (t=0) and steady state (t→∞) corotated normalized stiffness distributions cϕ⋆∕(τ0λ1λ2) along the whole azimuthal range ϕ for n=4, 6, 8, and 32

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Figure 8

Steady state stress distributions for material models with initially nonuniform fiber distributions (ξ=0.765 and ξ=1.262)

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Figure 7

Steady state shapes resulting from material models with initially nonuniform fiber distributions (ξ=0.765 and ξ=1.262)

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Figure 6

Corotated (normalized) spatial stiffness cϕ⋆∕(τ0λ1λ2) evaluated for the whole azimuthal range ϕ: distributions are shown for the initial behavior (t=0) and for the steady state behavior (t→∞), for ξ=1 (isotropic) and two different levels of anisotropy, ξ=0.765 and ξ=1.262 (compare with Fig. 1)




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