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TECHNICAL PAPERS: Soft Tissue

Multiscale, Structure-Based Modeling for the Elastic Mechanical Behavior of Arterial Walls

[+] Author and Article Information
Triantafyllos Stylianopoulos

Department of Chemical Engineering and Materials Science, 421 Washington Avenue S.E., University of Minnesota, Minneapolis, MN 55455

Victor H. Barocas1

Department of Biomedical Engineering, University of Minnesota, 7-105 Hasselmo Hall, 312 Church Street SE, Minneapolis, MN 55455baroc001@umn.edu

1

Corresponding author.

J Biomech Eng 129(4), 611-618 (Jan 24, 2007) (8 pages) doi:10.1115/1.2746387 History: Received July 12, 2006; Revised January 24, 2007

Passive elastic behavior of arterial wall remains difficult to model. Although phenomenological and structural models exist, the question of how the three-dimensional network structure of the collagen in the artery determines its mechanical properties is still open. A model is presented that incorporates a collagen network as well as the noncollagenous material that comprise the artery. The collagen architecture is represented as a network of interconnected fibers, and a neo-Hookean constitutive equation is used to describe the contribution of the noncollagenous matrix. The model is multiscale in that volume-averaging theory is applied to the collagen network, and it is structural in that parameters of the microstructure of the collagen network were considered instead of a macroscopic constitutive law. The computational results provided a good fit to published experimental data for decellularized porcine carotid arteries. The model predicted increased circumferential compliance for increased axial stretch, consistent with previously published reports, and a relatively small sensitivity to open angle. Even at large extensions, the model predicted that the noncollagenous matrix would be in compression, preventing collapse of the collagen network. The incorporation of fiber-fiber interactions led to an accurate model of artery wall behavior with relatively few parameters. The counterintuitive result that the noncollagenous component is in compression during extension and inflation of the tissue suggests that the collagen is important even at small strains, with the noncollagenous components supporting the network, but not resisting the load directly. More accurate representation of the microstructure of the artery wall is needed to explore this issue further.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of the model. A multiscale model for the collagen network is combined with a single-scale (macroscopic) model of the noncollagenous material. The initial state of the artery is described by radius Ri, wall thickness H, and open angle Θ.

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Figure 2

Simulation procedure: (a) initial, stress-free configuration with open angle; (b) the artery is closed to produce a hollow cylinder; (c) the artery is stretched axially by 30%; and (d) stretched artery is inflated to 150mmHg luminal pressure

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Figure 3

Pressure versus inner diameter for experimental (squares, Ref. 43) and computed (solid) results

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Figure 4

Wall thickness versus pressure for experimental (squares, Ref. 43) and computed (solid) results

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Figure 5

(a) Pressure versus inner diameter; and (b) axial force versus inner diameter for 26deg (solid) and 69deg (dashes) open angles, and axial stretches of 1.15, 1.30, and 1.55

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Figure 6

Distribution of fiber stretch ratio. The histogram shows the final distribution of fibers in an RVE after a macroscopic closure from 26deg open angle, extension to 55%, and inflation to 200mmHg.

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Figure 7

Collagen and matrix contributions to the circumferential stress. Results for 26deg open angle, 30% extension, and 200mmHg inflation. The noncollagenous matrix is in compression, while the collagen in tension.

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Figure 8

Schematic generation of collagen network

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Figure 9

Local fiber coordinates in calculation of Ω. r is the directional vector of the fiber.

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