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Research Papers

Remodeling of the Collagen Fiber Architecture Due to Compaction in Small Vessels Under Tissue Engineered Conditions

[+] Author and Article Information
Ana L. F. Soares

 Eindhoven University of Technology, Department of Biomedical Engineering, P.O. Box 513, 5600 MB Eindhoven, The Netherlandsa.l.f.soares@tue.nl

Maria Stekelenburg

 Eindhoven University of Technology, Department of Biomedical Engineering, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Frank P. T. Baaijens

 Eindhoven University of Technology, Department of Biomedical Engineering, P.O. Box 513, 5600 MB Eindhoven, The NetherlandsF.P.T.Baaijens@tue.nl

J Biomech Eng 133(7), 071002 (Jul 13, 2011) (8 pages) doi:10.1115/1.4003870 History: Received May 02, 2010; Revised March 17, 2011; Posted July 13, 2011; Published July 13, 2011; Online July 13, 2011

Mechanical loading protocols in tissue engineering (TE) aim to improve the deposition of a properly organized collagen fiber network. In addition to collagen remodeling, these conditioning protocols can result in tissue compaction. Tissue compaction is beneficial to tissue collagen alignment, yet it may lead to a loss of functionality of the TE construct due to changes in geometry after culture. Here, a mathematical model is presented to relate the changes in collagen architecture to the local compaction within a TE small blood vessel, assuming that under static conditions, compaction is the main factor responsible for collagen fiber organization. An existing structurally based model is extended to incorporate volumetric tissue compaction. Subsequently, the model is applied to describe the collagen architecture of TE constructs under either strain based or stress based stimulus functions. Our computations indicate that stress based simulations result in a helical collagen fiber distribution along the vessel wall. The helix pitch angle increases from a circumferential direction in the inner wall, over about 45 deg in the middle vessel layer, to a longitudinal direction in the outer wall. These results are consistent with experimental data from TE small diameter blood vessels. In addition, our results suggest a stress dependent remodeling of the collagen, suggesting that cell traction is responsible for collagen orientation. These findings may be of value to design improved mechanical conditioning protocols to optimize the collagen architecture in engineered tissues.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Bioreactor setup. The tubular construct (@ in b) is mounted over a silicone tubing (arrow in a) in the bioreactor and fixed by sutures (arrow in c). The ends of the tube are connected to small diameter metal vessels (* in c). These vessels enable the application of a dynamic internal pressure to the silicon tube. In this study; however, no internal pressure is applied to the silicone tube. The remaining two tubes (# in c) are used to refresh the culture medium during tissue culture (modified from [37]).

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Figure 2

Schematic representation of growth. Three configurations of a growing body: original stress-free configuration B(t0), stress-free configuration after growth B(t1), and loaded configuration B(t). The deformation tensor Fg maps from B(t0) to B(t1), F* maps from B(t1) to B(t), and F from B(t0) to B(t) (modified from [(11),12]).

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Figure 3

Schematic representation of the angular fiber distribution function φf. Indicated are the fiber direction e→f and the angle γ in a coordinate system spanned by the vectors e→θ and e→z. Also, the definitions of the distribution function main fiber angle α and the dispersity β are represented.

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Figure 4

Stress-free configuration of the TE vessel wall (red) mounted on a rubber tube (gray). Indicated are the inner radius Ri , the outer radius Ro , the thickness of the wall h, and the vessel length (L). Also shown is a schematic representation of the typical helical fiber distribution e→f0 and the local directions e→R, e→Θ, and e→Z.

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Figure 5

(a) Definition of the preferred main fiber angle αp with respect to the stimulus functions gθ and gz . (b) Preferred dispersity βp as a function of the ratio of the stimulus functions gθ and gz (modified from [7]).

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Figure 6

TPLSCM images of cells (blue) and collagen fibers (green) in the (a) inner surface and (b) outer surface of a TE vessel and the respective collagen fiber orientation analysis. (γ=0∘ indicates that collagen and cells are oriented circumferentially; γ=90∘ indicates that collagen and cells are oriented axially.)

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Figure 7

Fiber distribution of the inner (red), middle (green), and outer (blue) wall of the TE vessel. The results were obtained using a strain based (a) and stress based (b) modeling algorithm.

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Figure 8

Computed fiber distribution parameters as a function of the radius r in the vessel wall. (a) Main fiber angle α (deg) and (b) dispersity β (–).

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Figure 9

Relative frequency of the computed main fiber angles along the vessel wall, adopting a strain based algorithm (a) and a stress based algorithm (b). The results were obtained with different parameters. Also represented is the relative frequency of collagen alignment (c) in porcine engineered vessels (blue) and porcine carotid arteries (dotted pink) modified from Dahl [8].

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Figure 10

Principal Cauchy stresses σrr, σθθ, and σzz as a function of the deformed radius. (a) is obtained with a strain and (b) with a stress modeling algorithm. The hypothesized layered structure is also observed relating each color to each layer.

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