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Research Papers

Multiscale Mechanical Simulations of Cell Compacted Collagen Gels

[+] Author and Article Information
Maziar Aghvami

Department of Biomedical Engineering,
University of Iowa,
Iowa City, IA 52242

V. H. Barocas

Department of Biomedical Engineering,
University of Minnesota,
Minneapolis, MN 55455

E. A. Sander

Department of Biomedical Engineering,
University of Iowa,
Iowa City, IA 52242
e-mail: edward-sander@uiowa.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received January 8, 2013; final manuscript received May 1, 2013; accepted manuscript posted May 8, 2013; published online June 11, 2013. Assoc. Editor: Keith Gooch.

J Biomech Eng 135(7), 071004 (Jun 11, 2013) (9 pages) Paper No: BIO-13-1010; doi: 10.1115/1.4024460 History: Received January 08, 2013; Revised May 01, 2013; Accepted May 08, 2013

Engineered tissues are commonly stretched or compressed (i.e., conditioned) during culture to stimulate extracellular matrix (ECM) production and to improve the mechanical properties of the growing construct. The relationships between mechanical stimulation and ECM remodeling, however, are complex, interdependent, and dynamic. Thus, theoretical models are required for understanding the underlying phenomena so that the conditioning process can be optimized to produce functional engineered tissues. Here, we continue our development of multiscale mechanical models by simulating the effect of cell tractions on developing isometric tension and redistributing forces in the surrounding fibers of a collagen gel embedded with explants. The model predicted patterns of fiber reorganization that were similar to those observed experimentally. Furthermore, the inclusion of cell compaction also changed the distribution of fiber strains in the gel compared to the acellular case, particularly in the regions around the cells where the highest strains were found.

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Figures

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Fig. 1

“Strap” formation between explants and the multiscale modeling strategy. (A) A triangular explant configuration develops strong fiber alignment between fibroblast explants after 60 h. Images are montages of sixty 20 × DIC images (images from Dr. Sander's lab). (B) Multiscale models consist of cellular networks (blue) that are configured in an analogous manner to the experiments and that contract to 40% of their original length to produce tension and reorganization in the surrounding ECM networks.

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Fig. 2

Top-view of fiber network realignment after 40% compaction for case 1. ECM networks develop varying patterns of fiber alignment between explants in a configuration dependent manner. The color map indicates the change in the degree of fiber alignment (Δα) between the initial traction free configuration and 40% compaction. Also depicted are the principal directions of fiber alignment (white crosses). For clarity, directions are only shown for those elements with Δα > 0.08.

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Fig. 3

Strain developed during 20% and 40% compaction for three explants. (A), (D) Top, bottom, left, and right boundaries are fixed, (B), (E) top and bottom are fixed, and (C), (F) symmetry boundary conditions are applied to the left, bottom, and back faces. Maximum principal strain patterns change in accord with the applied boundary conditions. White arrows show principal direction.

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Fig. 4

Comparison of mechanical response. (A) The force on the boundary during uniaxial extension for the case of 40% compaction for three explants (circles) is higher than the case where all of the networks are ECM networks (i.e., no explants). The inset plot shows the increase in force that develops on the boundary during the compaction process prior to uniaxial extension. (B), (C) Regional differences in strain, particularly around the explants, are apparent at full stretch (λ = 1.5).

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Fig. 5

Histograms of fiber strain in all ECM networks for uniaxial stretch of the three explant model. (A), (B) During the compaction phase of the simulations a small fraction of fibers developed small tensile and compressive strains. (C) 25% uniaxial stretch, (D) 50% uniaxial stretch. With uniaxial stretch a wide range of fiber strains were observed, most of which were below the amount of stretch applied macroscopically (red line). The distribution of fiber strains in the no-explant model (data not shown) were similar in shape to those in (C) and (D).

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Fig. 6

Differences in average fiber-level strain at 50% uniaxial stretch. (A) Regional variations in the average fiber-level strain in each element were apparent when the strains in the no-explant model were subtracted from those in the three-explant model. The largest differences were found in the elements around the explants (white). Differences in fiber strain that exceeded ± 4% are highlighted with a star. Histograms of the strains for all 88,728 fibers in the starred elements for the (B) three-explant model and (C) no-explant model.

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Fig. 7

Behavior of selected networks. (A), (B) Average fiber strains in each element are depicted at select instances for the (A) Three-explant model and the no-explant model (B). The red circles highlight the locations of two networks depicted below. (C) Top-view of network 1, which is associated with an area of high fiber strain. The individual fibers reorganize to satisfy force equilibrium and are color coded to indicate the level of fiber strain. (D) Network 2 is associated with an area low average fiber strain. Prior to uniaxial stretch the network volume shrinks and some fibers are under compression. The fiber strain and kinematics in these networks are compared with those developed in the no-explant model (E), (F).

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