Research Papers

The Modulus of Fibroblast-Populated Collagen Gels is not Determined by Final Collagen and Cell Concentration: Experiments and an Inclusion-Based Model

[+] Author and Article Information
Michael C. Evans

Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455

Victor H. Barocas1

Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455baroc001@umn.edu



Corresponding author. Present address: 7-105 Nils Hasselmo Hall, 312 Church Street South East, Minneapolis, MN 55455.

J Biomech Eng 131(10), 101014 (Oct 13, 2009) (7 pages) doi:10.1115/1.4000064 History: Received August 20, 2008; Revised July 21, 2009; Posted September 01, 2009; Published October 13, 2009

The fibroblast-populated collagen lattice is an attractive model tissue for in vitro studies of cell behavior and as the basis for bioartificial tissues. In spite of its simplicity—containing only collagen and cells—the system is surprisingly difficult to describe mechanically because of the ability of the cells to remodel the matrix, including compaction at short times and synthesis and/or degradation (and cell proliferation) at longer times. The objectives of this work were to measure the equilibrium modulus of fibroblast-populated gels with different collagen and cell concentrations, and to use that characterization as the basis for a theoretical model that could be used to predict gel mechanics based on conditions. Although many observations were as expected (e.g., the gel compacts more when there are more cells in it, and the gel is stiffer when there is more collagen in it), an unexpected result arose: the final modulus of the gel was not dependent solely on the final composition. Even if it compacted more than a gel that was originally at a high collagen concentration, a gel that started at a low collagen concentration remained less stiff than the higher-concentration gel. In light of these results and experimental studies by others, we propose a model in which the gel compaction is not homogeneous but consists instead of extreme densification near the cells in an otherwise unchanged matrix. By treating the dense regions as spherical inclusions, we used classical composite material theory to develop an expression for the modulus of a compacted gel based on the initial collagen density and the final inclusion (i.e., cell) density. The new model fit the data for moderately compacted gels well but broke down, as expected, for larger volume fractions at which the underlying model assumptions did not apply.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Schematic of the mechanical test geometry

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Figure 2

Effect of 1 day on cell-driven compaction for different initial cell and collagen concentrations. All plots have initial cell concentrations from 0 cells/ml to 250,000 cells/ml on the abscissa and show lines for 1 mg/ml (solid line), 2 mg/ml (dotted line), and 3 mg/ml (dashed line) initial collagen concentrations. All points are mean ±s.d. (n=3). (a) Compaction ratio, defined as the initial volume divided by the final volume. (b) Final cell concentration, determined from the compaction ratio and initial cell concentration, assuming no significant proliferation or death within 24 h. (c) Final collagen concentration, determined from the compaction ratio and initial collagen concentration, assuming no significant synthesis or degradation within 24 h. (d) Equilibrium secant modulus in uniaxial tension at 30% stretch.

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Figure 3

Typical force-time curve for uniaxial extension. The plot shows force versus time for a 1-day compacted gel. The three spikes occur at the step stretches to 10%, 20%, and 30% stretch. A large initial stress relaxes quickly and approaches an equilibrium value within a few minutes.

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Figure 4

Modulus contours based on averaged final conditions. Modulus varies from low (black) to high (white). Dots indicate experimental points used to construct the plot. The nonmonotonicity of the contours (i.e., the decrease in modulus with increasing collagen concentration at some points) is an indication that the final cell and collagen concentration are not sufficient to describe the mechanical behavior of the cell-gel composite.

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Figure 5

Confocal reflection image of a NHDF within a 3D collagen matrix 4 h after the preparation of the tissue construct. NHDFs (5×104 cells/ml) were suspended in a 0.5 mg/ml solution of purified type I collagen acid—solubilized from pig skin and polymerized to form the tissue construct. Scale bar equals 20 μm. (Image is courtesy of K. Campana and S. Voytik-Harbin.)

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Figure 6

Schematic of former and proposed view of cell-driven compaction. (a) Old view. Cells drive homogeneous compaction, increasing the density of the gel throughout. (b) Proposed view. Cells create small, very dense inclusions in an otherwise largely unaltered gel.

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Figure 7

Modulus contours based on new model. Modulus varies from low (black) to high (white). Dots indicate experimental points used to construct the plot. The modulus contour plot is the same as in Fig. 4 except that final cell concentration and initial collagen density (which sets the modulus of the noninclusion region) are the axes. The contours are much smoother, indicating that the new model captures the mechanics of the composite more accurately.

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Figure 8

Modulus data (model versus experiment). The plot shows the new model (lines) and the experimental results, with inclusion volume fraction calculated as described in the text. Particularly at low volume fractions, the theory agrees well with the data with only the inclusion-free moduli and the inclusion size as fitting parameters.



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