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TECHNICAL PAPERS: Cell

Collagen Fiber Alignment Does Not Explain Mechanical Anisotropy in Fibroblast Populated Collagen Gels

[+] Author and Article Information
Stavros Thomopoulos1

Department of Orthopaedic Surgery, Washington University School of Medicine, 1 Barnes-Jewish Hospital Plaza, Suite 11300, Campus Box 8233, St. Louis, MO 63110ThomopoulosS@wudosis.wustl.edu

Gregory M. Fomovsky, Preethi L. Chandran, Jeffrey W. Holmes

Department of Biomedical Engineering, Columbia University, New York, NY 10027

1

Corresponding author.

J Biomech Eng 129(5), 642-650 (Feb 15, 2007) (9 pages) doi:10.1115/1.2768104 History: Received January 25, 2006; Revised February 15, 2007

Many load-bearing soft tissues exhibit mechanical anisotropy. In order to understand the behavior of natural tissues and to create tissue engineered replacements, quantitative relationships must be developed between the tissue structures and their mechanical behavior. We used a novel collagen gel system to test the hypothesis that collagen fiber alignment is the primary mechanism for the mechanical anisotropy we have reported in structurally anisotropic gels. Loading constraints applied during culture were used to control the structural organization of the collagen fibers of fibroblast populated collagen gels. Gels constrained uniaxially during culture developed fiber alignment and a high degree of mechanical anisotropy, while gels constrained biaxially remained isotropic with randomly distributed collagen fibers. We hypothesized that the mechanical anisotropy that developed in these gels was due primarily to collagen fiber orientation. We tested this hypothesis using two mathematical models that incorporated measured collagen fiber orientations: a structural continuum model that assumes affine fiber kinematics and a network model that allows for nonaffine fiber kinematics. Collagen fiber mechanical properties were determined by fitting biaxial mechanical test data from isotropic collagen gels. The fiber properties of each isotropic gel were then used to predict the biaxial mechanical behavior of paired anisotropic gels. Both models accurately described the isotropic collagen gel behavior. However, the structural continuum model dramatically underestimated the level of mechanical anisotropy in aligned collagen gels despite incorporation of measured fiber orientations; when estimated remodeling-induced changes in collagen fiber length were included, the continuum model slightly overestimated mechanical anisotropy. The network model provided the closest match to experimental data from aligned collagen gels, but still did not fully explain the observed mechanics. Two different modeling approaches showed that the level of collagen fiber alignment in our uniaxially constrained gels cannot explain the high degree of mechanical anisotropy observed in these gels. Our modeling results suggest that remodeling-induced redistribution of collagen fiber lengths, nonaffine fiber kinematics, or some combination of these effects must also be considered in order to explain the dramatic mechanical anisotropy observed in this collagen gel model system.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Collagen gels were biaxially (BIAX) or uniaxially (UNIAX) constrained for 72h of culture. Deformation of the central region of the gel was measured from the reference configuration at the beginning of culture to the remodeled state immediately prior to testing. Remodeling of the gel was defined by the deformation gradient (FR). At 72h gels underwent planar biaxial load-controlled mechanical testing, where the applied load is defined by the traction tensor T.

Grahic Jump Location
Figure 2

Biaxial mechanical tests of isotropic biaxially constrained (BIAX) gels were used to obtain parameters “A” and “B” describing the mechanical properties of the individual collagen fibers. The structural organization of the BIAX gels was assumed to be random. An optimization procedure was used to match the strain predicted by the model with the strain measured experimentally. These parameters were then combined with structural information to predict the mechanics of uniaxially constrained (UNIAX) gels. This basic procedure was applied to test both the structural continuum model and the network model.

Grahic Jump Location
Figure 3

Representative contour plots of the minimization function for the structural model demonstrate convergence to optimum parameters “A” and “B” for one BIAX gel. The optimum “A” and “B” is indicated by a black dot at A=7.7 and B=76.3. A wide range of parameters is shown on the top plot and a focused range of parameters for the same gel is shown on the bottom plot. The simplex search method was used to determine the optimum “A” and “B” for the structural continuum model.

Grahic Jump Location
Figure 4

Average fiber distributions for collagen gels are shown on the left. Fiber distributions in UNIAX gels were biased towards 0deg (defined as the x1, or constrained, direction). Fibers in BIAX gels were distributed randomly. Average biaxial mechanical properties for BIAX and UNIAX gels are shown on the right. BIAX gels displayed isotropic mechanical behavior while UNIAX gels displayed anisotropic mechanical behavior (N=9 for each group, error bars represent standard deviation). (Note: The plotted stress is the second Piola-Kirchhoff stress and the plotted strain is the Lagrangian strain).

Grahic Jump Location
Figure 5

BIAX gel mechanical behavior was fit to either the structural model (A, C) or to the network model (E) to determine collagen fiber parameters. Predictions of UNIAX behavior were then performed under three conditions: (B) Structural model with experimentally measured UNIAX fiber orientations, (D) structural model with UNIAX fiber orientations and lengths predicted by remodeling and affine transformation, and (F) network model with UNIAX fiber orientations and lengths determined by nonaffine kinematics. Both models accurately described BIAX gel behavior (A, C, E). Incorporation of measured fiber orientations in the structural model did not predict the mechanical anisotropy of the UNIAX gels. Incorporation of remodeling strains and affine transformation in the structural model overpredicted the mechanical anisotropy of the UNIAX gels. Incorporation of nonaffine kinematics in the network model underpredicted the mechanical anisotropy of the UNIAX gels. (Note: The plotted stress is the second Piola-Kirchhoff stress and the plotted strain is the Lagrangian strain. Experimental data are presented as the average plus or minus standard deviation).

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