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Research Papers

Planar Biaxial Mechanical Behavior of Bioartificial Tissues Possessing Prescribed Fiber Alignment

[+] Author and Article Information
Choon-Sik Jhun, Victor H. Barocas

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

Michael C. Evans

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

Robert T. Tranquillo1

Department of Biomedical Engineering, and Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455tranquillo@cems.umn.edu

1

Corresponding author.

J Biomech Eng 131(8), 081006 (Jul 02, 2009) (8 pages) doi:10.1115/1.3148194 History: Received February 22, 2008; Revised October 03, 2008; Published July 02, 2009

Though it is widely accepted that fiber alignment has a great influence on the mechanical anisotropy of tissues, a systematic study of the influence of fiber alignment on the macroscopic mechanical behavior by native tissues is precluded due to their predefined microstructure and heterogeneity. Such a study is possible using collagen-based bioartificial tissues that allow for alignment to be prescribed during their fabrication. To generate a systemic variation of strength of fiber alignment, we made cruciform tissue constructs in Teflon molds that had arms of different aspect ratios. We implemented our anisotropic biphasic theory of tissue-equivalent mechanics to simulate the compaction by finite element analysis. Prior to tensile testing, the construct geometry was standardized by cutting test samples with a 1:1 cruciform punch after releasing constructs from the molds. Planar biaxial testing was performed on these samples, after stretching them to their in-mold dimensions to recover in-mold alignment, to observe the macroscopic mechanical response with simultaneous fiber alignment imaging using a polarimetry system. We found that the strength of fiber alignment of the samples prior to release from the molds linearly increased with anisotropy of the mold. In testing after release, modulus ratio (modulus in fiber direction/modulus in normal direction) was greater as the initial strength of fiber alignment increased, that is, as the aspect ratio increased. We also found that the fiber alignment strength and modulus ratio increased in a hyperbolic fashion with stretching for a sample of given aspect ratio.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 5

Modulus versus stretch ratio plots show stiffening in both axes for all AR, but with unexpected trends (see text)

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Figure 6

Modulus ratio versus stretch ratio plots show increasing mechanical anisotropy and alignment with higher aspect ratio. The fiber alignment strength (average birefringence) also exhibits hyperbolic increase with stretch ratio in the cases where AR>1.

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Figure 7

Dependence of sensitivity of mechanical anisotropy relative to microstructural anisotropy on stretch ratio, showing the sensitivity is greater for the more aligned sample (AR=1:0.375) and also decreases with stretch ratio. Values were derived from derivatives of cubic polynomial fits to the data in Fig. 6. Differences between AR=1:0.5 and 1:0.375 are statistically significant for λ=1.00–1.03.

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Figure 8

Stretch ratios and fibril alignment strength possess a complex relationship in the cases where AR>1, particularly in the unstretching phase: (a) AR=1:1, (b) AR=1:0.5, and (c) AR=1:0.375

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Figure 4

Stress versus stretch ratio plots show stiffening and increasing mechanical anisotropy with stretching for AR>1

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Figure 3

(a) The strength of fiber alignment linearly increased with mold aspect ratio (i.e., with 1/Wn). The average value of the birefringence ⟨Δn⟩ within the central region prior to sample release is plotted. (b) ABT-based FEM simulation of compaction and alignment of cruciform-shaped tissue constructs predicts the observed dependence of strength of fiber alignment linearly increasing with mold aspect ratio (1/Wn). The average value of the principal eigenvalue within the central region is plotted.

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Figure 2

Cruciform-shaped Teflon molds with bioartificial tissue constructs possess alignment that varies with arm dimensions. ((a1) and (b1)) AR=1:1, ((a2) and (b2)) 1:0.75, ((a3) and (b3)) 1:0.5, ((a4) and (b4)) 1:0.375, and ((a5) and (b5)) 1:0.25: (a) photographs; (b) alignment maps, where each segment indicates the local-average direction and strength of fiber alignment and the gray level is mapped to the local alignment strength (i.e., pixelwise retardation), with white being maximum and black minimum alignment. Stronger alignment in the direction of the wider arm is evident as the other arm becomes thinner. ABT-based FEM simulation of compaction and alignment of cruciform tissue constructs predicts observed dependence on cruciform mold arm dimensions. The fiber direction and strength of fiber alignment are represented by eigenvectors and magnitude of eigenvalues, respectively, of the fiber orientation tensor in ((c1)–(c5)).

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Figure 1

Image of test sample, following punching to AR=1:1 from a retracted cruciform construct, mounting for biaxial mechanical testing, and stretching back to in-mold dimensions. Custom adjustable compressive grips especially designed for small-dimension cruciform constructs were attached to the ends of each actuator. The four dots at the center of the specimen were made with Voerhoff’s stain after mounting and stretching to track the local strain. The four dots visible at the corners, which were in the central region prior to punching the AR=1:1 test sample, were made prior to release from the mold and retraction to track local retraction. Another (third) set of dots no longer visible after punching the test sample from was marked near the Velcro at each arm prior release from the mold and used to measure global retraction.

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