Incorporation of Experimentally-Derived Fiber Orientation into a Structural Constitutive Model for Planar Collagenous Tissues

[+] Author and Article Information
Michael S. Sacks

Engineered Tissue Mechanics Laboratory, Department of Bioengineering, University of Pittsburgh, Pittsburg, PA 15261e-mail: msacks@pitt.edu

J Biomech Eng 125(2), 280-287 (Apr 09, 2003) (8 pages) doi:10.1115/1.1544508 History: Received September 01, 2001; Revised October 01, 2002; Online April 09, 2003
Copyright © 2003 by ASME
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(a) The fiber angular distribution R(θ) for native bovine pericardium from one specimen demonstrating the structural regularity, as indicated by relatively small variations R(θ) (error bars=1 standard error). (b) R(θ) results from another specimen at the reference state (undeformed) and after 15 percent equibiaxial strain, demonstrating little change. These results indicates that collagen crimp effects were negligible for determining R(θ). Also shown is the R(θ) results for the aortic valve, which by comparison is leptokurtic.
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Optical microscope images of native bovine pericardium showing the crimp at (a) reference and (b) 15 percent equibiaxial strain at approximately the same location in the tissue, demonstrating an increase in crimp period
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A representative example of the effective fiber stress-strain curve, along with the fit of the two-parameter fiber stress-strain law (Eq. 4), demonstrating an excellent fit
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(a) The effective fiber stress-strain curve Sf using fiber recruitment model (Eq. (5)), along with the fiber recruitment function D(ε). Both mean specimen and group results are shown. Note the close correlation between the group and individual specimen means, indicating low inter-specimen variations
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The “group” cumulative recruitment function F(ε), which predicted that at a Green-Lagrange strain of 0.16, ∼22 percent of all fibers bear load.
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An example of the structural model fit to the biaxial mechanical data for native pericardium, demonstrating an excellent fit. Note that only data from the equibiaxial test was utilized to determine form of the fiber stress-strain curve. Fit to the non-equibiaxial data demonstrates the predictive capabilities of the structural model. Labels indicate E11:E22 ratios for each protocol. Inset: biaxial strains for each protocol with the labels indicating the E11:E22 ratio.
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Graphical depictions of how the beta distribution was used to evaluate the sensitivity of the structural model objective function to R(θ). Specifically, both the mean (a) and variance (b) were varied, resulting the MSE distribution (in units of kPa2 ) shown in (c). Symbols in (a) and (b) indicate the distribution for R(θ) for native pericardium, and the dot in (c) indicates the location of the optimal (minimum) value. Overall, the structural model was more sensitive to variations in σ than for μ, underscoring the need for accurate determination of fiber angular dispersion.




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