The Role of Fiber-Matrix Interactions in a Nonlinear Fiber-Reinforced Strain Energy Model of Tendon

[+] Author and Article Information
Heather Anne Guerin

Department of Mechanical Engineering and Applied MechanicsDepartment of Orthopaedic Surgery, McKay Orthopaedic Research Laboratory,  University of Pennsylvania, 424 Stemmler Hall, Philadelphia, PA 19104-6081

Dawn M. Elliott1

Department of Mechanical Engineering and Applied Mechanicsdelliott@mail.med.upenn.eduDepartment of Orthopaedic Surgery, McKay Orthopaedic Research Laboratory,  University of Pennsylvania, 424 Stemmler Hall, Philadelphia, PA 19104-6081delliott@mail.med.upenn.edu


Corresponding author.

J Biomech Eng 127(2), 345-350 (Nov 18, 2004) (6 pages) doi:10.1115/1.1865212 History: Received April 05, 2004; Revised November 18, 2004

The objective of this study was to develop a nonlinear and anisotropic three-dimensional mathematical model of tendon behavior in which the structural components of fibers, matrix, and fiber-matrix interactions are explicitly incorporated and to use this model to infer the contributions of these structures to tendon mechanical behavior. We hypothesized that this model would show that: (i) tendon mechanical behavior is not solely governed by the isotropic matrix and fiber stretch, but is also influenced by fiber-matrix interactions; and (ii) shear fiber-matrix interaction terms will better describe tendon mechanical behavior than bulk fiber-matrix interaction terms. Model versions that did and did not include fiber-matrix interaction terms were applied to experimental tendon stress-strain data in longitudinal and transverse orientations, and the R2 goodness-of-fit was evaluated. This study showed that models that included fiber-matrix interaction terms improved the fit to longitudinal data (RToe2=0.88,RLin2=0.94) over models that only included isotropic matrix and fiber stretch terms (RToe2=0.36,RLin2=0.84). Shear fiber-matrix interaction terms proved to be responsible for the best fit to data and to contribute to stress-strain nonlinearity. The mathematical model of tendon behavior developed in this study showed that fiber-matrix interactions are an important contributor to tendon behavior. The more complete characterization of mechanical behavior afforded by this mathematical model can lead to an improved understanding of structure-function relationships in soft tissues and, ultimately, to the development of tissue-engineered therapies for injury or degeneration.

Copyright © 2005 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Tendon orientation with respect to applied load and stress-free boundary conditions on unloaded faces for (a). longitudinal and (b). transverse orientations.

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Figure 2

Representative plots of Models A–F: (a) isotropic matrix and fiber stretch interactions included in both toe and linear region; (b) fiber stretch removed from toe region, (c) isotropic matrix removed from linear region, (d) bulk and shear fiber-matrix interactions included (as well as isotropic matrix and fiber stretch), (e) bulk fiber-matrix interactions included, (f) shear fiber-matrix interactions included (selected as best model) (∎: longitudinal toe- and linear-region experimental data; ●: transverse experimental data; solid line: longitudinal toe- and linear-region model fits; dotted line: transverse model fit)

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Figure 3

Representative plot of transverse experimental data and model fit (●: transverse data; line: transverse model fit)



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