Abstract
Paired incremental uniaxial step (i.e., relaxation) and ramp tests were conducted simultaneously on four (nominally) identical samples of type I collagen gel, over a direct strain range 0 < ɛ < 0.2. The paired step and ramp responses could not both be predicted by a simple viscoelastic constitutive relation (either linear or Fung-type), but could be predicted reasonably accurately by a general nonlinear viscoelastic relation with a strain-dependent relaxation spectrum, of the form \(\sigma (t){} = \int {_{ - \infty}^t g(t - \tau ;\varepsilon )} [d\varepsilon (\tau )/d\tau ]d\tau .\) Based on a four-term exponential-series approximation, we measured the stiffness moduli and time constants of the relaxation function, g(t,\varepsilon ), for the four gel samples that we tested, and found that the time constants were independent of strain but the moduli increased strongly with strain. Further, we found that the time constants did not vary across the four gels, but the moduli varied by a factor of about 2 across the gels. Some additional tests show features of the response of collagen gels to cycles of application and removal of loading. © 2003 Biomedical Engineering Society.
PAC2003: 8380Kn, 8270Gg, 8715La
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References
Alberts, B., D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson, Molecular Biology of the Cell, 3rd ed. New York: Garland, 1994.
Birk, D. E., E. I. Zycband, S. Woodruff, D. A. Winkelmann, and R. L. Trelstad. Collagen fibrillogenesis: Fibril segments become long fibrils as the developing tendon matures. Dev. Dyn. 208:291–298, 1997.
Brightman, A. O., B. P. Rajwa, J. E. Sturgis, M. E. McCallister, J. P. Robinson, and S. L. Voytik-Harbin. Time-lapse confocal reflection microscopy of collagen fibrillogenesis and extracellular matrix assembly. Biopolymers54:222–234, 2000.
Christiansen, D. L., E. K. Huang, and F. H. Silver. Assembly of type I collagen: Fusion of fibril subunits and the influence of fibril diameter on mechanical properties. Matrix Biol. 19:409–420, 2000.
Fung, Y. C. Stress-strain-history relations of soft tissues in simple elongation. In: Biomechanics: Its Foundations and Objectives, edited by Y. C. Fung, N. Perrone, and M. Anliker. Englewood Cliffs, NJ: Prentice-Hall, 1972.
Fung, Y. C. Biomechanics: Mechanical Properties of Living Tissues, 2nd. ed. New York: Springer, 1993.
Kolodney, M. S., and E. L. Elson. Correlation of myosin light chain phosphorylation with isometric contraction of fibroblasts. J. Biol. Chem. 268:23850–23855, 1993.
Ozerdem, B., and A. Tozeren. Physical response of collagen gels to tensile strain. J. Biomech. Eng. 117:397–401, 1995.
Parsons, J. W., and R. N. Coger. A new device for measuring the viscoelastic properties of hydrated matrix gels. J. Biomech. Eng. 124:145–154, 2002.
Pins, G. D., D. L. Christiansen, R. Patel, and F. H. Silver. Self-assembly of collagen fibers. Influence of fibrillar alignment and decorin on mechanical properties. Biophys. J. 73:2164–2172, 1997.
Roeder, B. A., K. Kokini, J. E. Sturgis, J. P. Robinson, and S. L. Voytik-Harbin. Tensile mechanical properties of three-dimensional type I collagen extracellular matrices with varied microstructure. J. Biomech. Eng. 124:214–222, 2002.
Setton, L. A., W. Zhu, and V. C. Mow. The biphasic poroviscoelastic behavior of articular cartilage: Role of the surface zone in governing the compressive behavior. J. Biomech. 26:581–592, 1993.
Silver, F. H., D. L. Christiansen, P. B. Snowhill, and Y. Chen. Transition from viscous to elastic-based dependency of mechanical properties of self-assembled type I collagen fibers. J. Appl. Polym. Sci. 79:134–142, 2000.
Wagenseil, J. E., T. Wakatsuki, R. J. Okamoto, G. I. Zahalak, and E. L. Elson. One-dimensional viscoelastic behavior of fibroblast-populated collagen matrices. (in press).
Wakatsuki, T., M. S. Kolodney, G. I. Zahalak, and E. L. Elson. Cell mechanics studied by a reconstituted model tissue. Biophys. J. 79:2353–2368, 2000.
Zahalak, G. I., J. E. Wagenseil, T. Wakatsuki, and E. L. Elson. A cell-based constitutive relation for bio-artificial tissues. Biophys. J. 79:2369–2381, 2000.
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Pryse, K.M., Nekouzadeh, A., Genin, G.M. et al. Incremental Mechanics of Collagen Gels: New Experiments and a New Viscoelastic Model. Annals of Biomedical Engineering 31, 1287–1296 (2003). https://doi.org/10.1114/1.1615571
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DOI: https://doi.org/10.1114/1.1615571