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Nonlinear Ligament Viscoelasticity

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Abstract

Ligaments display time-dependent behavior, characteristic of a viscoelastic solid, and are nonlinear in their stress–strain response. Recent experiments25 reveal that stress relaxation proceeds more rapidly than creep in medial collateral ligaments, a fact not explained by linear viscoelastic theory but shown by Lakes and Vanderby17 to be consistent with non-linear theory. This study tests the following hypothesis: non-linear viscoelasticity of ligament requires a description more general than the separable quasilinear viscoelasticity (QLV) formulation commonly used. The experimental test for this hypothesis involves performing both creep and relaxation studies at various loads and deformations below the damage threshold. Freshly harvested, rat medial collateral ligaments (MCLs) were used as a model. Results consistently show a nonlinear behavior in which the rate of creep is dependent upon stress level and the rate of relaxation is dependent upon strain level. Furthermore, relaxation proceeds faster than creep; consistent with the experimental observations of Thornton et al.25 The above results from rat MCLs are not consistent with a separable QLV theory. Inclusion of these nonlinearities would require a more general formulation. © 2001 Biomedical Engineering Society.

PAC01: 8719Rr, 8385St, 8360Df

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REFERENCES

  1. Ambrosio, L., R. De Santis., S. Iannace., P. A. Netti., and L. Nicolais. Viscoelastic behavior of composite ligament prostheses. J. Biomed. Mater. Res.42.:6–12., 1998.

    Google Scholar 

  2. Arms, S., J. Boyle., R. Johnson., and M. Pope. Strain measurements in the medial collateral ligament of the human knee: An autopsy study. J. Biomech.16.:491–496., 1983.

    Google Scholar 

  3. Atkinson, T. S., B. J. Ewers., and R. C. Haut. The tensile and stress relaxation responses of human patellar tendon varies with specimen cross-sectional area. J. Biomech.32.:907–914., 1999.

    Google Scholar 

  4. Atkinson, T. S., R. C. Haut, and N. J. Altiero. A microstructural poroelastic model for patellar tendon. Proc. ASME Bioeng. Conf. 35:573, 1997.

    Google Scholar 

  5. Best, T. M., J. McElhaney., W. E. Garret., and B. S. Myers. Characterization of the passive responses of live skeletal muscle using the quasilinear theory of viscoelasticity. J. Biomech.27.:413–419., 1994.

    Google Scholar 

  6. Chelikani, S., and M. M. Panjabi. Biomechanical symmetry of the rabbit ACL. Presented at the 19th Annual Meeting of the American Society of Biomechanics, Stanford University, Stanford, CA, 1995 (unpublished).

  7. Chimich, D., N. Shrive., C. Frank., L. Marchuk., and R. Bray. Water content alters viscoelastic behavior of the normal adolescent rabbit medial collateral ligament. J. Biomech.25.:831–837., 1992.

    Google Scholar 

  8. ntFung, 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. Prentice Hall, Englewood Cliffs, NJ: Prentice Hall, 1972.

    Google Scholar 

  9. Graf, B., R. Vanderby., M. Ulm., R. Rogalski., and R. Thielke. The effect of preconditioning on the viscoelastic response of primate patellar tendon. Arthroscopy.10.:90–96., 1994.

    Google Scholar 

  10. Hannafin, J. A., and S. P. Arnoczky. Effect of cyclic and static tensile loading on the water content and solute diffusion in canine flexor tendons: An in vitro. study. J. Orthop. Res.12.:350–356., 1994.

    Google Scholar 

  11. Haut, R. C., and R. W. Little. Rheological properties of canine anterior cruciate ligaments. J. Biomech.2.:289–298., 1969.

    Google Scholar 

  12. Haut, R. C., and R. W. Little. A constitutive equation for collagen fibers. J. Biomech.5.:423–430., 1972.

    Google Scholar 

  13. Hull, M. L., G. S. Berns., H. Varma., and H. A. Patterson. Strain in the medial collateral ligament of the human knee under single and combined loads. J. Biomech.2.:199–206., 1996.

    Google Scholar 

  14. Holden, J. P., E. S. Grood., D. L. Korvick., J. F. Cummings., D. L. Butler., and D. I. Bylski-Austrow. In vivo. forces in the anterior cruciate ligament: Direct measurements during walking and trotting in a quadraped. J. Biomech.27.:517–526., 1994.

    Google Scholar 

  15. Johnson, G. A., G. A. Livesay., S. L-Y. Woo., and K. R. Rajagopal. A single integral finite strain viscoelastic model of ligaments and tendons. ASME J. Biomech. Eng.118.:221–226., 1996.

    Google Scholar 

  16. King, G. J., P. Edwards., R. F. Brant., N. G. Shrive., and C. B. Frank. Intraoperative graft tensioning alters viscoelastic but not failure behaviors of rabbit medial collateral ligament autografts. J. Orthop. Res.13.:915–922., 1995.

    Google Scholar 

  17. Lakes, R. S., and R. Vanderby. Interrelation of creep and relaxation: A modeling approach for ligaments. ASME J. Biomech. Eng.121.:612–615., 1999.

    Google Scholar 

  18. Lakes, R. S., J. L. Katz., and S. S. Sternstein. Viscoelastic properties of wet cortical bone: Part I, torsional and biaxial studies. J. Biomech.12.:657–678., 1979.

    Google Scholar 

  19. Lakes, R. S., and J. L. Katz. Viscoelastic properties of wet cortical bone: Part III, a nonlinear constitutive equation. J. Biomech.12.:689–698., 1979.

    Google Scholar 

  20. Panjabi, M. M., P. Moy., T. R. Oxland., and J. Cholewicki. Subfailure injury affects the relaxation behavior of rabbit ACL. Clin. Biomech.14.:24–31., 1999.

    Google Scholar 

  21. Provenzano, P. P., D. Heisey, K. Haysashi, R. S. Lakes, and R. Vanderby, Jr. Subfailure damage in ligament: A structural and cellular evaluation. J. Appl. Physiol., in press.

  22. Rousseau, E. P. M., A. A. H. J. Sauren., M. C. van Hout., and A. A. van Steenhoven. Elastic and viscoelastic material behavior of fresh and glutaraldehyde fixed porcine aortic valve tissue. J. Biomech.16.:339–348., 1983.

    Google Scholar 

  23. Sauren, A. A. H. J., M. C. van Hout., A. A. van Steenhoven., F. E. Veldpaus., and J. D. Janssen. The mechanical properties of porcine aortic valve tissues. J. Biomech.16.:327–337., 1983.

    Google Scholar 

  24. Thielke, R. J., R. Vanderby, and E. S. Grood. Volumetric changes in ligaments under tension. Proc. ASME Bioeng. Conf. 29:197, 1995.

    Google Scholar 

  25. Thornton, G. M., A. Oliynyk., C. B. Frank., and N. G. Shrive. Ligament creep cannot be predicted from stress relaxation at low stress: A biomechanical study of the rabbit medial collateral ligament., J. Orthop. Res.15.:652–656., 1997.

    Google Scholar 

  26. Thornton, G. M., C. B. Frank., and N. G. Shrive. Ligament creep behavior can be predicted from stress relaxation by incorporating fiber recruitment. J. Rheol.45.:493–507., 2001.

    Google Scholar 

  27. Thornton, G. M., G. P. Leask., N. G. Shrive., and C. B. Frank. Early medial collateral ligament scars have inferior creep behavior. J. Orthop. Res.18.:238–246., 2000.

    Google Scholar 

  28. urner, S. Creep in glassy polymers. In: The Physics of Glassy Polymers, edited by R. H. Howard. New York: Wiley, 1973.

    Google Scholar 

  29. Viidi, A..A rheological model for uncalcified parallel-fibered collagenous tissue. J. Biomech.1.:3–11., 1968.

    Google Scholar 

  30. Viidik, A..Simultaneous mechanical and light microscopic studies of collagen fibers. Z. Anat. Entwick. Gesch.136.:204–212., 1972.

    Google Scholar 

  31. Woo, S. L-Y., M. A. Gomez., and W. H. Akeso. Quasilinear viscoelastic property of normal articular cartilage. J. Biomech. Eng.102.:85–90., 1980.

    Google Scholar 

  32. Woo, S. L-Y., M. A. Gomez., and W. H. Akeson. The time and history-dependent viscoelastic properties of the canine medial collateral ligament. J. Biomech. Eng.103.:293–298., 1981.

    Google Scholar 

  33. Woo, S. L-Y..Mechanical properties of tendons and ligaments. I. Quasistatic and nonlinear viscoelastic properties. Biorheology.19.:385–396., 1982.

    Google Scholar 

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Authors and Affiliations

  1. Department of Biomedical Engineering and Division of Orthopedic Surgery, University of Wisconsin–Madison, Madison, WI

    Paolo Provenzano, Thomas Keenan & Ray vanderby Jr

  2. Department of Biomedical Engineering and Department of Engineering Physics, University of Wisconsin–Madison, Madison, WI

    Roderic Lakes

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  1. Paolo Provenzano
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  2. Roderic Lakes
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  3. Thomas Keenan
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  4. Ray vanderby Jr
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Provenzano, P., Lakes, R., Keenan, T. et al. Nonlinear Ligament Viscoelasticity. Annals of Biomedical Engineering 29, 908–914 (2001). https://doi.org/10.1114/1.1408926

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