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Viscoelastic Relaxation and Recovery of Tendon

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Abstract

Tendons exhibit complex viscoelastic behaviors during relaxation and recovery. Recovery is critical to predicting behavior in subsequent loading, yet is not well studied. Our goal is to explore time-dependent recovery of these tendons after loading. As a prerequisite, their strain-dependent viscoelastic behaviors during relaxation were also characterized. The porcine digital flexor tendon was used as a model of tendon behavior. Strain-dependent relaxation was observed in tests at 1, 2, 3, 4, 5, and 6% strain. Recovery behavior of the tendon was examined by performing relaxation tests at 6%, then dropping to a low but nonzero strain level. Results show that the rate of relaxation in tendon is indeed a function of strain. Unlike previously reported tests on the medial collateral ligament (MCL), the relaxation rate of tendons increased with increased levels of strain. This strain-dependent relaxation contrasts with quasilinear viscoelasticity (QLV), which predicts equal time dependence across various strains. Also, the tendons did not recover to predicted levels by nonlinear superposition models or QLV, though they did recover partially. This recovery behavior and behavior during subsequent loadings will then become problematic for both quasilinear and nonlinear models to correctly predict.

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References

  1. Batson, EL, RJ Paramour, TJ Smith, HL Birch, JC Patterson-Kane, AE Goodship. Are the material properties and matrix composition of equine flexor and extensor tendons determined by their functions? Equine Vet. J. 35(3): 314-318, 2003. doi:10.2746/042516403776148327.

    Article  PubMed  CAS  Google Scholar 

  2. Bonifasi-Lista, C, SP Lake, MS Small, JA Weiss. Viscoelastic properties of the human medial collateral ligament under longitudinal, transverse, and shear loading. J. Orthop. Res. 23: 67-76, 2005. doi:10.1016/j.orthres.2004.06.002.

    Article  PubMed  Google Scholar 

  3. Boyce, BL, RE Jones, TD Nguyen, JM Grazier. Stress-controlled viscoelastic tensile response of bovine cornea. J. Biomech. 40: 2367-2376, 2007. doi:10.1016/j.jbiomech.2006.12.001.

    Article  PubMed  CAS  Google Scholar 

  4. Cheng, T and RZ Gan. Mechanical properties of stapedial tendon in human middle ear. J. Biomech. Eng. 129: 913-918, 2007. doi:10.1115/1.2800837.

    Article  PubMed  Google Scholar 

  5. Ciarletta, P, S Micera, D Accoto, P Dario. A novel microstructural approach in tendon viscoelastic modeling at the fibrillar level. J. Biomech. 39: 2034-2042, 2006. doi:10.1016/j.jbiomech.2005.06.025.

    Article  PubMed  CAS  Google Scholar 

  6. Crisco, J, S Chelikani, R Brown, S Wolfe. The effect of exercise on ligamentous stiffness of the wrist. J. Hand Surg. 22A: 44-48, 1997.

    Google Scholar 

  7. Doehring, TC, AD Freed, EO Carew, I Vesely. Fractional order viscoelasticity of the aortic valve cusp: an alternative to quasilinear viscoelasticity. J. Biomech. Eng. 127(4): 700-708, 2005. doi:10.1115/1.1933900.

    Article  PubMed  Google Scholar 

  8. Eckstrom, L, A Kaigle, E Hult, S Holm, M Rostgat, T Hansson. Intervertebral disc response to cyclic loading: an animal model. Proc. Inst. Mech. Eng. 210:249-258, 1996. doi:10.1243/PIME_PROC_1996_210_421_02.

    Google Scholar 

  9. Elliot, DM, PS Robinson, JA Gimbel, JJ Sarver, JA Abboud, RV Iozzo, LJ Soslowsky. Effect of altered matrix proteins on quasilinear viscoelastic properties in transgenic mouse tail tendons. Ann. Biomed. Eng. 31: 599-605, 2003. doi:10.1114/1.1567282.

    Article  Google Scholar 

  10. Gedalia, U, M Solomonow, B Zhou, R Baratta, Y Lu, M Harris. Biomechanics of increased exposure to lumbar injury caused by cyclic loading II: recovery of reflexive muscular stability with rest. Spine 24(23): 2461-2467, 1999. doi:10.1097/00007632-199912010-00007.

    Article  PubMed  CAS  Google Scholar 

  11. Graf, BK, R Vanderby, MJ Ulm, RP Rogalski, RJ Thielke. Effect of preconditioning on the viscoelastic response of primate patellar tendon. Arthroscopy 10(1):90-96, 1994.

    Article  PubMed  CAS  Google Scholar 

  12. Han, S, SJ Gemmell, KG Helmer, P Grigg, JW Wellen, AH Hoffman, CH Sotak. Changes in ADC caused by tensile loading of rabbit achilles tendon: evidence for water transport. J. Mag. Reson. 144: 217-227, 2000. doi:10.1006/jmre.2000.2075.

    Article  CAS  Google Scholar 

  13. Hingorani, RV, PP Provenzano, RS Lakes, A Escarcega, R Vanderby. Nonlinear viscoelasticity in rabbit medical collateral ligament. Ann. Biomed. Eng. 32(2): 306-312, 2004. doi:10.1023/B:ABME.0000012751.31686.70.

    Article  PubMed  Google Scholar 

  14. Hirpara, KM, PJ Sullivan, ME O’Sullivan. The effects of freezing on the tensile properties of repaired porcine flexor tendon. J. Hand Surg. 33A: 353-358, 2008. doi:10.1016/j.jhsa.2007.12.011.

    Google Scholar 

  15. Lakes, R. S. Viscoelastic Materials. Cambridge: Cambridge University Press, 2009

  16. Lakes, RS, and R Vanderby. Interrelation of creep and relaxation: a modeling approach for ligaments. J. Biomech. Eng. 121: 612-615, 1999. doi:10.1115/1.2800861.

    Article  PubMed  CAS  Google Scholar 

  17. Ledoux, WR, DF Meaney, HJ Hillstrom. A quasi-linear, viscoelastic, structural model of the plantar soft tissue with frequency-sensitive damping properties. J. Biomech. Eng. 126(6): 831-837, 2004. doi:10.1115/1.1824133.

    Article  PubMed  Google Scholar 

  18. Lieber, RL, ME Leonard, CG Brown, CL Trestik. Frog semitendinosis tendon load-strain and stress-strain properties during passive loading. Am. J. Phys. 261: C86-C92, 1991.

    CAS  Google Scholar 

  19. Lin, Y, GH Koenderink, FC MacKintosh, DA Weitz. Viscoelastic properties of microtubules. Macromolecules 40(21): 7714-7720, 2007. doi:10.1021/ma070862l.

    Article  CAS  Google Scholar 

  20. Magnusson, SP, P Aagaard, JJ Nielson. Passive energy return after repeated stretches of the hamstring muscle-tendon unit. Med. Sci. Sports Exerc. 32(6): 1160-1164, 2002. doi:10.1097/00005768-200006000-00020.

    Google Scholar 

  21. McGill, S, and S Brown. Creep response of lumbar spine to prolonged full flexion. Clin. Biomech. 7:43-46, 1992. doi:10.1016/0268-0033(92)90007-Q.

    Article  Google Scholar 

  22. Moon, DK, SL Woo, Y Takakura, MT Gabriel, SD Abramowitch. The effects of refreezing on the viscoelastic and tensile properties of ligaments. J. Biomech. 39: 1153-1157, 2006. doi:10.1016/j.jbiomech.2005.02.012.

    Article  PubMed  Google Scholar 

  23. Mow, VC, AF Mak, WM Lai, LC Rosenberg, LH Tang. Viscoelastic properties of proteoglycan subunits and aggregates in varying solution concentrations. J. Biomech. 17(5): 325-38, 1984. doi:10.1016/0021-9290(84)90027-7.

    Article  PubMed  CAS  Google Scholar 

  24. Mow, VC, W Zhu, WM Lai, TE Hardingham, C Hughes, H Muir. The influence of link protein stabilization on the viscometric properties of proteoglycan aggregate solutions. Biochim Biophys Acta 992(2): 201-208, 1989.

    PubMed  CAS  Google Scholar 

  25. Navajas, D, GN Maksym, JHT Bates. Dynamic viscoelastic nonlinearity of lung parenchymal tissue. J. Appl. Physiol. 79(1): 348-356, 1995.

    PubMed  CAS  Google Scholar 

  26. Nekouzadeh, A, KM Pryse, EL Elson, GM Genin. A simplified approach to quasilinear viscoelastic modeling. J. Biomech. 40(14): 3070-3078, 2007. doi:10.1016/j.jbiomech.2007.03.019.

    Article  PubMed  Google Scholar 

  27. Oza, A, R Vanderby, RS Lakes. Interrelation of creep and relaxation for nonlinearly viscoelastic materials: application to ligament and metal. Rheol. Acta 42: 557-568, 2003. doi:10.1007/s00397-003-0312-0.

    Article  CAS  Google Scholar 

  28. Provenzano, P, D Heisey, K Hayashi, R Lakes, R Vanderby. Subfailure damage in ligament: a structural and cellular evaluation. J. Appl. Phys. 92: 362-371, 2002.

    Google Scholar 

  29. Provenzano, P, R Lakes, T Keenan, R Vanderby. Nonlinear ligament viscoelasticity. Ann. Biomed. Eng. 29: 908-914, 2001. doi:10.1114/1.1408926.

    Article  PubMed  CAS  Google Scholar 

  30. Rumian, AP, AL Wallace, HL Birch. Tendons and ligaments are anatomically distinct but overlap in molecular and morphological features – a comparative study in an ovine model. J. Orthop. Res. 25(4): 458-464, 2007. doi:10.1002/jor.20218.

    Article  PubMed  CAS  Google Scholar 

  31. Shadwick, RE. Elastic energy storage in tendons: mechanical differences related to function and age. J. Appl. Physiol. 68(3): 1033-1040, 1990. doi:10.1063/1.346741.

    Article  PubMed  CAS  Google Scholar 

  32. Solomonow, M, BH Zhou, RV Baratta, Y Lu, M Zhu, M Harris. Biexponential recovery model of lumbar viscoelasticity and reflexive muscular activity after prolonged cyclic loading. Clin. Biomech. 15:167-175, 2000. doi:10.1016/S0268-0033(99)00062-5.

    Article  CAS  Google Scholar 

  33. Sverdlik, A. and Y Lanir. Time-dependent mechanical behavior of sheep digital tendons, including the effects of preconditioning. J. Biomech. Eng. 124: 78-84, 2002. doi:10.1115/1.1427699.

    Article  PubMed  CAS  Google Scholar 

  34. van Dommelen, JAW, MM Jolandan, BJ Ivarsson, SA Millington, M Raut, JR Kerrigan, JR Crandall, DR Diduch. Nonlinear viscoelastic behavior of human knee ligaments subjected to complex loading histories. Ann. Biomed. Eng. 34(6):1008-1018, 2006. doi:10.1007/s10439-006-9100-1.

    Article  PubMed  Google Scholar 

  35. Woo, SL-Y, MA Gomez, WH Akeson. The time and history dependent viscoelastic properties of the canine medial collateral ligament. J. Biomech. Eng 103: 293-298, 1981.

    Article  PubMed  CAS  Google Scholar 

  36. Yang, W, TC Fung, KS Chian, CK Chong. Viscoelasticity of esophageal tissue and application of QLV model. J. Biomech. Eng. 128(6): 909-916, 2006. doi:10.1115/1.2372473.

    Article  PubMed  CAS  Google Scholar 

  37. Zhang, C, and ID Moore. Nonlinear mechanical response of high density polyethylene. Part 1: experimental investigation and model evaluation. Polym. Eng. Sci. 37(2): 404-413, 1997. doi:10.1002/pen.11683.

    Article  CAS  Google Scholar 

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Acknowledgments

This work was funded by NSF award 0553016. The authors thank Ron McCabe for his technical assistance.

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Correspondence to Roderic S. Lakes.

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Duenwald, S.E., Vanderby, R. & Lakes, R.S. Viscoelastic Relaxation and Recovery of Tendon. Ann Biomed Eng 37, 1131–1140 (2009). https://doi.org/10.1007/s10439-009-9687-0

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  • DOI: https://doi.org/10.1007/s10439-009-9687-0

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