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Effect of viscoelastic properties on passive torque variations at different velocities of the knee joint extension and flexion movements

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This study aimed to investigate the rate of passive torque variations of human knee joint in the different velocities of knee flexion and extension movements. Ten healthy men were invited to participate in the tests. All passive torque tests were performed for the knee joint extension and flexion on the sagittal plane in three different angular velocities of 15, 45, and 120°/s; in 5 consecutive cycles; and within 0° to 100° range of motion. The electrical activity of knee joint extensor and flexor muscles was recorded until there was no muscle activity signal. A Three-element Solid Model (SLS) was used to obtain the viscose and elastic coefficients. As the velocity increases, the stretch rate in velocity-independent tissues increases, and the stretch rate in velocity-dependent tissues decreases. By increasing the velocity, the resistance of velocity-dependent parts increases, and the velocity-independent parts are not affected by velocity. Since the first torque that resists the joint movement is passive torque, the elastic and viscous torques should be simultaneously used. It is better to perform the movement at a low velocity so that less energy is lost. The viscoelastic resistance of tissues diminishes.

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  1. Wikstrom EA, Tillman MD, Chmielewski TL, Borsa PA (2006) Measurement and evaluation of dynamic joint stability of the knee and ankle after injury. Sports Med 36(5):393–410.

    Article  PubMed  Google Scholar 

  2. Amankwah K, Triolo RJ, Kirsch R (2004) Effects of spinal cord injury on lower-limb passive joint moments revealed through a nonlinear viscoelastic model. J Rehabil Res Dev 41(1):15–32.

    Article  PubMed  Google Scholar 

  3. Fung YC (1993) Biomechanics: mechanical properties of living tissues, 2nd edn. Springer-Verlag, New York, pp 254–262 525–35

    Book  Google Scholar 

  4. Bennett DJ, Hollerbach JM, Xu Y, Hunter IW (1992) Time-varying stiffness of human elbow joint during cyclic voluntary movement. Exp Brain Res 88(2):433–442.

    Article  CAS  PubMed  Google Scholar 

  5. Wolbrecht E, Reinkensmeyer D, Bobrow J (2010) Pneumatic control of robots for rehabilitation. Int J Robot Res 29(1):23–38.

    Article  Google Scholar 

  6. Scarvell JM, Smith PN, Refshauge KM, Golloway H, Woods K (2005) Comparison of kinematics in the healthy and ACL injured knee using MRI. J Biomech 38(2):255–262.

    Article  PubMed  Google Scholar 

  7. Kondo E, Merican AM, Yasuda K, Amis AA (2014) Biomechanical analysis of knee laxity with isolated Anteromedial or Posterolateral bundle–deficient anterior cruciate ligament. J Arthrosc Relat Surg 30(3):335–343.

    Article  Google Scholar 

  8. Dejour D, Ntagiopoulos PG, Saggin PR, Panisset JC (2013) The diagnostic value of clinical tests, magnetic resonance imaging, and instrumented laxity in the differentiation of complete versus partial anterior cruciate ligament tears. J Arthrosc Relat Surg 29(3):491–499.

    Article  Google Scholar 

  9. Knutson JS, Kilgore KL, Mansour JM, Crago PE (2000) Intrinsic and extrinsic contributions to the passive moment at the metacarpophalangeal joint. J Biomech 33(12):1675–1681.

    Article  CAS  PubMed  Google Scholar 

  10. Beidokhti HN, Janssen D, van de Groes S, Verdonschot N (2018) The peripheral soft tissues should not be ignored in the finite element models of the human knee joint. Med Biol Eng Comput 56(7):1189–1199.

    Article  PubMed  Google Scholar 

  11. Gottlieb GL, Agarwal GC (1978) Dependence of human ankle compliance on joint angle. J Biomech 11(4):177–181.

    Article  CAS  PubMed  Google Scholar 

  12. Esteki A, Mansour JM (1996) An experimentally based nonlinear viscoelastic model of joint passive moment. J Biomech 29(4):443–450.

    Article  CAS  PubMed  Google Scholar 

  13. Silder A, Whittington B, Heiderscheit B (2007) Identification of passive elastic joint moment–angle relationships in the lower extremity. J Biomech 40(12):2628–2635.

    Article  PubMed  PubMed Central  Google Scholar 

  14. Piziali RL, Rastegar JC (1977) Measurement of the nonlinear, coupled stiffness characteristics of the human knee. J Biomech 10(1):45–51.

    Article  CAS  PubMed  Google Scholar 

  15. Meyer GA, McCulloch AD, Lieber RL (2011) A nonlinear model of passive muscle viscosity. J Biomech Eng 133(9):091007.

    Article  CAS  PubMed  Google Scholar 

  16. Nordez A, Casari P, Cornu C (2008) Effects of stretching velocity on passive resistance developed by the knee musculo-articular complex: contributions of frictional and viscoelastic behaviours. Eur J Appl Physiol 103(2):243–250.

    Article  CAS  PubMed  Google Scholar 

  17. Hatze H (1975) A new method for the simultaneous measurement of the movement of inertia, the damping coefficient and the location of the centre of mass of a body segment in situ. Eur J Appl Physiol Occup Physiol 34(4):217–226.

    Article  CAS  PubMed  Google Scholar 

  18. MG Pandy, JS Merritt, RE Barr (2009) Biomechanics of the musculoskeletal system. In: Myer Kutz, Biomedical Engineering and Design Handbook Volume I, Biomedical Engineering Fundamentals, 2d edition, McGraw Hill Professional, pp 125–194

  19. Long C, Thomas D, Crochetier WJ (1964) Objective measurement of muscle tone in the hand. Clin Pharmacol Ther 5(6 part2):909–917.

    Article  Google Scholar 

  20. Nordmark E, Andersson G (2002) Wartenberg pendulum test: objective quantification of muscle tone in children with spastic diplegia undergoing selective dorsal rhizotomy. Dev Med Child 44(1):26–33.

    Article  Google Scholar 

  21. Valle MS, Casabona A, Sgarlata R, Garozzo R, Vinci M, Cioni M (2006) The pendulum test as a tool to evaluate passive knee stiffness and viscosity of patients with rheumatoid arthritis. BMC Musculoskelet Disord 7(1):89.

    Article  PubMed  PubMed Central  Google Scholar 

  22. Vilimek M (2007) Musculotendon forces derived by different muscle models. Acta Bioeng Biomech 9(2):41–47 Wroclaw University of Technology

    PubMed  Google Scholar 

  23. Hill AV (1970) First and last experiments in muscle mechanics. Cambridge University Press

  24. Puttlitz CM, Shetye SS, Troyer KL (2015) Viscoelasticity of load-bearing soft tissues: constitutive formulation, numerical integration, and computational implementation. Comput Bioeng Chapter 5:95–122.

    Article  Google Scholar 

  25. Michael Lee (2006) Tissue Mechanics. Wiley encyclopedia of biomedical engineering, Wiley Online Library

  26. Haut RC (2002) Biomechanics of soft tissue. In: Accidental Injury, pp. 228–253

  27. Özkaya N, Goldsheyder D, Leger D, Nordin M (2012) Fundamentals of biomechanics: equilibrium, motion, and deformation, 3rd edn. Springer, Verlag.

    Book  Google Scholar 

  28. Toosizadeh N, Nussbaum MA (2013) Creep deformation of the human trunk in response to prolonged and repetitive flexion: measuring and modeling the effect of external moment and flexion rate. Ann Biomed Eng 41(6):1150–1161.

    Article  PubMed  Google Scholar 

  29. Vignes RM (2004) Modeling muscle fatigue in digital humans. University of Iowa

  30. Fung Y (1965) Foundations of solid mechanics. Prentice Hall

  31. Lee H-M, Huang Y-Z, Chen JJ, Hwang I-S (2002) Quantitative analysis of the velocity related pathophysiology of spasticity and rigidity in the elbow flexors. J Neurosurg Psychiatry 72(5):621–629.

    Article  Google Scholar 

  32. Prochazka A, Bennett DJ, Stephens J, Patrick SK (1997) Measurement of rigidity in Parkinson’s disease. Mov Disord 12(1):24–32.

    Article  CAS  PubMed  Google Scholar 

  33. Findley WN, Francis A (1976) Creep and relaxation of nonlinear viscoelastic materials with an introduction to linear viscoelasticity, 1st edn. Publishing, North-Holland

    Google Scholar 

  34. Hajrasouliha AR, Tavakoli S, Esteki A, Nafisi S, Noorolahi-Moghaddam H (2005) Abnormal viscoelastic behaviour of passive ankle joint movement in diabetic patients: an early or a late complication? Diabetologia 48(6):1225–1228.

    Article  CAS  PubMed  Google Scholar 

  35. Nordin M, Frankel VH (2012) Basic biomechanics of the musculoskeletal system, 4th edn. American edition, North

    Google Scholar 

  36. Lamontagne A, Malouin F, Richards CL, Dumas F (1997) Impaired viscoelastic behavior of spastic plantarflexors during passive stretch at different velocities. Clin Biomech 12:508–515.

    Article  Google Scholar 

  37. Lieber RL, Steinman S, Barash IA, Hank Chambers MD (2004) Structural and functional changes in spastic skeletal muscle. Muscle Nerve 29(5):615–627.

    Article  PubMed  Google Scholar 

  38. Given JD, Dewald JP, Rymer WZ (1995) Joint dependent passive stiffness in paretic and contralateral limbs of spastic patients with hemiparetic stroke. J Neurol Neurosurg Psychiatry 59:271–279.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  39. Lebiedowska MK, Fisk JR (2009) Knee resistance during passive stretch in patients with hypertonia. J Neurosci Methods 179(2):323–330.

    Article  PubMed  Google Scholar 

  40. Rehorn MR, Schroer AK, Blemker SS (2014) Passive properties of muscle fibers are velocity dependent. J Biomech 47(3):687–693.

    Article  PubMed  Google Scholar 

  41. Mahieu P, McNair MDM, Stevens V, Blanckaert I, Smits N, Witvrouw E (2007) Effect of static and ballistic stretching on the muscle-tendon tissue properties. Med Sci Sports Exerc 39(3):494–501.

    Article  PubMed  Google Scholar 

  42. De Lussanet MHE, Smeets JBJ, Brenner E (2002) Relative damping improves linear mass-spring models of goal-directed movements. Hum Mov Sci 21(1):85–100.

    Article  PubMed  Google Scholar 

  43. Bartoo ML, Linke WA, Pollack GH (1997) Basis of passive tension and stiffness in isolated rabbit myofibrils. Am J Phys 73:C266–C276.

    Article  Google Scholar 

  44. Ocarino JM, Fonseca ST, Silva PLP, Mancini MC, Gonçalves GGP (2008) Alterations of stiffness and resting position of the elbow joint following flexors resistance training. Man Ther 13(5):411–418.

    Article  PubMed  Google Scholar 

  45. Ashkani O, Maleki A, Jamshidi N (2017) Design, simulation and modelling of auxiliary exoskeleton to improve human gait cycle. Aust Phys Eng Sci Med 40(1):137–144.

    Article  CAS  Google Scholar 

  46. Lu T-W, Chang C-F (2012) Biomechanics of human movement and its clinical applications. Kaohsiung J Med Sci 28(2 Suppl):S13–S25.

    Article  PubMed  Google Scholar 

  47. Fan L, Yan L, Xiao J, Wang F (2017) Dynamics analysis and simulation verification of a novel knee joint exoskeleton. J Vibroeng 19(4):3008–3018.

    Article  Google Scholar 

  48. Blazevich AJ (2019) Adaptations in the passive mechanical properties of skeletal muscle to altered patterns of use. J Appl Physiol 126(5):1483–1491.

    Article  PubMed  Google Scholar 

  49. Kazemi M, Dabiri Y, Li LP (2013) Recent advances in computational mechanics of the human knee joint. Comput Math Methods Med 5:718423.

    Article  Google Scholar 

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Correspondence to Farhad Tabatabai Ghomsheh.

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Informed consent was obtained from all individual participants included in the study. This study has not been duplicate publication or submission elsewhere. The Local Ethics Committee approval was obtained. All authors confirm the consideration of ethical principles according to declaration of HELSINKI for submitted article.

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Amiri, M., Tabatabai Ghomsheh, F. & Ghazalian, F. Effect of viscoelastic properties on passive torque variations at different velocities of the knee joint extension and flexion movements. Med Biol Eng Comput 58, 2893–2903 (2020).

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