Skeletal muscle contraction in protecting joints and bones by absorbing mechanical impacts


We have previously hypothesized that the dissipation of mechanical energy of external impact is a fundamental function of skeletal muscle in addition to its primary function to convert chemical energy into mechanical energy. In this paper, a mathematical justification of this hypothesis is presented. First, a simple mechanical model, in which the muscle is considered as a simple Hookean spring, is considered. This analysis serves as an introduction to the consideration of a biomechanical model taking into account the molecular mechanism of muscle contraction, kinetics of myosin bridges, sarcomere dynamics, and tension of muscle fibers. It is shown that a muscle behaves like a nonlinear and adaptive spring tempering the force of impact and increasing the duration of the collision. The temporal profiles of muscle reaction to the impact as functions of the levels of muscle contraction, durations of the impact front, and the time constants of myosin bridges closing, are obtained. The absorption of mechanical shock energy is achieved due to the increased viscoelasticity of the contracting skeletal muscle. Controlling the contraction level allows for the optimization of the stiffness and viscosity of the muscle necessary for the protection of the joints and bones.

This is a preview of subscription content, log in to check access.


  1. 1.

    A. Sarvazyan, O. V. Rudenko, S. Aglyamov, and S. Emelianov, Med. Hypotheses 83, 6 (2014).

    Article  Google Scholar 

  2. 2.

    O. V. Rudenko and A. P. Sarvazyan, Acoust. Phys. 60, 710 (2014).

    ADS  Article  Google Scholar 

  3. 3.

    A. Sarvazyan, in Handbook of Elastic Properties of Solids, Liquids and Gases, Vol. 3. Elastic Properties of Solids: Theory, Elements and Compounds, Novel Materials, echnological Materials, Alloys, and Building Materials, Ed. by M. Levy, H. E. Bass, R.R. Stern, and V. Keppens, (Academic, 2001), Ch. 5, pp. 107–127.

  4. 4.

    A. P. Sarvazyan and C. R. Hill, in Physical Principles of Medical Ultrasonics. Ed. by C. R. Hill, J. C. Bamber, and G. R. TerHaar (Wiley, 2004), Ch. 7, pp. 223–235.

  5. 5.

    E. L. Madsen, H.J. Sathoff, and J. A. Zagzebski, J. Acoust. Soc. Am., 74, 1346 (1983).

    ADS  Article  Google Scholar 

  6. 6.

    T. A. Krouskop, D. R. Dougherty, and F. S. Vinson, J. Rehabil. Res. Dev. 24, 1 (1987).

    Google Scholar 

  7. 7.

    S. F. Levinson, M. Shinagawa, and T. Sato, J. Biomech. 28, 1145 (1995).

    Article  Google Scholar 

  8. 8.

    E. J. Chen, J. Novakofski, W. K. Jenkins, and W. D. O’Brien, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42, 191 (1996).

    Article  Google Scholar 

  9. 9.

    J. R. Basford, T. R. Jenkyn, A. Kai-Nan, R. L. Ehman, G. Heers, and K. R. Kaufman, Arch. Phys. Med. Rehabil. 83, 1530 (2002).

    Article  Google Scholar 

  10. 10.

    S. I. Ringleb, S. F. Bensamoun, Q. Chen, A. Manduca, K. N. An, and R. L. Ehman, J. Magn. Reson. Imaging 25, 301 (2007).

    Article  Google Scholar 

  11. 11.

    K. Hoyt, T. Kneezel, B. Castaneda, and K. J. Parker, Phys. Med. Biol. 53, 4063 (2008).

    Article  Google Scholar 

  12. 12.

    S. Chen, M. W. Urban, C. Pislaru, R. Kinnick, Y. Zheng, A. Yao, and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 55 (2009).

    Article  Google Scholar 

  13. 13.

    M. W. Urban and J. F. Greenleaf, Phys. Med. Biol. 54, 5919 (2009).

    Article  Google Scholar 

  14. 14.

    M. W. Urban, S. Chen, and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 748 (2009).

    Article  Google Scholar 

  15. 15.

    T. Deffieux, G. Montaldo, M. Tanter, and M. Fink, IEEE Trans. Med. Imaging 28, 313 (2009).

    Article  Google Scholar 

  16. 16.

    D. Klatt, S. Papazoglou, J. Braun, and I. Sack, Phys. Med. Biol. 55, 6445 (2010).

    Article  Google Scholar 

  17. 17.

    J.-L. Gennisson, T. Deffieux, E. Macé, G. Montaldo, M. Fink, and M. Tanter, Ultrasound Med. Biol. 36, 789 (2010).

    Article  Google Scholar 

  18. 18.

    T. Muraki, Z. J. Domire, M. B. McCullough, Q. Chen, and K. N. An, Clin. Biomech. 25, 499 (2010).

    Article  Google Scholar 

  19. 19.

    P. Song, S. Chen, Q. Chen, J. F. Greenleaf, and K. N. An, J. Biomech. 46, 2381 (2013).

    Article  Google Scholar 

  20. 20.

    L. Debernard, G.E. Leclerc, L. Robert, and S. F. Bensamoun, J. Musculoskelet Res. 16, 1350008 (2013).

    Article  Google Scholar 

  21. 21.

    M. Shinohara, K. Sabra, J. L. Gennisson, M. Fink, and M. Tanter, Muscle Nerve 42, 438 (2010).

    Article  Google Scholar 

  22. 22.

    G. Dubois, W. Kheireddine, C. Vergari, D. Bonneau, P. Thoreux, P. Rouch, M. Tanter, J. L. Gennisson, and W. Skalli, Ultrasound Med. Biol. 41, 2284 (2015).

    Article  Google Scholar 

  23. 23.

    A. Sarvazyan, T. J. Hall, M. W. Urban, M. Fatemi, S. R. Aglyamov, and B. Garra, Curr. Med. Imaging Rev. 7, 255 (2011).

    Article  Google Scholar 

  24. 24.

    K. Uffmann, S. Maderwald, W. Ajaj, C. G. Galban, S. Mateiescu, H. H. Quick, and M. E. Ladd, NMR Biomed. 17, 181 (2004).

    Article  Google Scholar 

  25. 25.

    S. F. Bensamoun, K. J. Glaser, S. I. Ringleb, Q. Chen, R. L. Ehman, and K. N. An, J. Magn. Reson. Imaging 27, 1083 (2008).

    Article  Google Scholar 

  26. 26.

    J. L. Gennisson, C. Cornu, S. Catheline, M. Fink, and P. Portero, J. Biomech. 38, 1543 (2005).

    Article  Google Scholar 

  27. 27.

    L. A. Chernak, R. J. DeWall, K. S. Lee, and D. G. Thelen, Physiol. Measur. 34, 713 (2013).

    ADS  Article  Google Scholar 

  28. 28.

    S. Chatelin, J. L. Gennisson, M. Bernal, M. Tanter, and M. Pernot, Phys. Med. Biol. 60, 3639 (2015).

    Article  Google Scholar 

  29. 29.

    A. Martin, B. Morlon, M. Pousson, and J. van Hoecke, Eur. J. Appl. Physiol. Occup. Physiol. 73, 157 (1996).

    Article  Google Scholar 

  30. 30.

    S. Sikdar, Q. Wei, and N. Cortes, Exerc. Sport Sci. Rev. 42, 126 (2014).

    Article  Google Scholar 

  31. 31.

    J. J. Ballyns, D. Turo, P. Otto, J. P. Shah, J. Hammond, T. Gebreab, L. H. Gerber, and S. Sikdar, J. Ultrasound Med. 31, 1209 (2012).

    Google Scholar 

  32. 32.

    S. Papazoglou, J. Braun, U. Hamhaber, and I. Sack, Phys. Med. Biol. 50, 1313 (2005).

    Article  Google Scholar 

  33. 33.

    M. Wang, B. Byram, M. Palmeri, N. Rouze, and K. Nightingale, IEEE Trans. Med. Imag. 32, 1671 (2013).

    Article  Google Scholar 

  34. 34.

    O. V. Rudenko and A. P. Sarvazyan, Acoust. Phys. 52, 720 (2006).

    ADS  Article  Google Scholar 

  35. 35.

    D. Royer, J. L. Gennisson, T. Deffieux, and M. Tanter, J. Acoust. Soc. Am. 129, 2757 (2011).

    ADS  Article  Google Scholar 

  36. 36.

    J. Brum, M. Bernal, J. L. Gennisson, and M. Tanter, Phys. Med. Biol. 59, 505 (2014).

    Article  Google Scholar 

  37. 37.

    A. F. Huxley, Proc. R. Soc. Biol. 178, 1 (1971).

    ADS  Article  Google Scholar 

  38. 38.

    D. T. Kirkendall and W. E. Garrett Jr, J. Athl. Train. 36, 328 (2001).

    Google Scholar 

  39. 39.

    A. I. King and D. C. Viano, in Biomechanics: Principles and Applications, Ed. by D. J. Schneck and J. D. Bronzino, (CRC Press, 2002), 1st ed., Ch. 6, pp. 107–118.

  40. 40.

    K. P. Granata, D. A. Padua, and S. E. Wilson, J. Electromyogr. Kinesiol. 12, 127 (2002).

    Article  Google Scholar 

  41. 41.

    H. Shinkai, H. Nunome, M. Isokawa, and Y. Ikegami, Med. Sci. Sports Exerc. 41, 889 (2009).

    Article  Google Scholar 

  42. 42.

    V. I. Deshcherevskiĭ, Biorheology 7, 147 (1971).

    Google Scholar 

  43. 43.

    A. V. Hill, Proc. R. Soc. Lond. B. 126, 136 (1938).

    ADS  Article  Google Scholar 

  44. 44.

    L. D. Landau, E. M. Lifshitz. Course of Theoretical Physics, Vol. 6. Fluid Mechanics, (Pergamon Press, 1987), § 81.

    Google Scholar 

  45. 45.

    O. V. Rudenko, Acoust. Phys. 60, 398 (2014).

    ADS  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to O. V. Rudenko.

Additional information

The article is published in the original.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Rudenko, O.V., Tsyuryupa, S. & Sarvazyan, A. Skeletal muscle contraction in protecting joints and bones by absorbing mechanical impacts. Acoust. Phys. 62, 615–625 (2016).

Download citation


  • biomechanics
  • acoustical testing
  • skeletal muscle
  • muscle viscoelasticity
  • muscle contraction
  • skeletal system