Skip to main content
Log in

Generalized Model of a Skeletal Muscle

  • Published:
Mechanics of Composite Materials Aims and scope

A new phenomenological model of a skeletal muscle consisting of a contractile and two nonlinear viscoelastic elements is proposed. The corresponding system of differential equations of the model is obtained, which allows one to derive time-dependent relations between the axial stress and the longitudinal strain in passive and activated states of the muscle. Methods for determining the viscoelastic and functional characteristics of the muscle as input parameters of the equations mentioned above are developed. These methods are based on the joint application of known experimental relations for a single muscle fiber and the results of muscle indentation in vivo on a “Miometer UT 98-01” device.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Miometer UT 98-01. University of Tarty (2002).

  2. M. I. Khaikova, Changes in the Mechanical Properties of Skeletal Muscles during Developing Stresses by Them. PhD thesis. 03.00.13. Moscow (1984).

  3. S. V. Shil’ko, D. A. Chernous, and K. K. Bondarenko, “Method of determination of skeletal muscles viscoelastic characteristics in vivo,” Russian Journal of Biomechanics, 11, No 1, 44-53 (2007).

  4. S. Yu. Bershitskii and A. K. Tsaturyan, “On the character of anisotropy of a muscular tissue,” Dokl. Akad. Nauk SSSR, 259, No. 1, 53-56 (1981).

    Google Scholar 

  5. K. K. Bondarenko, D. A. Chernous, and S. V. Shil’ko, “Biomechanical interpretation of skeletal muscles miometry for sportsmen,” Russian Journal of Biomechanics., 13, No. 1, 7-17 (2009).

    Google Scholar 

  6. R. L. Lieber and S. C. Bodine-Fowler, “Skeletal muscle mechanics: implications for rehabilitation,” Phys. Therapy, 73, No 12, 844-856 (1993).

    Google Scholar 

  7. Lee Eun-J., V. Joumaa, and W. Herzog, “New insights into the passive force enhancement in skeletal muscles,” J. Biomech., 40, No. 5, 719-727 (2007).

  8. V. I. Deshcherevskii, Mathematical Models of Muscular Contraction [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  9. S. V. Shil’ko and D. A. Chernous, “A phenomenological model of the muscle as an active composite,” Mekh. Mash. Mekhan. Mater., 6, No. 1, 88-92 (2009).

    Google Scholar 

  10. P. I. Begun and Yu. A. Shukeylo, Biomechanics [in Russian], Politekhnika, St. Petersburg (2000).

  11. H. S. Gasser and A. V. Hill, “The dynamic of muscular contraction,” Proc. Roy. Soc. London, B 96, No. 678, 398-437 (1924).

  12. G. B. Sokolov, Mathematic Simulation of Work of Skeletal Muscles. PhD. 05.13.18. St. Petersburg (2001).

  13. P. I. Begun and P. N. Afonin, Simulation in Biomechanics [in Russian], Vysshaya Shkola, Moscow (2004).

    Google Scholar 

  14. N. A. Fomin, Human Physiology [in Russian], Prosveshchenie, Moscow (1995).

    Google Scholar 

  15. D. Hawkins and M. Bey, “Muscle and tendon force-length properties and their interactions in vivo,” J. Biomech., 30, 63-70 (1997).

    Article  Google Scholar 

  16. E. M. H. Bosboom et al., “Passive transverse mechanical properties of skeletal muscle under in vivo compression” J. Biomech., 34, 1365-1368 (2001).

    Article  Google Scholar 

  17. B. R. Jewell and D. R. Wilkie, “An analysis of the mechanical components in frog striated muscle,” J. Physiol., 143, No 3, 515-540 (1958).

    Article  Google Scholar 

  18. S. V. Shil’ko, D. A. Chernous, and Yu. M. Pleskachevskii, “Nonlinear deformation of skeletal muscles in a passive state and in isotonic contraction,” Mech. Compos. Mater., 48, No. 3, 331-342 (2012).

    Article  Google Scholar 

  19. R. M. Christensen, Mechanics of Composite Materials, Dover Publ., Mineola, New York (2005).

    Google Scholar 

  20. K. A. Edman, C. Reggiani, S. Schiaffino, and G. Kronnie, “Maximum velocity of shortening related to myosin isoform composition in frog skeletal muscle fibers,” J. Physiol., 395, 679-694 (1988).

    Article  Google Scholar 

  21. F. E. Zajac, “Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control,” Crit. Rev. Biomed. Eng., 17, 359-411 (1989).

    Google Scholar 

Download references

Acknowledgments

This study was financially supported by the project Convergence 3.5.04.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. V. Shil’ko.

Additional information

Translated from Mekhanika Kompozitnykh Materialov, Vol. 51, No. 6, pp. 1119-1134 , November-December, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shil’ko, S.V., Chernous, D.A. & Bondarenko, K.K. Generalized Model of a Skeletal Muscle. Mech Compos Mater 51, 789–800 (2016). https://doi.org/10.1007/s11029-016-9549-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11029-016-9549-4

Keywords

Navigation