Fiber-Based Modeling of Muscles in the Musculoskeletal System

  • Michael H. GfrererEmail author
  • Bernd Simeon
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)


The aim of this contribution is to present a fiber-based modeling approach for the dynamic behavior of muscles within the musculoskeletal system. We represent the skeletal system as a rigid multi-body system which is actuated by muscles. We model each muscle as an one-dimensional cable with variable cross section undergoing large deformation and strains. In order to avoid penetration of the muscles and the skeleton, contact is considered. We use our framework to conduct a dynamic forward simulation of a simple upper limb model.



The authors thank Joachim Linn from Fraunhofer ITWM Kaiserslautern for fruitful discussions on the topic. The authors acknowledge the financial support by the Federal Ministry of Education and Research of Germany in the framework of DYMARA (project number 05M16UKD).


  1. 1.
    Arnold, A.S., Salinas, S., Hakawa, D.J., Delp, S.L.: Accuracy of muscle moment arms estimated from MRI-based musculoskeletal models of the lower extremity. Comput. Aided Surg. 5(2), 108–119 (2000)CrossRefGoogle Scholar
  2. 2.
    Blemker, S.S., Delp, S.L.: Three-dimensional representation of complex muscle architectures and geometries. Ann. Biomed. Eng. 33(5), 661–673 (2005)CrossRefGoogle Scholar
  3. 3.
    Delp, S.L., Loan, J.P., Hoy, M.G., Zajac, F.E., Topp, E.L., Rosen, J.M.: An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE Trans. Biomed. Eng. 37(8), 757–767 (1990)CrossRefGoogle Scholar
  4. 4.
    Heidlauf, T., Klotz, T., Rode, C., Altan, E., Bleiler, C., Siebert, T., Röhrle, O.: A multi-scale continuum model of skeletal muscle mechanics predicting force enhancement based on actin–titin interaction. Biomech. Model. Mechanobiol. 15(6), 1423–1437 (2016)CrossRefGoogle Scholar
  5. 5.
    Hwang, J., Knapik, G.G., Dufour, J.S., Aurand, A., Best, T.M., Khan, S.N., Mendel, E., Marras, W.S.: A biologically-assisted curved muscle model of the lumbar spine: model structure. Clin. Biomech. 37, 53–59 (2016)CrossRefGoogle Scholar
  6. 6.
    Maas, R.: Biomechanics and optimal control simulations of the human upper extremity. Ph.D. Thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg (2014)Google Scholar
  7. 7.
    Raknes, S., Deng, X., Bazilevs, Y., Benson, D., Mathisen, K., Kvamsdal, T.: Isogeometric rotation-free bending-stabilized cables: statics, dynamics, bending strips and coupling with shells. Comput. Methods Appl. Mech. Eng. 263, 127–143 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Röhrle, O., Sprenger, M., Schmitt, S.: A two-muscle, continuum-mechanical forward simulation of the upper limb. Biomech. Model. Mechanobiol. 16(3), 743–762 (2017)CrossRefGoogle Scholar
  9. 9.
    Rupp, T., Ehlers, W., Karajan, N., Günther, M., Schmitt, S.: A forward dynamics simulation of human lumbar spine flexion predicting the load sharing of intervertebral discs, ligaments, and muscles. Biomech. Model. Mechanobiol. 14(5), 1081–1105 (2015)CrossRefGoogle Scholar
  10. 10.
    Scholz, A., Sherman, M., Stavness, I., Delp, S., Kecskeméthy, A.: A fast multi-obstacle muscle wrapping method using natural geodesic variations. Multibody Syst. Dyn. 36(2), 195–219 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Shorten, P.R., OCallaghan, P., Davidson, J.B., Soboleva, T.K.: A mathematical model of fatigue in skeletal muscle force contraction. J. Muscle Res. Cell Motil. 28(6), 293–313 (2007)CrossRefGoogle Scholar
  12. 12.
    Simeon, B.: Computational Flexible Multibody Dynamics. Springer, Berlin (2013)CrossRefGoogle Scholar
  13. 13.
    Zajac, F.E.: Muscle and tendon properties models scaling and application to biomechanics and motor. Crit. Rev. Biomed. Eng. 17(4), 359–411 (1989)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Felix-Klein-Zentrum für MathematikUniversity of KaiserslauternKaiserslauternGermany

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