Lower Limb Stiffness Estimation during Running: The Effect of Using Kinematic Constraints in Muscle Force Optimization Algorithms

  • Roberto Bortoletto
  • Enrico Pagello
  • Davide Piovesan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8810)


The focus of this paper is on the effect of muscle force optimization algorithms on the human lower limb stiffness estimation. By using a forward dynamic neuromusculoskeletal model coupled with a muscle short-range stiffness model we computed the human joint stiffness of the lower limb during running. The joint stiffness values are calculated using two different muscle force optimization procedures, namely: Toque-based and Torque/Kinematic-based algorithm. A comparison between the processed EMG signal and the corresponding estimated muscle forces with the two optimization algorithms is provided. We found that the two stiffness estimates are strongly influenced by the adopted algorithm. We observed different magnitude and timing of both the estimated muscle forces and joint stiffness time profile with respect to each gait phase, as function of the optimization algorithm used.


joint stiffness muscle force optimization algorithms 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Anderson, F.C., Pandy, M.G.: Dynamic Optimization of Human Walking. ASME J. Biomech. Eng. 123(5), 381–390Google Scholar
  2. 2.
    Ackerman, M., van der Bogert, A.J.: Optimality Principles for Model-Based Prediction of Human Gait. J. Biomech. 43(6), 1055–1060Google Scholar
  3. 3.
    Arnold, E.M., Delp, S.L.: Fibre Operating Lengths of Human Lower Limb Muscle During Walking. Philos. T. R. Soc. B. 366(1570), 1530–1539Google Scholar
  4. 4.
    Hamner, S.R., Seth, A., Delp, S.L.: Muscle Contributions to Propulsion and Support During Running. J. Biomech. 43(14), 2709–2716Google Scholar
  5. 5.
    Steele, K.M., Seth, A., Hicks, J.L., Schwartz, M.S., Delp, S.L.: Muscle Contributions to Support and Progression During Single-Limb Stance in Crouch Gait. J. Biomech. 43(11), 2099–2105Google Scholar
  6. 6.
    Hill, A.V.: The Heat of Shortening and the Dynamic Constants of Muscle. Proc. R. Soc. Lond. B (1938)Google Scholar
  7. 7.
    Gordon, A.M., Huxley, A.F., Julian, F.J.: The variation in isometric tension with sarcomere length in vertebrate muscle fibres. J. of Phys. 184, 170–192 (1966)Google Scholar
  8. 8.
    Zajac, F.E.: Muscle and tendon: properties, models, scaling, and application to biomechanics and motor contro. Crit. Rev. Biomed. Eng. 17, 359–411 (1989)Google Scholar
  9. 9.
    Anderson, F.C., Pandy, M.G.: Static and dynamic optimization solutions for gait are pratically equivalent. J. Biomech. 34(2), 153–161 (2001)CrossRefGoogle Scholar
  10. 10.
    Erdemir, A., McLean, S., Herzog, W., van den Bogert, A.J.: Model-based estimation of muscle forces exerted during movements. Clinical Biomechanics 22, 131–154 (2007)CrossRefGoogle Scholar
  11. 11.
    Monaco, V., Coscia, M., Micera, S.: Cost function tuning improves muscle force estimation computed by static optimization during walking. In: Conf. Proc. IEEE Eng. Med. Biol. Soc. (2011)Google Scholar
  12. 12.
    Shamaei, K., Sawicki, G.S., Dollar, A.M.: Estimation of Quasi-Stiffness of the Human Hip in the Stance Phase of Walking. PloS One 8(12) (2013)Google Scholar
  13. 13.
    Pfeifer, S., Vallery, H., Hardegger, M., Riener, R., Perreault, E.J.: Model-based estimation of knee stiffness. IEEE Trans. on Bio-medical Engineering 59(9), 2604–2615 (2012)CrossRefGoogle Scholar
  14. 14.
    Shamaei, K., Sawicki, G.S., Dollar, A.M.: Estimation of quasi-stiffness of the human knee in the stance phase of walking. PloS One 8(3) (2013)Google Scholar
  15. 15.
    Shamaei, K., Sawicki, G.S., Dollar, A.M.: Estimation of quasi-stiffness and propulsive work of the human ankle in the stance phase of walking. PloS One 8(3) (2013)Google Scholar
  16. 16.
    Piovesan, D., Pierobon, A., DiZio, P., Lackner, J.R.: Experimental Measure of Arm Stiffness During Single Reaching Movements with a Time-Frequency Analysis. J. Neurophysiol. 110(10), 2484–2496 (2013)CrossRefGoogle Scholar
  17. 17.
    Piovesan, D., Casadio, M., Morasso, P., Giannoni, P.: Arm stiffness during assisted movements following stroke: the influence of visual feedback and training. IEEE Trans. Neural Syst. Rehabil. Eng. 21(3), 454–465 (2013)CrossRefGoogle Scholar
  18. 18.
    Piovesan, D., Pierobon, A., DiZio, P., Lackner, J.R.: Measuring Multi-Joint Stiffness during Single Movements: Numerical Validation of a Novel Time-Frequency Approach. PLoS ONE 7(3), e33086 (2012)Google Scholar
  19. 19.
    Bortoletto, R., Pagello, E., Piovesan, D.: How different human muscle models affect the estimation of lower limb joint stiffness during running. Accepted for publication in Proc. of Workshop on Neuro-Robotics for Patient-Specific Rehabilitation, July 18 (2014), IAS-13 Conf., Padua, July 15-19 (2014)Google Scholar
  20. 20.
    Yamaguchi, G.T., Zajac, F.E.: A planar model of the knee joint to characterize the knee extensor mechanism. J. Biomech. 22, 1–10 (1989)CrossRefGoogle Scholar
  21. 21.
    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), 757–767Google Scholar
  22. 22.
    Anderson, F.C., Pandy, M.G.: A Dynamic Optimization Solution for Vertical Jumping in Three Dimensions. Comput. Methods Biomech. Biomed. Engin. 2(3), 201–231 (1999)CrossRefGoogle Scholar
  23. 23.
    Ward, S.R., Eng, C.M., Smallwood, L.H., Lieber, R.L.: Are current measurements of lower extremity muscle architecture accurate? Clin. Orthop. Relat. Res. 467, 1074–1082 (2009)CrossRefGoogle Scholar
  24. 24.
    Dorn, T.W., Schache, A.G., Pandy, M.G.: Muscular startegy shift in human running: dependence of running speed on hip and ankle muscle performance. The J. of Exp. Biol. 215, 1944–1956 (2012)CrossRefGoogle Scholar
  25. 25.
    Thelen, D.G., Anderson, F.C., Delp, S.L.: Generating dynamic simulations of movement using computed muscle control. J. of Biomec. 36, 321–328 (2003)CrossRefGoogle Scholar
  26. 26.
    Thelen, D.G., Anderson, F.C.: Using computed muscle control to generate forward dynamic simulations of human walking from experimental data. J. Biomech. 39(6), 1107–1115 (2006)CrossRefGoogle Scholar
  27. 27.
    Thelen, D.G.: Adjustment of Muscle Mechanics Model Parameters to Simulate Dynamic Contractions in Older Adults. J. Biomech. Eng. 125(1), 70 (2003)CrossRefGoogle Scholar
  28. 28.
    Cui, L., Perreault, E.J., Maas, H., Sandercock, T.G.: Modeling short-range stiffness of feline lower hindlimb muscles. J. Biomech. 41, 1945–1952 (2008)CrossRefGoogle Scholar
  29. 29.
    Hu, X., Murray, W.M., Perreault, E.J.: Muscle short-range stiffness can be used to estimate the endpoint stiffness of the human arm. Journal of Neurophysiology 105(4), 1633–1641 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Roberto Bortoletto
    • 1
  • Enrico Pagello
    • 1
  • Davide Piovesan
    • 2
  1. 1.Department of Information EngineeringIntelligent Autonomous Systems Laboratory (IAS-Lab.), University of PaduaPadovaItaly
  2. 2.Biomedical Program, Mechanical Engineering DepartmentGannon UniversityErieUSA

Personalised recommendations