Ultrasound-Based Optimal Parameter Estimation Improves Assessment of Calf Muscle–Tendon Interaction During Walking

  • T. DelabastitaEmail author
  • M. Afschrift
  • B. Vanwanseele
  • F. De Groote
Original Article


We present and evaluate a new approach to estimate calf muscle–tendon parameters and calculate calf muscle–tendon function during walking. We used motion analysis, ultrasound, and EMG data of the calf muscles collected in six young and six older adults during treadmill walking as inputs to a new optimal estimation algorithm. We used estimated parameters or scaled generic parameters in an existing approach to calculate muscle fiber lengths and activations. We calculated the fit with experimental data in terms of root mean squared differences (RMSD) and coefficients of determination (R2). We also calculated the calf muscle metabolic energy cost. RMSD between measured and calculated fiber lengths and activations decreased and R2 increased when estimating parameters compared to using scaled generic parameters. Moreover, R2 between measured and calculated gastrocnemius medialis fiber length and soleus activations increased by 19 and 70%, and calf muscle metabolic energy decreased by 25% when using estimated parameters compared to using scaled generic parameters at speeds not used for estimation. This new approach estimates calf muscle–tendon parameters in good accordance with values reported in literature. The approach improves calculations of calf muscle–tendon interaction during walking and highlights the importance of individualizing calf muscle–tendon parameters.


Musculoskeletal modeling Optimal control Individualized calf muscle–tendon parameters Older adults 


Conflicts of interest

No conflicts of interest have to be declared.

Supplementary material

10439_2019_2395_MOESM1_ESM.pdf (789 kb)
Supplementary material 1 (PDF 789 kb)


  1. 1.
    Azizi, E., and T. J. Roberts. Biaxial strain and variable stiffness in aponeuroses. J. Physiol. 587:4309–4318, 2009.CrossRefGoogle Scholar
  2. 2.
    Bhargava, L. J., M. G. Pandy, and F. C. Anderson. A phenomenological model for estimating metabolic energy consumption in muscle contraction. J. Biomech. 37:81–88, 2004.CrossRefGoogle Scholar
  3. 3.
    Bolsterlee, B., S. C. Gandevia, and R. D. Herbert. Ultrasound imaging of the human medial gastrocnemius muscle: how to orient the transducer so that muscle fascicles lie in the image plane. J. Biomech. 49:1002–1008, 2016.CrossRefGoogle Scholar
  4. 4.
    Crowninshield, R. D., and R. A. Brand. A physiologically based criterion of muscle force prediction in locomotion. J. Biomech. 14:793–801, 1981.CrossRefGoogle Scholar
  5. 5.
    De Groote, F., T. De Laet, I. Jonkers, and J. De Schutter. Kalman smoothing improves the estimation of joint kinematics and kinetics in marker-based human gait analysis. J. Biomech. 41:3390–3398, 2008.CrossRefGoogle Scholar
  6. 6.
    De Groote, F., A. L. Kinney, A. V. Rao, and B. J. Fregly. Evaluation of direct collocation optimal control problem formulations for solving the muscle redundancy problem. Ann. Biomed. Eng. 44:2922–2936, 2016.CrossRefGoogle Scholar
  7. 7.
    De Groote, F., G. Pipeleers, I. Jonkers, B. Demeulenaere, C. Patten, J. Swevers, and J. De Schutter. A physiology based inverse dynamic analysis of human gait: potential and perspectives. Comput. Methods Biomech. Biomed. Eng. 12:563–574, 2009.CrossRefGoogle Scholar
  8. 8.
    De Groote, F., A. Van Campen, I. Jonkers, and J. De Schutter. Sensitivity of dynamic simulations of gait and dynamometer experiments to hill muscle model parameters of knee flexors and extensors. J. Biomech. 43:1876–1883, 2010.CrossRefGoogle Scholar
  9. 9.
    Delabastita, T., S. Bogaerts, and B. Vanwanseele. Age-related changes in Achilles tendon stiffness and impact on functional activities: a systematic review and meta-analysis. J. Aging Phys. Act. 2018. Scholar
  10. 10.
    Delp, S. L., F. C. Anderson, A. S. Arnold, P. Loan, A. Habib, C. T. John, E. Guendelman, and D. G. Thelen. OpenSim: open-source software to create and analyze dynamic simulations of movement. IEEE Trans. Biomed. Eng. 54:1940–1950, 2007.CrossRefGoogle Scholar
  11. 11.
    Farris, D. J., and G. A. Lichtwark. UltraTrack: software for semi-automated tracking of muscle fascicles in sequences of B-mode ultrasound images. Comput. Methods Programs Biomed. 128:111–118, 2016.CrossRefGoogle Scholar
  12. 12.
    Franz, J. R., L. C. Slane, K. Rasske, and D. G. Thelen. Non-uniform in vivo deformations of the human Achilles tendon during walking. Gait Posture 41:192–197, 2015.CrossRefGoogle Scholar
  13. 13.
    Franz, J. R., and D. G. Thelen. Imaging and simulation of Achilles tendon dynamics: implications for walking performance in the elderly. J. Biomech. 49:1403–1410, 2016.CrossRefGoogle Scholar
  14. 14.
    Fukunaga, T., K. Kubo, Y. Kawakami, S. Fukashiro, H. Kanehisa, and C. N. Maganaris. In vivo behaviour of human muscle tendon during walking. Proc. Biol. Sci. 268:229–233, 2001.CrossRefGoogle Scholar
  15. 15.
    Gerus, P., G. Rao, and E. Berton. Subject-specific tendon-aponeurosis definition in hill-type model predicts higher muscle forces in dynamic tasks. PLoS ONE 7:e44406, 2012.CrossRefGoogle Scholar
  16. 16.
    Gerus, P., G. Rao, and E. Berton. Ultrasound-based subject-specific parameters improve fascicle behaviour estimation in Hill-type muscle model. Comput. Methods Biomech. Biomed. Eng. 5842:37–41, 2015.Google Scholar
  17. 17.
    Karamanidis, K., and A. Arampatzis. Mechanical and morphological properties of human quadriceps femoris and triceps surae muscle-tendon unit in relation to aging and running. J. Biomech. 39:406–417, 2006.CrossRefGoogle Scholar
  18. 18.
    Lai, A., A. G. Schache, Y.-C. Lin, and M. G. Pandy. Tendon elastic strain energy in the human ankle plantar-flexors and its role with increased running speed. J. Exp. Biol. 217:3159–3168, 2014.CrossRefGoogle Scholar
  19. 19.
    Lichtwark, G. A., K. Bougoulias, and A. M. Wilson. Muscle fascicle and series elastic element length changes along the length of the human gastrocnemius during walking and running. J. Biomech. 40:157–164, 2007.CrossRefGoogle Scholar
  20. 20.
    Lichtwark, G. A., and A. M. Wilson. Interactions between the human gastrocnemius muscle and the Achilles tendon during incline, level and decline locomotion. J. Exp. Biol. 209:4379–4388, 2006.CrossRefGoogle Scholar
  21. 21.
    Lichtwark, G. A., and A. M. Wilson. Optimal muscle fascicle length and tendon stiffness for maximising gastrocnemius efficiency during human walking and running. J. Theor. Biol. 252:662–673, 2008.CrossRefGoogle Scholar
  22. 22.
    Mian, O. S., J. M. Thom, L. P. Ardigò, A. E. Minetti, and M. V. Narici. Gastrocnemius muscle-tendon behaviour during walking in young and older adults. Acta Physiol. 189:57–65, 2007.CrossRefGoogle Scholar
  23. 23.
    Mohammadi, R., and C. P. Phadke. The impact of incline and speed of treadmill on ankle muscle activity in middle-aged adults. J. Bodyw. Mov. Ther. 21:306–313, 2017.CrossRefGoogle Scholar
  24. 24.
    Monaco, V., and S. Micera. Age-related neuromuscular adaptation does not affect the mechanical efficiency of lower limbs during walking. Gait Posture 36:350–355, 2012.CrossRefGoogle Scholar
  25. 25.
    Neptune, R. R., K. Sasaki, and S. A. Kautz. The effect of walking speed on muscle function and mechanical energetics. Gait Posture 28:135–143, 2008.CrossRefGoogle Scholar
  26. 26.
    Passmore, E., A. Lai, M. Sangeux, A. G. Schache, and M. G. Pandy. Application of ultrasound imaging to subject-specific modelling of the human musculoskeletal system. Meccanica 2017. Scholar
  27. 27.
    Patterson, M. A., M. J. Weinstein, and A. V. Rao. An efficient overloaded method for computing derivatives of mathematical functions in MATLAB. ACM Trans. Math. Softw. 39:17:1–17:36, 2013.CrossRefGoogle Scholar
  28. 28.
    Rao, A. V., D. A. Benson, C. Darby, M. A. Patterson, C. Francolin, I. Sanders, and G. T. Huntington. GPOPS—II: a MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming. ACM Trans. Math. Softw. 37:1–39, 2010.CrossRefGoogle Scholar
  29. 29.
    Saule, C., and R. Giegerich. Pareto optimization in algebraic dynamic programming. Algorithms Mol. Biol. 10:1–20, 2015.CrossRefGoogle Scholar
  30. 30.
    Sergi, G., C. Trevisan, N. Veronese, P. Lucato, and E. Manzato. Imaging of sarcopenia. Eur. J. Radiol. 85:1519–1524, 2016.CrossRefGoogle Scholar
  31. 31.
    Stenroth, L., J. Peltonen, N. J. Cronin, S. Sipila, and T. Finni. Age-related differences in Achilles tendon properties and triceps surae muscle architecture in vivo. J. Appl. Physiol. 113:1537–1544, 2012.CrossRefGoogle Scholar
  32. 32.
    Van Campen, A., G. Pipeleers, F. De Groote, I. Jonkers, and J. De Schutter. A new method for estimating subject-specific muscle–tendon parameters of the knee joint actuators: a simulation study network. Int. J. Numer. Methods Biomed. Eng. 30:969–987, 2014.CrossRefGoogle Scholar
  33. 33.
    Van Rossom, S., C. R. Smith, L. Zevenbergen, D. G. Thelen, B. Vanwanseele, D. Van Assche, and I. Jonkers. Knee cartilage thickness, T1ρ and T2 relaxation time are related to articular cartilage loading in healthy adults. PLoS ONE 12:1–16, 2017.Google Scholar
  34. 34.
    Wächter, A., and L. Biegler. On the implementation of a interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Programs 106:25–57, 2006.CrossRefGoogle Scholar
  35. 35.
    Winter, D. A., and H. J. Yack. EMG profiles during normal human walking: stride-to-stride and inter-subject variability. Electroencephalogr. Clin. Neurophysiol. 67:402–411, 1987.CrossRefGoogle Scholar
  36. 36.
    Zajac, F. E. Muscle and tendon: properties, models, scaling and application to biomechanics and motor control. Crit. Rev. Biomed. Eng. 17:359–411, 1989.PubMedGoogle Scholar

Copyright information

© Biomedical Engineering Society 2019

Authors and Affiliations

  1. 1.Department of Movement SciencesKU LeuvenLeuvenBelgium

Personalised recommendations