Estimation of muscular forces from SSA smoothed sEMG signals calibrated by inverse dynamics-based physiological static optimization

  • F. RomeroEmail author
  • F. J. Alonso
  • C. Gragera
  • U. Lugrís
  • J. M. Font-Llagunes
Technical Paper


The estimation of muscular forces is useful in several areas such as biomedical or rehabilitation engineering. As muscular forces cannot be measured in vivo non-invasively they must be estimated by using indirect measurements such as surface electromyography (sEMG) signals or by means of inverse dynamic (ID) analyses. This paper proposes an approach to estimate muscular forces based on both of them. The main idea is to tune a gain matrix so as to compute muscular forces from sEMG signals. To do so, a curve fitting process based on least-squares is carried out. The input is the sEMG signal filtered using singular spectrum analysis technique. The output corresponds to the muscular force estimated by the ID analysis of the recorded task, a dumbbell weightlifting. Once the model parameters are tuned, it is possible to obtain an estimation of muscular forces based on sEMG signal. This procedure might be used to predict muscular forces in vivo outside the space limitations of the gait analysis laboratory.


Electromyography Muscle modelling Muscular forces Inverse dynamics analysis Singular spectrum analysis 



This work was supported by the Spanish Ministry of Economy and Competitiveness under project DPI2012-38331-C03, co-financed by the European Union through EFRD funds. The support is gratefully acknowledged.

Compliance with ethical standards

Conflict of interest

All authors confirm that there are no competing interests associated with this publication.

Ethical approval

The experimental procedure was approved by the Ethics Committee of the University of La Coruña (CE-UDC), and confirmed by the Spanish Ministry of Economy and Competitiveness by the endorsement of the project DPI2012-38331-C03 that involves the three participant universities.


  1. 1.
    Ackermann M (2007) Dynamics and energetics of walking with prostheses. PhD thesis, University of StuttgartGoogle Scholar
  2. 2.
    Erdemir A, McLean S, Herzog W, van den Bogert AJ (2007) Model-based estimation of muscle forces exerted during movements. Clin Biomech 22(2):131–154CrossRefGoogle Scholar
  3. 3.
    Silva MT (2003) Human motion analysis using multibody dynamics and optimization tools. PhD thesis, Instituto Superior Técnico (Universidade Técnica de Lisboa)Google Scholar
  4. 4.
    Menegaldo LL, Fleury AT, Weber HI (2006) A cheap optimal control approach to estimate muscles forces in musculoskeletal systems. J Biomech 39:1787–1795CrossRefGoogle Scholar
  5. 5.
    Pipeleers G, Demeulenaere B, Jonkers I, Spaepen P, Van der Perre G, Spaepen A, Swevers J, De Schutter J (2007) Dynamic simulation of human motion: numerically efficient inclusion of muscle physiology by convex optimization. Optim Eng 9(3):213–238MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ambrosio JAC, Kecskemethy A (2007) Multibody dynamics of biomechanical models for human motion via optimization. Multibody Dynamics, pp 245–272Google Scholar
  7. 7.
    Darryl G, Thelen DG, Anderson FC (2006) Using computed muscle control to generate forward dynamic simulations of human walking from experimental data. J Biomech 39(6):1107–1115CrossRefGoogle Scholar
  8. 8.
    Lloyd DG, Besier TF (2003) An emg-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo. J Biomech 36(6):765–776CrossRefGoogle Scholar
  9. 9.
    Buchanan TS, Moniz MJ, Dewald JP, Rymer WZ (1993) Estimation of muscle forces about the wrist joint during isometric tasks using an EMG coefficient method. J Biomech 26(4):547–560CrossRefGoogle Scholar
  10. 10.
    Stuart M, McGill SM (1992) A myoelectrically based dynamic three-dimensional model to predict loads on lumbar spine tissues during lateral bending. J Biomech 25(4):395–414CrossRefGoogle Scholar
  11. 11.
    Buchanan TS, Lloyd DG, Manal K, Besier TF (2004) Neuromusculoskeletal modeling: estimation of muscle forces and joint moments and movements from measurements of neural command. J Appl Biomech 20(4):367CrossRefGoogle Scholar
  12. 12.
    De Luca CJ, Adam A, Wotiz R, Gilmore LD, Nawab SH (2006) Decomposition of surface EMG signals. J Neurophysiol 96:1646–1657CrossRefGoogle Scholar
  13. 13.
    Wei G, Wang C, Tang G, Tian F (2012) A wavelet-based method to predict muscle forces from surface electromyography signals in weightlifting. J Bionic Eng 9:48–58CrossRefGoogle Scholar
  14. 14.
    Zhang Xu, Xhou Ping (2013) Filtering of surface emg using ensemble empirical mode decomposition. Med Eng Phys 35:537–542CrossRefGoogle Scholar
  15. 15.
    Amis AA, Dowson D, Wright V (1979) Muscle strengths and musculoskeletal geometry of the upper limb. Eng Med 8(1):41–48CrossRefGoogle Scholar
  16. 16.
    Amis AA, Dowson D, Wright V (1980) Analysis of elbow forces due to high-speed forearm movements. J Biomech 13(10):825–831CrossRefGoogle Scholar
  17. 17.
    Freivalds A (2011) Biomechanics of the upper limbs: mechanics, modeling and musculoskeletal injuries. CRC press, Boca RatonGoogle Scholar
  18. 18.
    Holzbaur KR, Murray WM, Delp SL (2005) A model of the upper extremity for simulating musculoskeletal surgery and analyzing neuromuscular control. Ann Biomed Eng 33(6):829–840CrossRefGoogle Scholar
  19. 19.
    Garner BA, Pandy MG (2003) Estimation of musculotendon properties in the human upper limb. Ann Biomed Eng 31(2):207–220CrossRefGoogle Scholar
  20. 20.
    Alonso Javier, Romero Francisco, Pàmies-Vilà Rosa, Lugrís Urbano, Font-Llagunes Josep Maria (2012) A simple approach to estimate muscle forces and orthosis actuation in powered assisted walking of spinal cord-injured subjects. Multibody Syst Dyn 28(1–2):109–124MathSciNetCrossRefGoogle Scholar
  21. 21.
    Nigg BM, Herzog W (1999) Biomechanics of the musculo-skeletal system, vol 192. Wiley, New YorkGoogle Scholar
  22. 22.
    Silva MPT, Ambrósio JAC (2002) Kinematic data consistency in the inverse dynamic analysis of biomechanical systems. Multibody Syst Dyn 8(2):219–239CrossRefzbMATHGoogle Scholar
  23. 23.
    Alonso FJ, Del Castillo JM, Pintado P (2005) Application of singular spectrum analysis to the smoothing of raw kinematic signals. J Biomech 38(5):1085–1092CrossRefGoogle Scholar
  24. 24.
    Gerritsen KGM, van den Bogert AJ, Hulliger M, Zernicke RF (1998) Intrinsic muscle properties facilitate locomotor control: a computer simulation study. Motor Control 2:206–220CrossRefGoogle Scholar
  25. 25.
    Hill AV (1938) The heat of shortening and the dynamic constants of muscle. Proc R Soc B Biol Sci 126(843):136–195CrossRefGoogle Scholar
  26. 26.
    Zajac F (1989) Muscle and tendon: properties, models, scaling and applications to biomechanics and motor control. Crit Rev Biomed Eng 17:359–411Google Scholar
  27. 27.
    Yamaguchi GT (2001) Dynamic modeling of musculoskeletal motion: a vectorized approach for biomechanical analysis in three dimensions. Kluwer Academic Publishers, NorwellCrossRefzbMATHGoogle Scholar
  28. 28.
    Thelen DG (2003) Adjustment of muscle mechanics model parameters to simulate dynamic contractions in older adults. J Biomech Eng 125(1):70–77CrossRefGoogle Scholar
  29. 29.
    Ramsay JW, Hunter BV, Gonzalez RV (2009) Muscle moment arm and normalized moment contributions as reference data for musculoskeletal elbow and wrist joint models. J Biomech 42(4):463–473CrossRefGoogle Scholar
  30. 30.
    Aschero G, Gizdulich P (2010) Denoising of surface EMG with a modified wiener filtering approach. J Electromyogr Kinesiol 20(2):366–373CrossRefGoogle Scholar
  31. 31.
    Mello RGT, Oliveira LF, Nadal J (2007) Digital Butterworth filter for substracting noise from low magnitude surface electromyogram. Comput Methods Progr Biomed 87(1):28–35CrossRefGoogle Scholar
  32. 32.
    Golyandina N, Nekrutkin V, Zhigljavsky AA (2001) Analysis of time series structure: SSA and related techniques, vol 90. Chapman & Hall, LondonzbMATHGoogle Scholar
  33. 33.
    Romero F, Alonso FJ, Cubero J, Galán-Marín G (2015) An automatic ssa-based de-noising and smoothing technique for surface electromyography signals. Biomed Signal Process Control 18:317–324CrossRefGoogle Scholar
  34. 34.
    Massimo Sartori, Monica Reggiani, Cristiano Mezzato, Enrico Pagello (2009) A lower limb emg-driven biomechanical model for applications in rehabilitation robotics. In IEEE International Conference on Advanced Robotics, 2009. ICAR 2009., pp 1–7Google Scholar
  35. 35.
    Hermens HJ, Freriks B, Disselhorst-Klug C, Rau G (2000) Development of recommendations for semg sensors and sensor placement procedures. J Electromyogr Kinesiol 10(5):361–374CrossRefGoogle Scholar
  36. 36.
    Criswell E (2010) Cram’s introduction to surface electromyography. Jones & Bartlett Publishers, BurlingtonGoogle Scholar
  37. 37.
    Cavanagh PR, Komi PV (1979) Electromechanical delay in human skeletal muscle under concentric and eccentric contractions. Eur J Appl Physiol Occup Physiol 42(3):159–163CrossRefGoogle Scholar
  38. 38.
    Vos EJ, Mullender MG, van Ingen Schenau GJ (1990) Electromechanical delay in the vastus lateralis muscle during dynamic isometric contractions. Eur J Appl Physiol Occup Physiol 60(6):467–471CrossRefGoogle Scholar
  39. 39.
    Zhou S, Lawson DL, Morrison WE, Fairweather I (1995) lectromechanical delay in isometric muscle contractions evoked by voluntary, reflex and electrical stimulation. Eur J Appl Physiol Occup Physiol 70(2):138–145CrossRefGoogle Scholar
  40. 40.
    Menegaldo LL, Oliveira LF (2012) The influence of modeling hypothesis and experimental methodologies in the accuracy of muscle force estimation using EMG-driven models. Multibody Syst Dyn 28(1–2):21–36CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2016

Authors and Affiliations

  • F. Romero
    • 1
    Email author
  • F. J. Alonso
    • 1
  • C. Gragera
    • 1
  • U. Lugrís
    • 2
  • J. M. Font-Llagunes
    • 3
  1. 1.Department of Mechanical, Energetic and Materials EngineeringUniversity of ExtremaduraBadajozSpain
  2. 2.Department of Industrial Engineering IIUniversity of La CoruñaFerrolSpain
  3. 3.Department of Mechanical Engineering and Biomedical Engineering Research Centre (CREB)Universitat Politècnica de CatalunyaBarcelonaSpain

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