Journal of Bionic Engineering

, Volume 9, Issue 2, pp 211–223 | Cite as

Can Quick Release Experiments Reveal the Muscle Structure? A Bionic Approach

  • D. F. B. HaeufleEmail author
  • M. Günther
  • R. Blickhan
  • S. Schmitt


The goal of this study was to understand the macroscopic mechanical structure and function of biological muscle with respect to its dynamic role in the contraction. A recently published muscle model, deriving the hyperbolic force-velocity relation from first-order mechanical principles, predicts different force-velocity operating points for different load situations. With a new approach, this model could be simplified and thus, transferred into a numerical simulation and a hardware experiment. Two types of quick release experiments were performed in simulation and with the hardware setup, which represent two extreme cases of the contraction dynamics: against a constant force (isotonic) and against an inertial mass. Both experiments revealed hyperbolic or hyperbolic-like force-velocity relations. Interestingly, the analytical model not only predicts these extreme cases, but also additionally all contraction states in between. It was possible to validate these predictions with the numerical model and the hardware experiment. These results prove that the origin of the hyperbolic force-velocity relation can be mechanically explained on a macroscopic level by the dynamical interaction of three mechanical elements. The implications for the interpretation of biological muscle experiments and the realization of muscle-like bionic actuators are discussed.


force-velocity relation isotonic quick release proof of concept artificial muscle 


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  1. [1]
    Hill A V. The heat of shortening and the dynamic constants of muscle. Proceedings of the Royal Society of London: Series B, 1938, 126, 136–195.CrossRefGoogle Scholar
  2. [2]
    Ettema G J C, Huijing P A. Isokinetic and isotonic force-velocity characteristics of rat EDL at muscle optimum length. In Groot G D, Hollander A P, Huijing P A, Van Ingen Schenau G J (eds.) Biomechanics XI-A, Free University Press, Amsterdam, 1988, 58–62.Google Scholar
  3. [3]
    Rassier D E, MacIntosh B R, Herzog W. Length dependence of active force production in skeletal muscle. Journal of applied physiology, 1999, 86, 1445–1457.CrossRefGoogle Scholar
  4. [4]
    Bobbert M F, Ettema G C, Huijing P A. The force-length relationship of a muscle-tendon complex: Experimental results and model calculations. European Journal of Applied Physiology and Occupational Physiology, 1990, 61, 323–329.CrossRefGoogle Scholar
  5. [5]
    Gordon A M, Huxley A F, Julian F J. The variation in isometric tension with sarcomere length in vertebrate muscle fibres. The Journal of physiology, 1966, 184, 170–192.CrossRefGoogle Scholar
  6. [6]
    Bressler B H, Clinch N F. The compliance of contracting skeletal muscle. The Journal of physiology, 1974, 237, 477–493.CrossRefGoogle Scholar
  7. [7]
    Barclay C J, Constable J K, Gibbs C L. Energetics of fast-and slow-twitch muscles of the mouse. The Journal of physiology, 1993, 472, 61–80.CrossRefGoogle Scholar
  8. [8]
    Siebert T, Rode C, Herzog W, Till O, Blickhan R. Nonlin-earities make a difference: Comparison of two common Hill-type models with real muscle. Biological Cybernetics, 2008, 98, 133–143.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Till O, Siebert T, Rode C, Blickhan R. Characterization of isovelocity extension of activated muscle: A Hill-type model for eccentric contractions and a method for parameter determination. Journal of Theoretical Biology, 2008, 255, 176–187.CrossRefGoogle Scholar
  10. [10]
    Jewell B R, Wilkie D R. An analysis of the mechanical components in frog’s striated muscle. The Journal of Physiology, 1958, 143, 515–540.CrossRefGoogle Scholar
  11. [11]
    Cavagna G A, Citterio G. Effect of stretching on the elastic characteristics and the contractile component of frog striated muscle. The Journal of Physiology, 1974, 239, 1–14.CrossRefGoogle Scholar
  12. [12]
    van Zandwijk J P, Bobbert M F, Baan G C, Huijing P A. From twitch to tetanus: Performance of excitation dynamics optimized for a twitch in predicting tetanic muscle forces. Biological Cybernetics, 1996, 75, 409–417.CrossRefzbMATHGoogle Scholar
  13. [13]
    Wilkie D R. The relation between force and velocity in human muscle. The Journal of Physiology, 1949, 110, 249–280.CrossRefGoogle Scholar
  14. [14]
    Günther M, Schmitt S, Wank V. High-frequency oscillations as a consequence of neglected serial damping in Hill-type muscle models. Biological Cybernetics, 2007, 97, 63–79.CrossRefzbMATHGoogle Scholar
  15. [15]
    Huxley A F. Muscle structure and theories of contraction. Progress in Biophysics and Biophysical Chemistry, 1957, 7, 255–318.Google Scholar
  16. [16]
    Huxley A F. A note suggesting that the cross-bridge attachment during muscle contraction may take place in two stages. Proceedings of the Royal Society of London: Series B, 1973, 183, 83–86.CrossRefGoogle Scholar
  17. [17]
    Cooke R, White H, Pate E. A model of the release of myosin heads from actin in rapidly contracting muscle fibers. Biophysical Journal, 1994, 66, 778–788.CrossRefGoogle Scholar
  18. [18]
    Piazzesi G, Lombardi V. A cross-bridge model that is able to explain mechanical and energetic properties of shortening muscle. Biophysical Journal, 1995, 68, 1966–1979.CrossRefGoogle Scholar
  19. [19]
    Piazzesi G, Lombardi V. Simulation of the rapid regeneration of the actinmyosin working stroke with a tight coupling model of muscle contraction. Journal of Muscle Research and Cell Motility, 1996, 17, 45–53.CrossRefGoogle Scholar
  20. [20]
    Barclay C J. A weakly coupled version of the Huxley crossbridge model can simulate energetics of amphibian and mammalian skeletal muscle. Journal of Muscle Research and Cell Motility, 1999, 20, 163–176.CrossRefGoogle Scholar
  21. [21]
    Chin L, Yue P, Feng J J, Seow C Y. Mathematical simulation of muscle cross-bridge cycle and force-velocity relationship. Biophysical Journal, 2006, 91, 3653–3663.CrossRefGoogle Scholar
  22. [22]
    Lan G, Sun S X. Dynamics of myosin-driven skeletal muscle contraction: I. Steady-state force generation. Biophysical Journal, 2005, 88, 4107–4117.CrossRefGoogle Scholar
  23. [23]
    Walcott S, Sun S X. Hysteresis in cross-bridge models of muscle. Physical Chemistry Chemical Physics: PCCP, 2009, 11, 4871–4881.CrossRefGoogle Scholar
  24. [24]
    Zajac F E. Muscle and tendon: Properties, models, scaling, and application to biomechanics and motor control. Critical Reviews in Biomedical Engineering, 1989, 17, 359–411.Google Scholar
  25. [25]
    Winters J M. Hill-based muscle models: A systems engineering perspective. In Winters J M, Woo S Y (eds), Multiple Muscle Systems: Biomechanics and Movement Organization, Springer-Verlag Berlin and Heidelberg, New York, 1990, 69–93.CrossRefGoogle Scholar
  26. [26]
    van Soest A J, Bobbert M F. The contribution of muscle properties in the control of explosive movements. Biological Cybernetics, 1993, 69, 195–204.CrossRefGoogle Scholar
  27. [27]
    Hatze H. The complete optimization of a human motion. Mathematical Biosciences, 1976, 28, 99–135.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    Pandy M G, Zajac F E, Sim E, Levine W S. An optimal control model for maximum-height human jumping. Journal of Biomechanics, 1990, 23, 1185–1198.CrossRefGoogle Scholar
  29. [29]
    Günther M, Ruder H. Synthesis of two-dimensional human walking: A test of the lambda-model. Biological Cybernetics, 2003, 89, 89–106.CrossRefzbMATHGoogle Scholar
  30. [30]
    Geyer H, Herr H. A muscle-reflex model that encodes principles of legged mechanics produces human walking dynamics and muscle activities. IEEE Transactions on Neural Systems and Rehabilitation, 2010, 18, 263–273.CrossRefGoogle Scholar
  31. [31]
    Bobbert M F, Casius L J R. Spring-like leg behaviour, musculoskeletal mechanics and control in maximum and submaximum height human hopping. Philosophical Transactions of the Royal Society of London: Series B, 2011, 366, 1516–1529.CrossRefGoogle Scholar
  32. [32]
    Happee R. Inverse dynamic optimization including muscular dynamics, a new simulation method applied to goal directed movements. Journal of Biomechanics, 1994, 27, 953–960.CrossRefGoogle Scholar
  33. [33]
    Erdemir A, McLean S, Herzog W, van den Bogert A J. Model-based estimation of muscle forces exerted during movements. Clinical Biomechanics, 2007, 22, 131–154.CrossRefGoogle Scholar
  34. [34]
    Gerritsen K G M, van Den Bogert A J, Hulliger M, Zernicke R F. Intrinsic muscle properties facilitate locomotor control — a computer simulation study. Motor Control, 1998, 2, 206–220.CrossRefGoogle Scholar
  35. [35]
    Geyer H, Seyfarth A, Blickhan R. Positive force feedback in bouncing gaits? Proceedings of the Royal Society of London: Series B, 2003, 270, 2173–2183.CrossRefGoogle Scholar
  36. [36]
    van der Krogt M M, de Graaf W W, Farley C T, Moritz C T, Casius L J R, Bobbert M F. Robust passive dynamics of the musculoskeletal system compensate for unexpected surface changes during human hopping. Journal of Applied Physiology, 2009, 107, 801–808.CrossRefGoogle Scholar
  37. [37]
    Haeufle D F B, Grimmer S, Seyfarth A. The role of intrinsic muscle properties for stable hopping–stability is achieved by the force—velocity relation. Bioinspiration & Biomimetics, 2010, 5, 016004 (11pp).Google Scholar
  38. [38]
    Ettema G C. Effects of contraction history on control and stability in explosive actions. Journal of Electromyography and Kinesiology, 2002, 12, 455–461.CrossRefGoogle Scholar
  39. [39]
    Alexander R M. Three uses for sSprings in legged locomotion. The International Journal of Robotics Research, 1990, 9, 53–61.CrossRefGoogle Scholar
  40. [40]
    Lindstedt S L, LaStayo P C, Reich T E. When active muscles lengthen: Properties and consequences of eccentric contractions. News in Physiological Sciences, 2001, 16, 256–261.Google Scholar
  41. [41]
    Blickhan R, Seyfarth A, Geyer H, Grimmer S, Wagner H, Günther M. Intelligence by mechanics. Philosophical Transactions of the Royal Society of London: Series A, 2007, 365, 199–220.MathSciNetCrossRefGoogle Scholar
  42. [42]
    Schmitt S, Günther M. Human leg impact: Energy dissipation of wobbling masses. Archive of Applied Mechanics, 2010, 81, 887–897.CrossRefzbMATHGoogle Scholar
  43. [43]
    Raibert M H. Legged robots. Communications of the ACM, 1986, 29, 499–514.CrossRefzbMATHGoogle Scholar
  44. [44]
    Webb B. Using robots to model animals: A cricket test. Robotics and Autonomous Systems, 1995, 16, 117–134.CrossRefGoogle Scholar
  45. [45]
    Atkeson C G, Hale J G, Pollick F, Riley M, Kotosaka S, Schaul S, Shibata T, Tevatia G, Ude A, Vijayakumar S, Kawato E, Kawato M. Using humanoid robots to study human behavior. IEEE Intelligent Systems and Their Applications, 2000, 15, 46–56.CrossRefGoogle Scholar
  46. [46]
    Dillmann R, Albiez J, Gassmann B, Kerscher T, Zöllner M. Biologically inspired walking machines: design, control and perception. Philosophical Transactions of the Royal Society of London, Series A, 2007, 365, 133–151.MathSciNetCrossRefGoogle Scholar
  47. [47]
    Pfeifer R, Lungarella M, Iida F. Self-organization, embodiment, and biologically inspired robotics. Science, 2007, 318, 1088–1093.CrossRefGoogle Scholar
  48. [48]
    Ijspeert A J, Crespi A, Ryczko D, Cabelguen J-M. From swimming to walking with a salamander robot driven by a spinal cord model. Science, 2007, 315, 1416–1420.CrossRefGoogle Scholar
  49. [49]
    Pratt G A, Williamson M M. Series elastic actuators. Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems, Pittsburgh, Pennsylvania, USA, 1995, 399–406.Google Scholar
  50. [50]
    Hannaford B, Jaax K, Klute G K. Bio-inspired actuation and sensing. Autonomous Robots, 2001, 11, 267–272.CrossRefzbMATHGoogle Scholar
  51. [51]
    Albu-Schäffer A, Eiberger O, Grebenstein M, Haddadin S, Ott C, Wimböck T, Wolf S, Hirzinger G. Soft robotics. IEEE Robotics & Automation Magazine, 2008, 15, 20–30.CrossRefGoogle Scholar
  52. [52]
    Hurst J, Rizzi A. Series compliance for an effcient running gait. IEEE Robotics & Automation Magazine, 2008, 15, 42–51.CrossRefGoogle Scholar
  53. [53]
    Günther M, Schmitt S. A macroscopic ansatz to deduce the Hill relation. Journal of Theoretical Biology, 2010, 263, 407–418.MathSciNetCrossRefGoogle Scholar
  54. [54]
    Haeufle D F B, Günther M, Blickhan R, Schmitt S. Proof of concept: Model based bionic muscle with hyperbolic force-velocity relation. Applied Bionics and Biomechanics, 2012, published online.Google Scholar
  55. [55]
    Abbott B C, Aubert X M. The force exerted by active striated muscle during and after change of length. The Journal of Physiology, 1952, 117, 77–86.CrossRefGoogle Scholar
  56. [56]
    Rode C, Siebert T, Blickhan R. Titin-induced force enhancement and force depression: A “sticky-spring” mechanism in muscle contractions? Journal of Theoretical Biology, 2009, 259, 350–360.CrossRefGoogle Scholar
  57. [57]
    Schmitt S, Haeufle D F B, Blickhan R, Günther M. Nature as an engineer: One simple solution of a bio-inspired functional artificial muscle. Bioinspiration & Biomimetics, 2012, in review.Google Scholar
  58. [58]
    van Ingen Schenau G J, Bobbert M F, Ettema G C, de Graaf J B, Huijing P A. A simulation of rat edl force output based on intrinsic muscle properties. Journal of Biomechanics, 1988, 21, 815–824.CrossRefGoogle Scholar
  59. [59]
    Durfee W K, Palmer K I. Estimation of force-activation, force-length, and force-velocity properties in isolated, electrically stimulated muscle. IEEE Transactions on Bio-Medical Engineering, 1994, 41, 205–216.CrossRefGoogle Scholar
  60. [60]
    Zuurbier C J, Heslinga J W, Lee-de Groot M B E, van der Laarse W J. Mean sarcomere length-force relationship of rat muscle fibre bundles. Journal of Biomechanics, 1995, 28, 83–87.CrossRefGoogle Scholar
  61. [61]
    Rode C, Siebert T, Herzog W, Blickhan R. The effects of parallel and series elastic components on the active cat so-leus force-length relationship. Journal of Mechanics in Medicine and Biology, 2009, 9, 105–122.CrossRefGoogle Scholar
  62. [62]
    Forcinito M, Epstein M, Herzog W. Can a rheological muscle model predict force depression/enhancement? Journal of Biomechanics, 1998, 31, 1093–1099.CrossRefGoogle Scholar
  63. [63]
    Meijer K, Grootenboer H J, Koopman H F J M, van der Linden B J J J, Huijing P A. A Hill type model of rat medial gastrocnemius muscle that accounts for shortening history effects. Journal of Biomechanics, 1998, 31, 555–563.CrossRefGoogle Scholar
  64. [64]
    Herzog W, Leonard T R. Force enhancement following stretching of skeletal muscle: A new mechanism. The Journal of Experimental Biology, 2002, 205, 1275–1283.Google Scholar
  65. [65]
    Herzog W. History dependence of skeletal muscle force production: Implications for movement control. Human Movement Science, 2004, 23, 591–604.CrossRefGoogle Scholar
  66. [66]
    Garcia E, Arevalo J, Muñoz G, Gonzalez-de Santos P. Combining series elastic actuation and magneto-rheological damping for the control of agile locomotion. Robotics and Autonomous Systems, 2001, 59, 827–839.CrossRefGoogle Scholar
  67. [67]
    Nachtigall W. Bionik, 2nd ed, Springer, Berlin, Germany, 2002.Google Scholar
  68. [68]
    McMahon T A. Muscles, Reflexes, and Locomotion, Princeton University Press, Princeton, NJ, USA, 1984.Google Scholar
  69. [69]
    Ritzmann R E, Quinn R D, Watson J T, Zill S N. Insect walking and biorobotics: A relationship with mutual benefits. BioScience, 2000, 50, 23–33.CrossRefGoogle Scholar
  70. [70]
    Grimmer S, Ernst M, Günther M, Blickhan R. Running on uneven ground: Leg adjustment to vertical steps and self-stability. The Journal of Experimental Biology, 2008, 211, 2989–3000.CrossRefGoogle Scholar
  71. [71]
    Lieber R L. Skeletal muscle is a biological example of a linear electroactive actuator. Proceedings of SPIE’s 6th Annual International Symposium on Smart Structures and Materials, 1999, 3669, 19–25.Google Scholar
  72. [72]
    Baughman R H. Playing nature’s game with artificial muscles. Science, 2005, 308, 63–65.CrossRefGoogle Scholar

Copyright information

© Jilin University 2012

Authors and Affiliations

  • D. F. B. Haeufle
    • 1
    • 2
    Email author
  • M. Günther
    • 1
    • 2
  • R. Blickhan
    • 3
  • S. Schmitt
    • 1
    • 2
  1. 1.Institute of Sports and Exercise-ScienceUniversity of StuttgartStuttgartGermany
  2. 2.Stuttgart Research Centre for Simulation Technology (SRC SimTech)University of StuttgartStuttgartGermany
  3. 3.Institute of Motion ScienceFriedrich-Schiller-UniversityJenaGermany

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