Skip to main content
SpringerLink
Log in

An improved muscle-reflex actuator for use in large-scale neuromusculoskeletal models

  • Starkfest: Vision & Movement in Man and Machines
  • Modeling Motor Control Processes
  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

This paper extends the systematic approach described in Winters and Stark (62) for developing muscle models. The underlying motivation is our finding that for larger scale shoulder and head-neck postural systems to be mechanically stable, open-loop muscle properties are often not sufficient. There are three primary contributions. First, the previous muscle mechanical model structure and parameter estimation process of (62) is updated to reflect recent experimental findings. Second, an intrafusal (IF) muscle model is developed that includes a γ static motoneuron (MN) drive, a Hill muscle model, and a muscle spindle sensor across the IF series element; this provides a more appropriate muscle spindle output signal, especially for studies of posture. Third, the conceptual cut between the neurocontrol input and the actuator is raised from just below the MN summing junction to a higher location, allowing a “musclereflex actuator” to be defined that satisfies the formal theoretical requirement for possessing passive spring-like behavior when the neurocontrol input is constant. α−ψ MN coactivation is assumed, and three types of intrinsic autogenic reflex responses (spindle, Golgi tendon organ, Rhenshaw cell) are developed. Default feedback gains are set based on the criteria that inherent feedback should not sculpt the feedforward excitation drive by more than ±10% of maximum. This new actuator model only mildly affects voluntary goal-directed dynamic performance, but enhances spring-like performance around the postural equilibrium state, in line with available animal and human studies and with several theories on postural regulation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abbott, B. C., and D. R. Wilkie. The relation between velocity of shortening and the tension-length curve of skeletal muscle.J. Physiol. 120:214–223, 1953.

    PubMed  CAS  Google Scholar 

  2. Alexander, R. McN., and R. F. Ker. The architecture of leg muscles. InMultiple Muscle Systems: Biomechanics and Movement Organization. edited by J. M. Winters and S. L.-Y. Woo, New York: Springer-Verlag. 1990, pp. 568–577.

    Google Scholar 

  3. Bagley, A. M. Analysis of Human Response to Slow Isokinetic Movement. Tempe: Arizona State University, M.S. Thesis, 1987.

    Google Scholar 

  4. Bagust, J., S. Knott, D. M. Lewis, J. C. Luck, and R. A. Westerman. Isometric contractions of motor units in a fast twitch muscle of the cat.J. Physiol. 231:87–104, 1973.

    PubMed  CAS  Google Scholar 

  5. Bahler, A. S. Modeling of mammalian skeletal muscle.IEEE Trans. Biomed. Eng. BME-13:248–257, 1968.

    Google Scholar 

  6. Daru, K. M. Computer Simulation and Static Analysis of the Human Head, Neck and Torso. Tempe: Arizona State University, M.A. Thesis, 1989

    Google Scholar 

  7. Esbashi, S., and E. Endo. Calcium and muscle contraction.Progr. Biophys. 18:123–183, 1968.

    Article  Google Scholar 

  8. Ettema, G. J. C., and P. Huijing. Architecture and elastic properties of the series elastic element of muscle-tendon complex. In.Multiple Muscle Systems: Biomechanics and Movement Organization, edited by J. M. Winters and S. L.-Y. Woo. New York: Springer-Verlag, 1990, pp. 57–68.

    Google Scholar 

  9. Feldman, A. G. Functional tuning of the nervous system during control of movement or maintenance of a steady posture. II. controllable parameters of muscle.Biophysiology 11:565–578, 1966.

    Google Scholar 

  10. Feldman, A. G., S. V. Adamovich, D. J. Ostry, and J. R. Flanagan. The origin of electromyograms—explanations based on the equilibrium point hypothesis. In.Multiple Muscle Systems: Biomechanics and Movement Organization, edited by J. M. winters and S. L.-Y. Woo. New York: Springer-Verlag, 1990, pp. 195–213.

    Google Scholar 

  11. Gielen, C. C. A. M., and J. C. Houk. A model of the tor servo: incorporating nonlinear spindle receptor and muscle mechanical properties.Biol. Cybern. 57:217–231, 1987.

    Article  PubMed  CAS  Google Scholar 

  12. Gordon, A. M., A. F. Huxley, and F. J. Julian. The variation in isometric tension with sarcomere length in vertebrate muscles.J. Physiol. 184:170–192, 1966.

    PubMed  CAS  Google Scholar 

  13. Hannaford, B., and L. Stark. Late agonist burst (PC) required for optimal head movements: a simulation study.Biol. Cybern. 57:321–330, 1987.

    Article  PubMed  CAS  Google Scholar 

  14. Hannaford, B., and J. M. Winters. Actuator properties and movement control: biological and technological actuators. In:Multiple Muscle Systems: Biomechanics and Movement Organization, edited by J. M. Winters and S. L.-Y. Woo. New York: Springer-Verlag, 1990, pp. 69–93.

    Google Scholar 

  15. Hannaford, B., J. M. Winters, C.-P. Chou, and P.-H. Marbot. The anthroform biorobotic arm: a system for the study of spinal circuits.Ann. Biomed. Eng. 1995, in press.

  16. Hasan, Z. A model of spindle afferent response to muscle stretch.J. Neurophys. 49:989–1005, 1983.

    CAS  Google Scholar 

  17. Hatze, H. A general myocybernetic control model of skeletal muscle.Biol. Cybern. 28:143–157, 1978.

    Article  PubMed  CAS  Google Scholar 

  18. He, J., W. S. Levine and G. E. Loeb. Feedback gains for correcting small perturbations to standing posture.IEEE Trans. Autom. Control. 36:322–332, 1991.

    Article  Google Scholar 

  19. Hill, A. V. The heat of shortening and the dynamic constants of muscle.Proc. Roy. Soc. 126B:136–195, 1938.

    Google Scholar 

  20. Hill, A. V.First and Last Experiments in Muscle Mechanics. Cambridge, UK: Cambridge University Press, 1970, 140 pp.

    Google Scholar 

  21. Hoffer, J. A., and S. Andreasson. Regulation of soleus muscle stiffness in premammilary cats: intrinsic and reflex components.J. Neurophys. 45:267–285, 1981.

    CAS  Google Scholar 

  22. Hogan, N. Adaptive control of mechanical impedance by coactivation of antagonistic muscles.IEEE Trans. Autom. Control. AC-29:681–690, 1984.

    Article  Google Scholar 

  23. Hogan, N. Principles underlying movement organization: upper limb. In:Multiple Muscle Systems: Biomechanics and Movement Organization, edited by J. M. Winters and S. L.-Y. Woo. New York: Springer-Verlag, 1990, pp. 149–164.

    Google Scholar 

  24. Hogan, N., and J. M. Winters. Principles underlying movement organization: upper limb and single joint. In:Multiple Muscle Systems: Biomechanics and Movement Organization, edited by J. M. Winters and S. L.-Y. Woo. New York: Springer-Verlag, 1990, pp. 182–194.

    Google Scholar 

  25. Houk, J. C. Regulation of stiffness by skeletomotor reflexes.Ann. Rev. Physiol. 41:99–114, 1979.

    Article  CAS  Google Scholar 

  26. Houk, J. C., and W. Z. Rymer. Neural control of muscle length and tension. In:Handbook of Physiology—The Nervous System II, vol. 8, edited by E.R. Kandel. 1981, pp. 257–323.

  27. Joyce, G. C., P. M. H. Rack, and D. R. Westbury. The mechanial properties of cat soleus muscle during controlled lengthening and shortening movements.J. Physiol. 204:461–474, 1969.

    PubMed  CAS  Google Scholar 

  28. Katz, B. The relation between force and speed in muscular contraction.J. Physiol. 96:45–64, 1939.

    PubMed  CAS  Google Scholar 

  29. Kleweno, D. G., and J. M. Winters. Effect of initial upper limb alignment on muscle contributions to isometric strength curves.J. Biomech. 26:143–153, 1993.

    Article  PubMed  Google Scholar 

  30. Lacquaniti, F., F. Licita and J. F. Soechting. The mechanical behavior of the human forearm in response to transient perturbations.Biol. Cybern. 44:35–46, 1982.

    Article  PubMed  CAS  Google Scholar 

  31. Lehman, S. L. A detailed biophysical model of human extraocular muscle. Berkeley: University of California, Ph.D. Dissertation, 1982.

    Google Scholar 

  32. Lehman, S., and L. Stark. Three algorithms for interpreting models consisting of ordinary differential equations: sensitivity coefficients, sensitivity functions, global optimization.Math. Biosci. 62:107–122, 1982.

    Article  Google Scholar 

  33. Liddell, E. G. T., and C. S. Sherrington. Reflexes in response to stretch (myotatic reflexes).Proc. Roy. Soc. Lond. 96B:212–242, 1924.

    Article  Google Scholar 

  34. Lieber, R. L., C. G. Brown, and C. L. Trestik. Model of muscle-tendon interaction during frog semitendinosis fixed-end contractions.J. Biomech. 25:421–428, 1992.

    Article  PubMed  CAS  Google Scholar 

  35. Loeb, G. E. The control and responses of mammalian muscle spindles during normally executed motor tasks.Exer. Sport Sci. Rev. 12:157–204, 1984.

    Article  CAS  Google Scholar 

  36. Loeb, G. E., and W. Levine. Linking musculoskeletal mechanics to sensorimotor neurophysiology. In:Multiple Muscle Systems: Biomechanics and Movement Organization, edited by J. M. Winters and S. L.-Y. Woo. New York: Springer-Verlag, 1990, pp. 165–181.

    Google Scholar 

  37. Ma, S., and G. I. Zahalak. Activation dynamics for a distribution-moment model of skeletal muscle. Proc. 6th Conf. Math Modelling, vol. 11. St. Louis, MO, pp. 778–782, 1987.

  38. Matthews, P. B. C. Muscle spindles and their motor control.Physiol. Rev. 44:219–288, 1964.

    PubMed  CAS  Google Scholar 

  39. Matthews, P. B. C. Evidence from the use of vibration that the human long-latency stretch reflex depends upon the spindle secondary afferents.J. Physiol. 348:383–415, 1986.

    Google Scholar 

  40. Morgan, D. From sarcomeres to whole muscles.J. Exp. Biol. 115:69–78, 1985.

    PubMed  CAS  Google Scholar 

  41. Morgan, D. Modeling of lengthening muscle: the role of inter-sarcomere dynamics. In:Multiple Muscle Systems: Biomechanics and Movement Organization, edited by J. M. Winters and S. L.-Y. Woo. New York: Springer-Verlag, 1990, pp. 46–56.

    Google Scholar 

  42. Mussa-Ivaldi, F., N. Hogan and E. Bizzi. Neural, mechanical, and geometric factors subserving arm posture in humans.J. Neurosci. 5:2732–2743, 1985.

    PubMed  CAS  Google Scholar 

  43. Nashner, L. M. and P. J. Cordo. Relation of automatic postural responses and reaction-time voluntary movements of human leg muscles.Exp. Brain Res. 43:395–405, 1981.

    Article  PubMed  CAS  Google Scholar 

  44. Otten, E., K. A. Scheepstra, and M. Hulliger. An integrated model of the mammalian muscle spindle. InAlpha and Gamma Motor Systems, edited by A. Taylor and M. Gladden. 1995, in press.

  45. Ramos, C. F., and L. W. Stark. Simulation studies of descending and reflex control of fast movements.J. Motor Behav. 19:38–61, 1987.

    Google Scholar 

  46. Ramos, C. F., and L. Stark. Are detailed models of the muscle spindle appropriate for simulation studies of the stretch reflex? A general method for model comparisons.Comp. Biomed. Res. 1995, in press.

  47. Rack, P. M., and D. R. Westbury. The short range stiffness of active mammalian muscle and its effect on mechanical properties.J. Physiol. 240:331–350, 1974.

    PubMed  CAS  Google Scholar 

  48. Schaafsma, A., E. Otten and J. D. van Willigen. A muscle spindle model for primary afferent firing based on a simulation of intrafusal mechanical events.J. Neurophys. 65:1297–1311, 1991.

    CAS  Google Scholar 

  49. Scott, S. H. Studies of the Morphometry and Mechanical Properties of Mammalian Muscle. Kingston: Queen's University, Ph.D. Dissertation, 1993.

    Google Scholar 

  50. Scott, S. H., and G. E. Loeb. The mechanical properties of the aponeurosis and tendon of the cat soleus muscle during whole-muscle isometric contractions.J. Morphol. 1995, in press.

  51. Shoemaker, M., and B. Hannaford. A study and model of the role of the Rhenshaw cell in regulating the transient firing of the motoneuron.Biol. Cybern. 71:251–262, 1994.

    PubMed  CAS  Google Scholar 

  52. Seif-Naraghi, A. H., and J. M. Winters. Effect of taskspecific linearization on musculoskeletal system control strategies. 1989 Biomech. Symp. ASME, AMD-98, 1989, pp. 347–350.

  53. Stark, L.Neurological Control Systems. New York: Plenum Press, 1968, 428 pp.

    Google Scholar 

  54. Stein, R. B., and T. Gordon, Nonlinear stiffness-force relationships in whole mammalian skeletal muscles.Can. J. Physiol. Pharmacol. 64:1236–1244, 1986.

    PubMed  CAS  Google Scholar 

  55. Stein, R. B., and M. N. Oguztoreli. The role of gammamotoneurons in mammalian reflex systems.Biol. Cybern. 39:171–179, 1981.

    Article  PubMed  CAS  Google Scholar 

  56. Stephenson, D. G., and D. A. Williams. Effects of sarcomere length of the force-pCa relation in fast- and slowtwitch skinned muscle fibres from the rat.J. Physiol. 333:637–653, 1982.

    PubMed  CAS  Google Scholar 

  57. Van der Helm, F. C. T. The Shoulder Mechanism: A Dynamic Approach. Delft: Delft University of Technology, Ph.D. Dissertation, 1991.

    Google Scholar 

  58. Willems, M. Architectural Heterogeneity and Function of Bi-Articular Muscle. Amsterdam: Free University, Ph.D. Thesis, 1994.

    Google Scholar 

  59. Winters, J. M. Generalized Analysis and Design of Antagonistic Muscle Models: Effect of Nonlinear Muscle-Joint Properties on the Control of Fundamental Movements. Berkeley: University of California, Ph.D. Dissertation, 1985.

    Google Scholar 

  60. Winters, J. M. Hill-based muscle models: a systems engineering perspective. In:Multiple Muscle Systems: Biomechanics and Movement Organization. edited by J. M. Winters and S. L.-Y. Woo. New York: Springer-Verlag, 1990, pp. 69–93.

    Google Scholar 

  61. Winters, J. M. Concepts in neuro-muscular modeling. In:3-D Analysis of Human Movement, Human Kinetics, edited by P. Allard, I. A. F. Stokes, and J.-P. Blanchi, 1993, pp. 257–292.

  62. Winters, J. M., and L. Stark. Analysis of fundamental movement patterns through the use of in-depth antagonistic muscle models.IEEE Trans. Biomed. Eng. BME-32:826–839, 1985.

    Article  CAS  Google Scholar 

  63. Winters, J. M., and L. Stark. Task-specific second-order movement models are encompassed by a global eighth-order nonlinear musculo-skeletal model. Proc. IEEE System, Man and Cybern., Tuscon, AZ, 1985, pp. 1111–1115.

  64. Winters, J. M., and L. Stark. Muscle models: what is gained and what is lost by varying model complexity.Biol. Cybern. 55:403–420, 1987.

    Article  PubMed  CAS  Google Scholar 

  65. Winters, J. M., L. Stark, and A. H. Seif-Naraghi. An analysis of the sources of muscle-joint system impedance.J. Biomech. 12:1011–1025, 1988.

    Article  Google Scholar 

  66. Winters, J. M., and F. C. T. Van der Helm. A field-based musculoskeletal framework for studying human posture and manipulation in 3D. Proc. of the Symp. on Modeling and Control of Biomed. Sys., Intern. Fed. on Autom. Control., Galveston, TX, 1994, pp. 410–415.

  67. Zahalak, G. I. Modeling musclemechanics (and energetics). In:Multiple Muscle Systems: Biomechanics and Movement Organization, edited by J. M. Winters, S. L.-Y. Woo. New York: Springer-Verlag, 1990, pp. 1–23.

    Google Scholar 

  68. Zajac, F. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control.CRC Crit. Review Biomed. Eng. 17:359–410, 1989.

    CAS  Google Scholar 

  69. Zajac, F., and J. M. Winters. Modeling musculoskeletal movement systems: joint and body-segment dynamics, musculotendon actuation, and neuromuscular control. In:Multiple Muscle Systems: Biomechanics and Movement Organizations, edited by J. M. Winters and S. L.-Y. Woo, New York: Springer-Verlag, 1990, pp. 121–148.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Biomedical Engineering Program, Department of Mechanical Engineering, Catholic University of America, Washington, DC

    Jack M. Winters

Authors
  1. Jack M. Winters
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Winters, J.M. An improved muscle-reflex actuator for use in large-scale neuromusculoskeletal models. Ann Biomed Eng 23, 359–374 (1995). https://doi.org/10.1007/BF02584437

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02584437

Keywords

Search

Navigation