Skip to main content
SpringerLink
Log in

Neural and Mechanical Contributions to the Stretch Reflex: A Model Synthesis

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

A model for the soleus stretch reflex in the decerebrate cat was synthesized from models of the neural and muscular components, including the two proprioceptors (the muscle spindle and Golgi tendon organ) and their associated afferents (Ia, II, and Ib), the α motoneuron pool with its reflex pathways, the branches of the α motoneurons to the intrafusal muscles (β innervation), and the extrafusal muscle. Parameters for the muscle and receptor models were chosen independently to match their responses in isolation. Reflex gains and γ inputs were estimated to fit the response to stretch measured by Nichols and Houk. The chosen reflex gains and γ inputs are not unique; many different combinations reproduced the characteristic stretch response. With a single set of fixed parameters, the model predicted many mechanical properties of the stretch reflex, including linearization effects (when the stretch magnitude and direction are varied), as well as the dependence on operating force and initial muscle length. The model did not accurately predict the responses at higher stretch velocities, due to failure of the extrafusal muscle model. © 2002 Biomedical Engineering Society.

PAC02: 8719Ff, 8719Rr, 8719La

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. Adal, M. N., and D. Barker. Intramuscular branching of fusimotor fibers. J. Physiol. (London) 177:288-299, 1965.

    Google Scholar 

  2. Appelberg, B., H. Johansson, and P. Sojka. Fusimotor re-flexes in triceps surae muscle elicited by stretch of muscles in the contralateral hind limb of the cat. J. Physiol. (London) 373:419-441, 1986.

    Google Scholar 

  3. Appenteng, K., T. Morimoto, and A. Taylor. Fusimotor activity in masseter nerve to the cat during reflex jaw movements. J. Physiol. (London) 305:415-431, 1980.

    Google Scholar 

  4. Baldissera, F., P. Campadelli, and L. Piccinelli. The dynamic response of cat a-motoneurones investigated by intracellular injection of sinusoidal currents. Exp. Brain Res. 54:275-282, 1984.

    Google Scholar 

  5. Barker, D., F. Emonet-Denand, D. W. Harker, L. Jami, and Y. Laporte. Types of intra-and extrafusal muscle fiber innervated by dynamic skeleto-fusimotor axons in cat peroneus brevis and tenuissimus muscles, as determined by the glycogen-depletion method. J. Physiol. (London) 266:713-726, 1977.

    Google Scholar 

  6. Bennett, D. J., S. J. De Serres, and R. B. Stein. Regulation of soleus muscle spindle sensitivity in decerebrate and spinal cats during postural and locomotor activities. J. Physiol. (London) 495:835-50, 1996.

    Google Scholar 

  7. Bennett, D. J., H. Hultborn, B. Fedirchuk, and M. Gorassini. Synaptic activation of plateaus in hindlimb motoneurons of decerebrate cats. J. Neurophysiol. 80:2023-2037, 1998.

    Google Scholar 

  8. Carter, R., P. Crago, and M. Keith. Stiffness regulation by reflex action in the normal human hand. J. Neurophysiol. 64:105-118, 1990.

    Google Scholar 

  9. Crago, P. E., J. C. Houk, and W. Z. Rymer. Sampling of total muscle force by tendon organs. J. Neurophysiol. 47:1069-1083, 1982.

    Google Scholar 

  10. Edin, B. B., and A. B. Vallbo. Muscle afferent responses to isometric contractions and relaxations in humans. J. Neurophysiol. 63:1307-1313, 1990.

    Google Scholar 

  11. Ekeberg, O., P. Wallen, A. Lansner, H. Traven, L. Brodin, and S. Grillner. A computer based model for realistic simulations of neural networks. I. The single neuron and synaptic interaction. Biol. Cybern. 65:81-90, 1991.

    Google Scholar 

  12. Elek, J., A. Prochazka, M. Hulliger, and S. Vincent. In-series compliance of gastrocnemius muscle in cat step cycle: Do spindles signal origin-to-insertion length? J. Physiol. (London) 429:237-258, 1990.

    Google Scholar 

  13. Emonet-Denand, F., and Y. Laporte. Proportion of muscle spindles supplied by skeletofusimotor axons (b-axons) in peroneus brevis muscle of the cat. J. Neurophysiol. 38:1390-1394, 1975.

    Google Scholar 

  14. Gielen, C. C. A. M., and J. C. Houk. A model of the motor servo: Incorporating nonlinear spindle receptor and muscle mechanical properties. Biol. Cybern. 57:217-231, 1987.

    Google Scholar 

  15. Greer, J. J., and R. B. Stein. Fusimotor control of muscle spindle sensitivity during respiration in the cat. J. Physiol. (London) 422:245-264, 1990.

    Google Scholar 

  16. Haftel, V. K., J. F. Prather, C. J. Heckman, and T. C. Cope. Recruitment of cat motoneurons in the absence of homonymous afferent feedback. J. Neurophysiol. 86:616-628, 2001.

    Google Scholar 

  17. Harker, D. W., L. Jami, Y. Laporte, and J. Petit. Fastconducting skeletofusimotor axons supplying intrafusal chain fibers in the cat peroneus tertius muscle. J. Neurophysiol. 40:791-799, 1977.

    Google Scholar 

  18. Heckman, C. J., and M. D. Binder. Computer simulation of the steady-state input-output function of the cat medial gastrocnemius motoneuron pool. J. Neurophysiol. 65:952-967, 1991.

    Google Scholar 

  19. Hoffer, J. A., and S. Andreassen. Regulation of soleus muscle stiffness in premammillary cats: Intrinsic and reflex components. J. Neurophysiol. 45:267-285, 1981.

    Google Scholar 

  20. Houk, J. C., P. E. Crago, and W. Z. Rymer. Function of the spindle dynamic response in stiffness regulation-A predictive mechanism provided by nonlinear feedback. In: Muscle Receptors and Movement, edited by A. Taylor and A. Prochazka. London: Macmillan, 1981.

    Google Scholar 

  21. Houk, J. C., and W. Simon. Responses of Golgi tendon organs to forces applied to muscle tendon. J. Neurophysiol. 30:1466-1481, 1967.

    Google Scholar 

  22. Houk, J. C., J. J. Singer, and M. R. Goldman. An evaluation of length and force feedback to soleus muscles of decerebrate cats. J. Neurophysiol. 33:784-811, 1970.

    Google Scholar 

  23. Jami, L., K. S. K. Murphy, and J. Petit. A quantitative study of skeletofusimotor innervation in the cat peroneus tertius muscle. J. Physiol. (London) 325:125-144, 1982.

    Google Scholar 

  24. Jankowska, E., and D. A. McCrea. Shared reflex pathways from Ib tendon organ afferents and Ia muscle spindle afferents in the cat. J. Physiol. (London) 338:99-111, 1983.

    Google Scholar 

  25. Kanda, K., and W. Z. Rymer. An estimate of the secondary spindle receptor afferent contribution to the stretch reflex in extensor muscles of the decerebrate cat. J. Physiol. (London) 264:63-87, 1977.

    Google Scholar 

  26. Kirsch, R. F., and W. Z. Rymer. Neural compensation for muscular fatigue: Evidence for significant force regulation in man. J. Neurophysiol. 37:1893-1910, 1987.

    Google Scholar 

  27. Koehler, W., and U. Windhorst. Responses of the spinal a-motoneurone-Renshaw cell system to various differentially distributed segmental afferent and descending inputs. Biol. Cybern. 51:417-426, 1985.

    Google Scholar 

  28. Lee, H. C., and J. H. Milsum. Statistical analysis of multiunit multipath neural communication. Math. Biosci. 11:181-202, 1971.

    Google Scholar 

  29. Lin, C. C. K., and P. E. Crago. Structural model of the muscle spindle. Ann. Biomed. Eng. 30:68-83, 2002.

    Google Scholar 

  30. Lindsay, A. D., and M. D. Binder. Distribution of effective synaptic currents underlying recurrent inhibition on cat triceps surae motoneurons. J. Neurophysiol. 65:168-177, 1991.

    Google Scholar 

  31. Matthews, P. B. C. Evolving views on the internal operation and functional role of the muscle spindle. J. Physiol. (London) 320:1-30, 1981.

    Google Scholar 

  32. Matthews, P. B. C. Interaction between short-and longlatency components of the human stretch reflex during sinusoidal stretching. J. Physiol. (London) 462:503-527, 1993.

    Google Scholar 

  33. McWilliam, P. N. A quantitative study of b innervation of muscle spindles in small muscles of the hind limb of the cat. J. Physiol. (London) 239:43-44, 1974.

    Google Scholar 

  34. Munson J. B. Synaptic inputs to type-identified motor units. In: The Segmental Motor System, edited by M. D. Binder and L. M. Mendell. London: Oxford University Press, 1990, pp. 291-307.

    Google Scholar 

  35. Nichols, T. R., and J. C. Houk. Improvement in linearity and regulation of stiffness that results from actions of stretch reflex. J. Neurophysiol. 39:119-142, 1976.

    Google Scholar 

  36. Nichols, T. R., and D. Koffler-Smulevitz. Mechanical analysis of heterogenic inhibition between soleus muscle and the pretibial flexors in the cat. J. Neurophysiol. 66:1139-1155, 1991.

    Google Scholar 

  37. Noth, J. Autogenetic inhibition of extensor g-motoneurones revealed by electrical stimulation of group I fibers in the cat. J. Physiol. (London) 342:51-65, 1983.

    Google Scholar 

  38. Powers, R. K., and M. D. Binder. Summation of effective synaptic currents and firing rate modulation in cat spinal motoneurons. J. Neurophysiol. 83:483-500, 2000.

    Google Scholar 

  39. Prochazka, A., and M. Gorassini. Ensemble firing of muscle afferents recorded during normal locomotion in cats. J. Physiol. (London) 507:293-304, 1998.

    Google Scholar 

  40. Ramos, C. F., S. S. Haxisalihzade, and L. W. Stark. Behaviour space of a stretch reflex model and its implications for the neural control of voluntary movement. Med. Biol. Eng. Comput. 28:15-23, 1990.

    Google Scholar 

  41. Rymer, W. Z., and Z. Hasan. Absence of force-feedback regulation in soleus muscle of the decerebrate cat. Brain Res. 184:203-209, 1980.

    Google Scholar 

  42. Scott, J. J. A., H. Kummel, and M. Illert. Skeletofusimotor (?) innervation of proximal and distal forelimb muscles of the cat. Neurosci. Lett. 190:1-4, 1995.

    Google Scholar 

  43. Shue, G-H., and P. E. Crago. Muscle-tendon model with length history dependent activation-velocity coupling. Ann. Biomed. Eng. 26:369-380, 1998.

    Google Scholar 

  44. Slot, P. J., and T. Sinkjaer. Simulations of the alpha motoneuron pool electromyogram reflex at different preactivation levels in man. Biol. Cybern. 70:351-358, 1994.

    Google Scholar 

  45. Taylor, A., P. H. Ellaway, R. Durbaba, and S. Rawlinson. Distinctive patterns of static and dynamic gamma motor activity during locomotion in the decerebrate cat. J. Physiol. (London) 529:825-836, 2000.

    Google Scholar 

  46. Williams, W. J. Transfer characteristics of dispersive nerve bundles. IEEE Trans. Syst. Man. Cybern. 2:72-85, 1972.

    Google Scholar 

  47. Windhorst, U. Activation of Renshaw cells. Prog. Neurobiol. (Oxford) 35:135-179, 1990.

    Google Scholar 

  48. Winters, J. M. An improved muscle-reflex actuator for use in large-scale neuromusculoskeletal models. Ann. Biomed. Eng. 23:359-374, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Cleveland FES Center, L.B. Stokes VA Medical Center, and Department of Biomedical Engineering, Case Western Reserve University, Cleveland, OH

    Chou-Ching K. Lin & Patrick E. Crago

Authors
  1. Chou-Ching K. Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrick E. Crago
    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

Lin, CC.K., Crago, P.E. Neural and Mechanical Contributions to the Stretch Reflex: A Model Synthesis. Annals of Biomedical Engineering 30, 54–67 (2002). https://doi.org/10.1114/1.1432692

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1114/1.1432692

Search

Navigation