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

AbstractA 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

[1]  K. Appenteng,et al.  Fusimotor activity in masseter nerve of the cat during reflex jaw movements. , 1980, The Journal of physiology.

[2]  R. R. Carter,et al.  Stiffness regulation by reflex action in the normal human hand. , 1990, Journal of neurophysiology.

[3]  A. Lindsay,et al.  Distribution of effective synaptic currents underlying recurrent inhibition in cat triceps surae motoneurons. , 1991, Journal of neurophysiology.

[4]  J. Houk,et al.  Sampling of total muscle force by tendon organs. , 1982, Journal of neurophysiology.

[5]  J. Houk,et al.  An evaluation of length and force feedback to soleus muscles of decerebrate cats. , 1970, Journal of neurophysiology.

[6]  B. Edin,et al.  Muscle afferent responses to isometric contractions and relaxations in humans. , 1990, Journal of neurophysiology.

[7]  J. Houk,et al.  Function of the spindle dynamic response in stiffness regulation—a predictive mechanism provided by non-linear feedback , 1981 .

[8]  Patrick E. Crago,et al.  Muscle–Tendon Model with Length History-Dependent Activation–Velocity Coupling , 1998, Annals of Biomedical Engineering.

[9]  J. Noth Autogenetic inhibition of extensor gamma‐motoneurones revealed by electrical stimulation of group I fibres in the cat. , 1983, The Journal of physiology.

[10]  Thomas Sinkjær,et al.  Simulations of the alpha motoneuron pool electromyogram reflex at different preactivation levels in man , 1994, Biological Cybernetics.

[11]  Jack M. Winters,et al.  An improved muscle-reflex actuator for use in large-scale neuromusculoskeletal models , 1995, Annals of Biomedical Engineering.

[12]  A Prochazka,et al.  Ensemble firing of muscle afferents recorded during normal locomotion in cats , 1998, The Journal of physiology.

[13]  R. Stein,et al.  Fusimotor control of muscle spindle sensitivity during respiration in the cat. , 1990, The Journal of physiology.

[14]  U. Windhorst,et al.  Activation of renshaw cells , 1990, Progress in Neurobiology.

[15]  C. Heckman,et al.  Recruitment of cat motoneurons in the absence of homonymous afferent feedback. , 2001, Journal of neurophysiology.

[16]  D. McCrea,et al.  Shared reflex pathways from Ib tendon organ afferents and Ia muscle spindle afferents in the cat. , 1983, The Journal of physiology.

[17]  Örjan Ekeberg,et al.  A computer based model for realistic simulations of neural networks , 1991, Biological Cybernetics.

[18]  M. Illert,et al.  Skeletofusimotor (β) innervation of proximal and distal forelimb muscles of the cat , 1995, Neuroscience Letters.

[19]  W. Rymer,et al.  Neural compensation for muscular fatigue: evidence for significant force regulation in man. , 1987, Journal of neurophysiology.

[20]  Chou-Ching K. Lin,et al.  Structural Model of the Muscle Spindle , 2004, Annals of Biomedical Engineering.

[21]  H. C. Lee,et al.  Statistical analysis of multiunit multipath neural communication , 1971 .

[22]  U. Windhorst,et al.  Responses of the spinal α-motoneurone-Renshaw cell system to various differentially distributed segmental afferent and descending inputs , 1985, Biological Cybernetics.

[23]  J. Houk,et al.  Improvement in linearity and regulation of stiffness that results from actions of stretch reflex. , 1976, Journal of neurophysiology.

[24]  J. Petit,et al.  Fast-conducting skeletofusimotor axons supplying intrafusal chain fibers in the cat peroneus tertius muscle. , 1977, Journal of neurophysiology.

[25]  J Houk,et al.  Responses of Golgi tendon organs to forces applied to muscle tendon. , 1967, Journal of neurophysiology.

[26]  C. F. Ramos,et al.  Behaviour space of a stretch reflex model and its implications for the neural control of voluntary movement , 2006, Medical and Biological Engineering and Computing.

[27]  D. Barker,et al.  Intramuscular branching of fusimotor fibres , 1965, The Journal of physiology.

[28]  M D Binder,et al.  Computer simulation of the steady-state input-output function of the cat medial gastrocnemius motoneuron pool. , 1991, Journal of neurophysiology.

[29]  P. Matthews,et al.  Interaction between short‐ and long‐latency components of the human stretch reflex during sinusoidal stretching. , 1993, The Journal of physiology.

[30]  F. Emonet-Dénand,et al.  Types of intra‐ and extrafusal muscle fibre innervated by dynamic skeleto‐fusimotor axons in cat peroneus brevis and tenuissimus muscles, as determined by the glycogen‐depletion method. , 1977, The Journal of physiology.

[31]  M. Binder,et al.  Summation of effective synaptic currents and firing rate modulation in cat spinal motoneurons. , 2000, Journal of neurophysiology.

[32]  A Prochazka,et al.  In‐series compliance of gastrocnemius muscle in cat step cycle: do spindles signal origin‐to‐insertion length? , 1990, The Journal of physiology.

[33]  J. Petit,et al.  A quantitative study of skeletofusimotor innervation in the cat peroneus tertius muscle. , 1982, The Journal of physiology.

[34]  R. Stein,et al.  Regulation of soleus muscle spindle sensitivity in decerebrate and spinal cats during postural and locomotor activities. , 1996, The Journal of physiology.

[35]  W. Rymer,et al.  Absence of force-feedback regulation in soleus muscle of the decerebrate cat , 1980, Brain Research.

[36]  T. Nichols,et al.  Mechanical analysis of heterogenic inhibition between soleus muscle and the pretibial flexors in the cat. , 1991, Journal of neurophysiology.

[37]  W. Rymer,et al.  An estimate of the secondary spindle receptor afferent contribution to the stretch reflex in extensor muscles of the decerebrate cat. , 1977, The Journal of physiology.

[38]  R. Durbaba,et al.  Distinctive patterns of static and dynamic gamma motor activity during locomotion in the decerebrate cat , 2000, The Journal of physiology.

[39]  H Johansson,et al.  Fusimotor reflexes in triceps surae muscle elicited by stretch of muscles in the contralateral hind limb of the cat. , 1986, The Journal of physiology.

[40]  C. C. A. M. Gielen,et al.  A model of the motor servo: Incorporating nonlinear spindle receptor and muscle mechanical properties , 1987, Biological Cybernetics.

[41]  S. Andreassen,et al.  Regulation of soleus muscle stiffness in premammillary cats: intrinsic and reflex components. , 1981, Journal of neurophysiology.

[42]  P. Matthews Evolving views on the internal operation and functional role of the muscle spindle. , 1981, The Journal of physiology.

[43]  F. Emonet-Dénand,et al.  Proportion of muscles spindles supplied by skeletofusimotor axons (beta-axons) in peroneus brevis muscle of the cat. , 1975, Journal of neurophysiology.

[44]  William J. Williams,et al.  Transfer Characteristics of Dispersive Nerve Bundles , 1972, IEEE Trans. Syst. Man Cybern..

[45]  H Hultborn,et al.  Synaptic activation of plateaus in hindlimb motoneurons of decerebrate cats. , 1998, Journal of neurophysiology.

[46]  F. Baldissera,et al.  The dynamic response of cat α-motoneurones investigated by intracellular injection of sinusoidal currents , 2004, Experimental Brain Research.