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Neural Control of Muscle Length and Tension

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Abstract

The sections in this article are:

1 Control Theory Concepts
1.1 Systems and Models
1.2 Control Systems
1.3 Feedback, Feedforward, and Adaptive Systems
1.4 Principle of Negative Feedback
1.5 Regulated Variables and Properties
1.6 Control Configurations
1.7 Summary
2 Hypotheses of Motor Servo Function
2.1 Salient Features of the Available Sensors
2.2 Follow‐up Servo Hypothesis
2.3 Spindle Receptors as Model‐Reference Error Detectors
2.4 Conditional Feedback and Servo Assistance
2.5 β‐System and the Possibility for Zero Sensitivity
2.6 Stiffness Regulation
2.7 Summary Model
2.8 Adaptive Models
2.9 Summary
3 Muscle Mechanical Stiffness
3.1 Stiffness Definitions
3.2 Length Dependence
3.3 Recruitment of Motor Units
3.4 Rate Modulation of Motor Units
3.5 Instantaneous Stiffness and Short‐Range Elasticity
3.6 Instantaneous Stiffness Beyond the Short‐Range Region
3.7 Ramp Responses: Transient Properties and Nonlinearity
3.8 Natural Combinations of Recruitment and Rate Modulation
3.9 Summary
4 Central Pathways
4.1 Primary Ending Projections
4.2 Tendon Organ Projections
4.3 Projections From Secondary Endings and Group II Free Nerve Endings
4.4 Projections From Groups III and IV Free Nerve Endings
4.5 Clasp‐Knife Reflex
4.6 Long‐Loop Reflexes
4.7 Summary
5 Simplified Animal Models
5.1 Decerebrate Preparation
5.2 Spinal Preparation
5.3 Summary
6 Tonic Stretch Reflex in Functionally Isolated Muscles
6.1 Basic Features of the Stretch Reflex
6.2 Static Force‐Length Relations
6.3 Normalized Stiffness
6.4 Mechanically and Neurally Mediated Components
6.5 Actions of Control Signals on the Motor Servo
6.6 Dependence of Incremental Stiffness on Initial Force
6.7 Loop Gain of Force Feedback
6.8 Summary
7 Static Regulatory Characteristics in Intact Subjects
7.1 Skeletal Mechanics and Coordinate Systems
7.2 Steady‐State Responses to Changes in Load Force
7.3 Torque‐Angle Relations
7.4 Equivalent Stiffness and the Concept of Composite Motor Servos
7.5 Effect of Instructional Set
7.6 Gain Variation vs. Gain Control
7.7 Summary
8 Dynamic Responses to Mechanical Disturbances
8.1 Dynamic Features of Force Development
8.2 Dependence of Transient Responses on Initial Force
8.3 Amplitude Dependence and Linearity
8.4 Asymmetry of Motor Servo Response
8.5 Compensation for Yielding
8.6 Predictive Compensation: Feedforward vs. Nonlinear Feedback Viewpoints
8.7 Vibration and the Stretch Reflex
8.8 Velocity Dependence and Damping
8.9 Summary
9 Implementation of Movement Commands
9.1 α‐γ‐Relations
9.2 Positional Stiffness Deduced From Spindle Relations
9.3 β‐Innervation of Muscle Spindles
9.4 Analytical Approaches to Actions of α‐, β‐, and γ‐Motoneurons
9.5 Equilibrium Point Control
9.6 Stiffness Regulation vs. Stiffness Control
9.7 Perturbations During Movement
9.8 Compliance, Load Compensation, and Biological Design
9.9 Summary
Figure 1. Figure 1.

Basic organizational plan of the motor servo. Muscle and load forces act on load properties (e.g., inertia) to produce length changes. Muscle force is regulated by motor output from skeletomotor neurons (reflex action) but also varies in response to changes in length (so‐called mechanical response). Muscle length (and velocity) is monitored by spindle receptors and force by Golgi tendon organs. These signals provide excitation and inhibition, respectively, to skeletomotor neurons by way of central pathways (certainly segmental, and perhaps also suprasegmental). Neural control signals are sent to skeletomotor and fusimotor neurons and to interneurons in the reflex pathways.

Figure 2. Figure 2.

System models and their inverses. A: the system operator S converts an input x into an output y. B: the inverse of S, written S−1, converts y back into x.

Adapted from Houk . Systems and models. In: Medical Physiology (14th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1980
Figure 3. Figure 3.

Basic signals and components of a control system. Command signals designating desired performance are operated on by controller to produce forcing functions. These are inputs to the controlled system that produce desired changes in controlled variables. Uncontrolled inputs act as disturbances and produce undesired changes in controlled variables.

From Houk . Homeostasis and control principles. In: Medical Physiology (14th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1980
Figure 4. Figure 4.

Feedforward and feedback configurations for regulation. The function of a regulator is to diminish the effects that disturbances have on regulated variables. In a feedforward system regulatory actions are based on signals from sensors that detect potential disturbances, whereas in a feedback system regulatory actions are based on signals from sensors that detect the effects disturbances have on regulated variables.

From Houk . Homeostasis and control principles. In: Medical Physiology (14th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1980
Figure 5. Figure 5.

Simple example of a negative‐feedback system. Appropriate forcing functions are generated by 2 elementary operations—error detection (subtraction) and amplification.

From Houk . Homeostasis and control principles. In: Medical Physiology (14th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1980
Figure 6. Figure 6.

Generalized negative‐feedback system. The regulated variable y is expressed in terms of 2 components. Open loop (uncompensated) response to a disturbance (yd) and the compensatory response (yc) produced by the feedback system. The system is characterized by loop gain (G).

From Houk . Homeostasis and control principles. In: Medical Physiology (14th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1980
Figure 7. Figure 7.

Model‐reference control systems. A: forcing functions are sent to both the controlled system S1 and a model of the controlled system S2. A reference error is computed as the difference between actual output y1 and model output y2. Options 1, 2, and 3 show different ways in which the reference error signal can be used. B: diagram to illustrate how the spindle receptor can be seen as a model reference error detector. The controlled system is main muscle and its load, intrafusal muscle is assumed to the model system, and the spindle afferent endings are situated to detect differences between main and intrafusal muscle shortening.

From Houk . Homeostasis and control principles. In: Medical Physiology (14th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1980
Figure 8. Figure 8.

Block diagram illustrating α‐γ‐relations. α‐Commands produce shortening of extrafusal muscle and γ‐commands produce shortening of intrafusal muscle. α‐Commands reduce spindle discharge, whereas γ‐commands increase it, suggesting that spindle receptors may function as reference error detectors as in Figure .

Figure 9. Figure 9.

Block diagram illustrating the organization of β‐innervation. Forcing functions from β‐motoneurons promote both extrafusal and intrafusal shortening. As in Figures and , spindle receptors are shown detecting the difference between intrafusal and extrafusal shortening, a reference error. The positive‐feedback loop from β‐motoneurons through intrafusal muscle and spindle receptors back on β‐motoneurons raises the possibility of zero‐sensitivity operation.

Figure 10. Figure 10.

Component analysis of hypothetical stretch reflex. Stretch from L0 to L1 causes force to increase from F0 to F1. Reflex stiffness is defined by the slope of the line segment a‐d equal to (F1F0)/(L1L0). The diagram dissects this overall response into 3 components: the muscular‐mechanical component arises from the length‐tension properties of the muscle (dashed curve), the length‐feedback component originates in spindle discharge and increases stiffness, and the force‐feedback component originates in tendon organ discharge and decreases stiffness.

From Houk . Feedback control of muscle: a synthesis of the peripheral mechanisms. In: Medical Physiology (13th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1974
Figure 11. Figure 11.

Summary model of the motor servo. Solid line represents the static relationship between muscle force and length observed when control signals (cf. Fig. ) remain constant. Control signals could act to change the threshold length (dashed curve) or to alter the slope of the force‐length relation (dotted curve). The usual mode of control appears to be the former. Trajectories a, b, and c illustrate the load dependence of responses to a control signal.

From Houk . Reproduced, with permission, from Annu. Rev. Physiol., vol. 41. © 1979 by Annual Reviews, Inc
Figure 12. Figure 12.

Block diagram to illustrate the interaction between motor servo properties (represented by the operator ϕ) and the mechanical load. The operator L represents load properties, fd is a disturbance force, f is muscle force, x is muscle length, and x0 is the threshold length of the strength reflex (Fig. ) established by central motor commands.

Figure 13. Figure 13.

Two‐stage model of adaptive motor control. Motor output signals are assumed to be generated by 2 parallel processes that have rather different characteristic properties. Continuous Processor is assumed to operate in an analogue fashion, combining inputs from stretch receptors to produce continuous feedback compensation. The S‐R (stimulus‐response) Processor is assumed to operate more like a logical device, using sensory cues to trigger the release of preselected motor programs in a discontinuous fashion. Adaptive control is assumed to result mainly from the establishment of flexible S‐R relations rather than from alterations in the gain of the continuous‐feedback loops.

From Houk . Posture and Movement: Perspective for Integrating Sensory and Motor Research on the Mammalian Nervous System, edited by R. E. Talbott and D. R. Humphrey. New York: Raven, © 1979
Figure 14. Figure 14.

Length‐tension characteristic of skeletal muscle. Active + Passive curve shows the force produced by a typical muscle that is maximally activated, as a function of length throughout the physiological range. Passive curve shows the corresponding force when the muscle is entirely relaxed. Shaded region, represents the control zone within which muscle force can be modulated by recruitment and rate modulation of motor units.

Figure 15. Figure 15.

Length‐tension relations in cat soleus. The broken curves represent the length‐tension plots obtained at different stimulus rates. The solid curves are the force‐length trajectories obtained when the muscle was stretched at constant velocity (7.2 mm/s) beginning from each of the points (the x's) on the length tension curves.

From Joyce et al.
Figure 16. Figure 16.

Responses of cat soleus muscle to ramp‐and‐hold stretch (5 mm at 7.2 mm/s) applied while the muscle was being stimulated at each of 3 rates. Dashed box encloses the incremental transient response, shown as a function of ramp amplitude and direction in Figure .

Adapted from Joyce et al.
Figure 17. Figure 17.

Incremental transient responses of cat soleus muscle obtained with different amplitudes of stretch and release. Muscle was stimulated at 13.3 impulses/s before and throughout each force record. First vertical marker indicates the time of ramp plateau (160 ms) and the second indicates 1 s after ramp initiation. Note that the changes in force are not scaled versions of each other as they would be for a linear system.

From Nichols
Figure 18. Figure 18.

Summary of the major autogenetic connections of muscle afferents to spinal motoneurons. Well‐documented pathways such as Ia, Ib, and flexor‐reflex afferents (“FRA”) are shown as continuous lines. More speculative or incompletely documented connections are shown as dashed lines. ○, Excitatory interneurons; •, inhibitory interneurons. Renshaw cells are omitted for simplicity.

Figure 19. Figure 19.

Neural elements involved in clasp‐knife reflex. Primary and secondary spindle afferents provide autogenetic excitation to extensor motoneurons. These neurons also receive tonic excitatory input from the vestibulospinal tract. In the decerebrate state, dorsal reticular neurons that inhibit segmental FRA interneurons are also active, reducing flexor‐reflex activity. Section of the dorsolateral quadrants of the cord interrupts the dorsal reticulospinal pathway, thereby releasing segmental flexion reflexes. These include the clasp‐knife reflex.

Figure 20. Figure 20.

Averaged rectified EMG response from wrist extensors of a normal subject following sudden flexor displacements of the wrist. The vertical line indicates when torque motor was turned on. Subject was instructed to actively return the handle to the central zone as soon as the displacement occurred. Onset latencies for the components of the response: M1 = 32 ms; M2 = 59 ms; M3 = 85 ms; “voluntary” activity = 107 ms. Downward deflection of handle position trace represents flexion at the wrist.

From Lee and Tatton
Figure 21. Figure 21.

Response to a fast brief stretch of the long thumb flexor in a patient with a lesion in the right brain stem (due to stroke), causing loss of pain and temperature sensation in the left arm and loss of appreciation of joint position, vibration, and tactile discrimination in the right arm, but no apparent motor deficit. The upper records show the angular position of the right and left thumbs. The middle and lower records show the full‐wave rectified EMG recorded from flexor pollicis longus of the left and right hands. Subject held the thumb stationary against a standing force of 2 N. At time 0, indicated by the vertical marker, a force of 30 N was applied for 3 ms. Each trace is the average of 24 trials. In the EMG record from the left long thumb flexor there are clear responses at monosynaptic latency (25 ms), and later responses at 40 and 55 ms. In the record for the right long thumb flexor, the monosynaptic response is still evident, but the medium‐ and long‐latency responses are not apparent.

From Marsden et al.
Figure 22. Figure 22.

Stretch reflex of quadriceps muscle of decerebrate cat. Trace T shows the time course of stretch, M shows the force produced in the muscle with autogenic reflexes intact, and P shows the passive muscle force produced after cutting the motor nerve.

From Liddell and Sherrington
Figure 23. Figure 23.

Stretch reflex of the soleus muscle of decerebrate cat. Upper curve shows total tension during stretch at 1.7 mm/s. The stretch was maintained for 2 s before shortening muscle at the same velocity to obtain the descending curve. Lower curves show the passive tension obtained during stretch and release while the reflex was being inhibited.

From Matthews
Figure 24. Figure 24.

Comparison of tonic stretch reflex with length‐tension curves for the soleus muscle of decerebrate cat. The heavy line represents the static force‐length relationship obtained by waiting 30 s for adaptation at each successive length. Other curves are length‐tension curves obtained at the end of the experiment by stimulating different proportions of the cut ventral roots at 8 pulses/s. The passive curve is dotted.

From Nichols
Figure 25. Figure 25.

Family of force‐length relations obtained at different intensities of Deiters' nucleus stimulation. The ordinate is the force in g·wt and the abscissa is muscle extension in mm. Reflex force was registered while the muscle (gastrocnemius in decerebrate cat) was stretched slowly to its maximal physiological length. Deiters' nucleus stimulation at a fixed rate was delivered before and throughout the period of stretching, to mimic a constant level of central motor command. The numbers represent stimulus intensity (V) and the unlabeled curve is the response of the passive muscle.

From Fel'dman and Orlovski
Figure 26. Figure 26.

Incremental stiffness of the stretch reflex in the decerebrate cat as a function of initial force and initial length. At each initial length the initial (or operating) force was modulated by eliciting a strong reflex, and stiffness was measured from responses to 1‐mm pulses lasting 200 ms that were applied to the soleus muscle as force progressively decayed. Each point represents the incremental force‐to‐length ratio at the end of one pulse.

From Hoffer and Andreassen
Figure 27. Figure 27.

Comparison of reflex and muscle mechanical responses at different levels of initial force. The input was a 2‐mm ramp stretch applied at 12.5 mm/s to the soleus muscle. Initial force was modulated with a crossed‐extension reflex to 5 different steady values in the case of the reflex responses. The muscle mechanical responses represent the force change recorded in an areflexive muscle that was electrically stimulated at 8 pulses/s. The mechanical response obtained was scaled (simulated recruitment) to watch the initial conditions.

From Nichols
Figure 28. Figure 28.

Summary of relation between motor servos regulating contraction of single muscles (muscle A and muscle B) and their combined action as synergists. A given motor servo is represented by the loop that includes the muscle and its autogenetic feedback pathway. Factors that couple output from the two muscles are 1) both muscles act on the same load, 2) muscle afferent signals from one muscle are also distributed to the other muscle as synergistic feedback, 3) connections between neural elements of each motor servo (internal linkage) may coordinate action between muscles, and 4) central motor commands may be distributed to each motor servo.

Figure 29. Figure 29.

Stretch and unloading reflexes in human arm. Symmetrical step increases or decreases in load force produce essentially symmetrical displacements of forearm, whereas biceps EMG responses are quite asymmetrical under these conditions. Step change in load force is depicted in uppermost traces as dashed lines, while resultant arm force, recorded by a load cell mounted within the apparatus, is a continuous line. Heavy traces represent responses to step increases in load force and light traces to equal but opposite decreases. EMG responses are full wave rectified and filtered (30 ms time constant) and calibrated in units of isometric force. Responses are ensemble averages taken from 2 different subjects using the no‐intervention instruction (cf. Fig. ).

From Crago, Houk, and Hasan
Figure 30. Figure 30.

Reflex (a) and reaction‐time (b) components of response to a disturbance in force. Muscle length is determined by the interaction between the motor servo and the opposing load. •, Initial equilibrium point, at which the force generated by the stretch reflex is equal and opposite to the initial load force. An increase in load force stretches the muscle along the force‐length trajectory a, reaching a new equilibrium position (○), which is the point where final load is equal and opposite to stretch reflex force. The new equilibrium has been achieved at the expense of a significant length increase. The final load can be supported at the same length if the force‐length relation is shifted to reach the position shown by dashed line. This shift may appear as a reaction‐time movement causing shortening along trajectory b.

Figure 31. Figure 31.

Torque‐angle curves relating the total moment developed by muscles at the elbow joint to the static joint angle, recorded following a series of load changes. ○, Joint positions reached following the change in load. Solid lines connect the angles achieved following load changes introduced from particular initial angles α6(1), α6(2), and α6(3). Dashed lines describe the external moments produced by the corresponding loads.

Adapted from Asatryan and Fel'dman
Figure 32. Figure 32.

The response to stretch of the long thumb flexor in human subjects depends upon prior instruction. At the outset, thumb is held flexed at 151°, supporting a force of 2 N, and it is then stretched abruptly at the point marked 0. Subject is instructed to either hold the thumb in a steady position (N), to relax (L), or to pull as hard as possible (P). The upper records show superimposed traces of angular position, the center traces show full wave rectified EMG (recorded from surface electrodes place over flexor pollicis longus), and the lower traces are fully integrated EMG records.

From Marsden et al.
Figure 33. Figure 33.

Features of reaction‐time movements of the arm, initiated in response to step change in load force. Force change occurs at time zero. The subject is told either to compensate (C) or “do not intervene voluntarily” (NI). In the latter case, both subjects (A, B) produced simple springlike response (NI traces). When the subject attempts to compensate for the perturbation (C), the initial trajectory is similar to that of NI but deviates at a point whose latency varies from trial to trial and with increasing choice (compensate vs. do not intervene). Upper trace in B depicts an inappropriate response, obtained with the compensate instruction. Records are of single trials, following ±18 N load changes in A and ±15 N change in B.

From Crago, Houk, and Hasan
Figure 34. Figure 34.

Dependence of reflex (R) and mechanical (M) responses on the amplitude and direction of length change of soleus muscle in the decerebrate cat. Ramp changes in length had the same duration (160 ms) but were of differing amplitude. The amplitude of length change and the initial force are shown to the left of each record. The mechanical response (M) was derived from a different soleus muscle during stimulation of the ventral roots in a distributed manner at 8 pulses/s. Records in A represent responses to stretch, while those in B represent response to symmetrical release.

From Nichols and Houk
Figure 35. Figure 35.

Asymmetry of reflex action and its origin in primary endings. The response of soleus muscle in the decerebrate cat to stretch and release applied at 12.5 mm/s are compared in A. The responses labeled mechanical represent the changes in force that would occur if there were no reflexly generated changes in motor unit discharge or in the number of motor units recruited. Reflex action is the difference between the overall reflex and its mechanical component. Part B illustrates the response of primary spindle afferent, examined under closely comparable conditions. The greater reflex action associated with stretch, as contrasted with release, appears to be due mainly to the greater dynamic response of primary endings to stretch, as contrasted with release.

From Houk, Rymer, and Crago
Figure 36. Figure 36.

EMG responses from left triceps brachii collected during a series of 60 falls, in which subject falls forward until movement is arrested by outstretched arms. Records are centered about the moment of impact. Upper traces in each panel are rectified EMG. Lower traces are of vertical force exerted against a platform. Panel A shows averaged responses to first 20 falls, Panel B, the response to the last 20 falls in the sequence.

From Dietz et al.
Figure 37. Figure 37.

Vibration of the soleus muscle in the decerebrate cat prevents reflex compensation for muscle yield. Longitudinal tendon vibration was used to block the stretch response of primary endings to demonstrate the importance of the dynamic response in the transient phase of stiffness regulation. The initial force of the normal reflex response was augmented to match that developed in the presence of vibration with a cross‐extensor reflex. The difference between reflex and vibration traces is attributed mainly to primary endings, whereas the difference between vibration and mechanical traces is attributed mainly to secondary endings, although tendon organ inhibition may limit the magnitude of this component. Mechanical trace is an estimate, based on stretch of muscle stimulated electrically at 8 pulses/s via the ventral roots. Reflex and vibration responses are ensemble averages.

From Houk, Rymer, and Crago
Figure 38. Figure 38.

Lack of dependence of EMG and force of the soleus on stretch velocity. Records show averaged response to 10 mm stretch, applied at three velocities, 1, 10, and 100 mm/s. Force output, measured at ramp end, shows approximately a 2‐fold increase for a 100‐fold increase in stretch velocity. EMG increment measured at the same point is slightly larger, but increase is still modest in comparison with increase in velocity. Dashed traces represent the mechanical responses.

From Houk
Figure 39. Figure 39.

Movements made by a normal human subject and by an analogue model of the limb. A: position and velocity records of movements made by subject during performance of visually guided step tracking task. B: analogous traces obtained from the model in which movements were produced by a step change in resting spring constant. C: a representation of a model in which the static position of a limb is treated as the point of equilibrium of opposing springs of variable stiffness. D: phase plane plots of movements obtained from human subject and from model. In the model, different movement amplitudes were produced by varying the size of the step in spring constant.

From Cooke


Figure 1.

Basic organizational plan of the motor servo. Muscle and load forces act on load properties (e.g., inertia) to produce length changes. Muscle force is regulated by motor output from skeletomotor neurons (reflex action) but also varies in response to changes in length (so‐called mechanical response). Muscle length (and velocity) is monitored by spindle receptors and force by Golgi tendon organs. These signals provide excitation and inhibition, respectively, to skeletomotor neurons by way of central pathways (certainly segmental, and perhaps also suprasegmental). Neural control signals are sent to skeletomotor and fusimotor neurons and to interneurons in the reflex pathways.



Figure 2.

System models and their inverses. A: the system operator S converts an input x into an output y. B: the inverse of S, written S−1, converts y back into x.

Adapted from Houk . Systems and models. In: Medical Physiology (14th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1980


Figure 3.

Basic signals and components of a control system. Command signals designating desired performance are operated on by controller to produce forcing functions. These are inputs to the controlled system that produce desired changes in controlled variables. Uncontrolled inputs act as disturbances and produce undesired changes in controlled variables.

From Houk . Homeostasis and control principles. In: Medical Physiology (14th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1980


Figure 4.

Feedforward and feedback configurations for regulation. The function of a regulator is to diminish the effects that disturbances have on regulated variables. In a feedforward system regulatory actions are based on signals from sensors that detect potential disturbances, whereas in a feedback system regulatory actions are based on signals from sensors that detect the effects disturbances have on regulated variables.

From Houk . Homeostasis and control principles. In: Medical Physiology (14th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1980


Figure 5.

Simple example of a negative‐feedback system. Appropriate forcing functions are generated by 2 elementary operations—error detection (subtraction) and amplification.

From Houk . Homeostasis and control principles. In: Medical Physiology (14th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1980


Figure 6.

Generalized negative‐feedback system. The regulated variable y is expressed in terms of 2 components. Open loop (uncompensated) response to a disturbance (yd) and the compensatory response (yc) produced by the feedback system. The system is characterized by loop gain (G).

From Houk . Homeostasis and control principles. In: Medical Physiology (14th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1980


Figure 7.

Model‐reference control systems. A: forcing functions are sent to both the controlled system S1 and a model of the controlled system S2. A reference error is computed as the difference between actual output y1 and model output y2. Options 1, 2, and 3 show different ways in which the reference error signal can be used. B: diagram to illustrate how the spindle receptor can be seen as a model reference error detector. The controlled system is main muscle and its load, intrafusal muscle is assumed to the model system, and the spindle afferent endings are situated to detect differences between main and intrafusal muscle shortening.

From Houk . Homeostasis and control principles. In: Medical Physiology (14th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1980


Figure 8.

Block diagram illustrating α‐γ‐relations. α‐Commands produce shortening of extrafusal muscle and γ‐commands produce shortening of intrafusal muscle. α‐Commands reduce spindle discharge, whereas γ‐commands increase it, suggesting that spindle receptors may function as reference error detectors as in Figure .



Figure 9.

Block diagram illustrating the organization of β‐innervation. Forcing functions from β‐motoneurons promote both extrafusal and intrafusal shortening. As in Figures and , spindle receptors are shown detecting the difference between intrafusal and extrafusal shortening, a reference error. The positive‐feedback loop from β‐motoneurons through intrafusal muscle and spindle receptors back on β‐motoneurons raises the possibility of zero‐sensitivity operation.



Figure 10.

Component analysis of hypothetical stretch reflex. Stretch from L0 to L1 causes force to increase from F0 to F1. Reflex stiffness is defined by the slope of the line segment a‐d equal to (F1F0)/(L1L0). The diagram dissects this overall response into 3 components: the muscular‐mechanical component arises from the length‐tension properties of the muscle (dashed curve), the length‐feedback component originates in spindle discharge and increases stiffness, and the force‐feedback component originates in tendon organ discharge and decreases stiffness.

From Houk . Feedback control of muscle: a synthesis of the peripheral mechanisms. In: Medical Physiology (13th ed.), edited by V. B. Mountcastle. St. Louis, MO: The C. V. Mosby Co., 1974


Figure 11.

Summary model of the motor servo. Solid line represents the static relationship between muscle force and length observed when control signals (cf. Fig. ) remain constant. Control signals could act to change the threshold length (dashed curve) or to alter the slope of the force‐length relation (dotted curve). The usual mode of control appears to be the former. Trajectories a, b, and c illustrate the load dependence of responses to a control signal.

From Houk . Reproduced, with permission, from Annu. Rev. Physiol., vol. 41. © 1979 by Annual Reviews, Inc


Figure 12.

Block diagram to illustrate the interaction between motor servo properties (represented by the operator ϕ) and the mechanical load. The operator L represents load properties, fd is a disturbance force, f is muscle force, x is muscle length, and x0 is the threshold length of the strength reflex (Fig. ) established by central motor commands.



Figure 13.

Two‐stage model of adaptive motor control. Motor output signals are assumed to be generated by 2 parallel processes that have rather different characteristic properties. Continuous Processor is assumed to operate in an analogue fashion, combining inputs from stretch receptors to produce continuous feedback compensation. The S‐R (stimulus‐response) Processor is assumed to operate more like a logical device, using sensory cues to trigger the release of preselected motor programs in a discontinuous fashion. Adaptive control is assumed to result mainly from the establishment of flexible S‐R relations rather than from alterations in the gain of the continuous‐feedback loops.

From Houk . Posture and Movement: Perspective for Integrating Sensory and Motor Research on the Mammalian Nervous System, edited by R. E. Talbott and D. R. Humphrey. New York: Raven, © 1979


Figure 14.

Length‐tension characteristic of skeletal muscle. Active + Passive curve shows the force produced by a typical muscle that is maximally activated, as a function of length throughout the physiological range. Passive curve shows the corresponding force when the muscle is entirely relaxed. Shaded region, represents the control zone within which muscle force can be modulated by recruitment and rate modulation of motor units.



Figure 15.

Length‐tension relations in cat soleus. The broken curves represent the length‐tension plots obtained at different stimulus rates. The solid curves are the force‐length trajectories obtained when the muscle was stretched at constant velocity (7.2 mm/s) beginning from each of the points (the x's) on the length tension curves.

From Joyce et al.


Figure 16.

Responses of cat soleus muscle to ramp‐and‐hold stretch (5 mm at 7.2 mm/s) applied while the muscle was being stimulated at each of 3 rates. Dashed box encloses the incremental transient response, shown as a function of ramp amplitude and direction in Figure .

Adapted from Joyce et al.


Figure 17.

Incremental transient responses of cat soleus muscle obtained with different amplitudes of stretch and release. Muscle was stimulated at 13.3 impulses/s before and throughout each force record. First vertical marker indicates the time of ramp plateau (160 ms) and the second indicates 1 s after ramp initiation. Note that the changes in force are not scaled versions of each other as they would be for a linear system.

From Nichols


Figure 18.

Summary of the major autogenetic connections of muscle afferents to spinal motoneurons. Well‐documented pathways such as Ia, Ib, and flexor‐reflex afferents (“FRA”) are shown as continuous lines. More speculative or incompletely documented connections are shown as dashed lines. ○, Excitatory interneurons; •, inhibitory interneurons. Renshaw cells are omitted for simplicity.



Figure 19.

Neural elements involved in clasp‐knife reflex. Primary and secondary spindle afferents provide autogenetic excitation to extensor motoneurons. These neurons also receive tonic excitatory input from the vestibulospinal tract. In the decerebrate state, dorsal reticular neurons that inhibit segmental FRA interneurons are also active, reducing flexor‐reflex activity. Section of the dorsolateral quadrants of the cord interrupts the dorsal reticulospinal pathway, thereby releasing segmental flexion reflexes. These include the clasp‐knife reflex.



Figure 20.

Averaged rectified EMG response from wrist extensors of a normal subject following sudden flexor displacements of the wrist. The vertical line indicates when torque motor was turned on. Subject was instructed to actively return the handle to the central zone as soon as the displacement occurred. Onset latencies for the components of the response: M1 = 32 ms; M2 = 59 ms; M3 = 85 ms; “voluntary” activity = 107 ms. Downward deflection of handle position trace represents flexion at the wrist.

From Lee and Tatton


Figure 21.

Response to a fast brief stretch of the long thumb flexor in a patient with a lesion in the right brain stem (due to stroke), causing loss of pain and temperature sensation in the left arm and loss of appreciation of joint position, vibration, and tactile discrimination in the right arm, but no apparent motor deficit. The upper records show the angular position of the right and left thumbs. The middle and lower records show the full‐wave rectified EMG recorded from flexor pollicis longus of the left and right hands. Subject held the thumb stationary against a standing force of 2 N. At time 0, indicated by the vertical marker, a force of 30 N was applied for 3 ms. Each trace is the average of 24 trials. In the EMG record from the left long thumb flexor there are clear responses at monosynaptic latency (25 ms), and later responses at 40 and 55 ms. In the record for the right long thumb flexor, the monosynaptic response is still evident, but the medium‐ and long‐latency responses are not apparent.

From Marsden et al.


Figure 22.

Stretch reflex of quadriceps muscle of decerebrate cat. Trace T shows the time course of stretch, M shows the force produced in the muscle with autogenic reflexes intact, and P shows the passive muscle force produced after cutting the motor nerve.

From Liddell and Sherrington


Figure 23.

Stretch reflex of the soleus muscle of decerebrate cat. Upper curve shows total tension during stretch at 1.7 mm/s. The stretch was maintained for 2 s before shortening muscle at the same velocity to obtain the descending curve. Lower curves show the passive tension obtained during stretch and release while the reflex was being inhibited.

From Matthews


Figure 24.

Comparison of tonic stretch reflex with length‐tension curves for the soleus muscle of decerebrate cat. The heavy line represents the static force‐length relationship obtained by waiting 30 s for adaptation at each successive length. Other curves are length‐tension curves obtained at the end of the experiment by stimulating different proportions of the cut ventral roots at 8 pulses/s. The passive curve is dotted.

From Nichols


Figure 25.

Family of force‐length relations obtained at different intensities of Deiters' nucleus stimulation. The ordinate is the force in g·wt and the abscissa is muscle extension in mm. Reflex force was registered while the muscle (gastrocnemius in decerebrate cat) was stretched slowly to its maximal physiological length. Deiters' nucleus stimulation at a fixed rate was delivered before and throughout the period of stretching, to mimic a constant level of central motor command. The numbers represent stimulus intensity (V) and the unlabeled curve is the response of the passive muscle.

From Fel'dman and Orlovski


Figure 26.

Incremental stiffness of the stretch reflex in the decerebrate cat as a function of initial force and initial length. At each initial length the initial (or operating) force was modulated by eliciting a strong reflex, and stiffness was measured from responses to 1‐mm pulses lasting 200 ms that were applied to the soleus muscle as force progressively decayed. Each point represents the incremental force‐to‐length ratio at the end of one pulse.

From Hoffer and Andreassen


Figure 27.

Comparison of reflex and muscle mechanical responses at different levels of initial force. The input was a 2‐mm ramp stretch applied at 12.5 mm/s to the soleus muscle. Initial force was modulated with a crossed‐extension reflex to 5 different steady values in the case of the reflex responses. The muscle mechanical responses represent the force change recorded in an areflexive muscle that was electrically stimulated at 8 pulses/s. The mechanical response obtained was scaled (simulated recruitment) to watch the initial conditions.

From Nichols


Figure 28.

Summary of relation between motor servos regulating contraction of single muscles (muscle A and muscle B) and their combined action as synergists. A given motor servo is represented by the loop that includes the muscle and its autogenetic feedback pathway. Factors that couple output from the two muscles are 1) both muscles act on the same load, 2) muscle afferent signals from one muscle are also distributed to the other muscle as synergistic feedback, 3) connections between neural elements of each motor servo (internal linkage) may coordinate action between muscles, and 4) central motor commands may be distributed to each motor servo.



Figure 29.

Stretch and unloading reflexes in human arm. Symmetrical step increases or decreases in load force produce essentially symmetrical displacements of forearm, whereas biceps EMG responses are quite asymmetrical under these conditions. Step change in load force is depicted in uppermost traces as dashed lines, while resultant arm force, recorded by a load cell mounted within the apparatus, is a continuous line. Heavy traces represent responses to step increases in load force and light traces to equal but opposite decreases. EMG responses are full wave rectified and filtered (30 ms time constant) and calibrated in units of isometric force. Responses are ensemble averages taken from 2 different subjects using the no‐intervention instruction (cf. Fig. ).

From Crago, Houk, and Hasan


Figure 30.

Reflex (a) and reaction‐time (b) components of response to a disturbance in force. Muscle length is determined by the interaction between the motor servo and the opposing load. •, Initial equilibrium point, at which the force generated by the stretch reflex is equal and opposite to the initial load force. An increase in load force stretches the muscle along the force‐length trajectory a, reaching a new equilibrium position (○), which is the point where final load is equal and opposite to stretch reflex force. The new equilibrium has been achieved at the expense of a significant length increase. The final load can be supported at the same length if the force‐length relation is shifted to reach the position shown by dashed line. This shift may appear as a reaction‐time movement causing shortening along trajectory b.



Figure 31.

Torque‐angle curves relating the total moment developed by muscles at the elbow joint to the static joint angle, recorded following a series of load changes. ○, Joint positions reached following the change in load. Solid lines connect the angles achieved following load changes introduced from particular initial angles α6(1), α6(2), and α6(3). Dashed lines describe the external moments produced by the corresponding loads.

Adapted from Asatryan and Fel'dman


Figure 32.

The response to stretch of the long thumb flexor in human subjects depends upon prior instruction. At the outset, thumb is held flexed at 151°, supporting a force of 2 N, and it is then stretched abruptly at the point marked 0. Subject is instructed to either hold the thumb in a steady position (N), to relax (L), or to pull as hard as possible (P). The upper records show superimposed traces of angular position, the center traces show full wave rectified EMG (recorded from surface electrodes place over flexor pollicis longus), and the lower traces are fully integrated EMG records.

From Marsden et al.


Figure 33.

Features of reaction‐time movements of the arm, initiated in response to step change in load force. Force change occurs at time zero. The subject is told either to compensate (C) or “do not intervene voluntarily” (NI). In the latter case, both subjects (A, B) produced simple springlike response (NI traces). When the subject attempts to compensate for the perturbation (C), the initial trajectory is similar to that of NI but deviates at a point whose latency varies from trial to trial and with increasing choice (compensate vs. do not intervene). Upper trace in B depicts an inappropriate response, obtained with the compensate instruction. Records are of single trials, following ±18 N load changes in A and ±15 N change in B.

From Crago, Houk, and Hasan


Figure 34.

Dependence of reflex (R) and mechanical (M) responses on the amplitude and direction of length change of soleus muscle in the decerebrate cat. Ramp changes in length had the same duration (160 ms) but were of differing amplitude. The amplitude of length change and the initial force are shown to the left of each record. The mechanical response (M) was derived from a different soleus muscle during stimulation of the ventral roots in a distributed manner at 8 pulses/s. Records in A represent responses to stretch, while those in B represent response to symmetrical release.

From Nichols and Houk


Figure 35.

Asymmetry of reflex action and its origin in primary endings. The response of soleus muscle in the decerebrate cat to stretch and release applied at 12.5 mm/s are compared in A. The responses labeled mechanical represent the changes in force that would occur if there were no reflexly generated changes in motor unit discharge or in the number of motor units recruited. Reflex action is the difference between the overall reflex and its mechanical component. Part B illustrates the response of primary spindle afferent, examined under closely comparable conditions. The greater reflex action associated with stretch, as contrasted with release, appears to be due mainly to the greater dynamic response of primary endings to stretch, as contrasted with release.

From Houk, Rymer, and Crago


Figure 36.

EMG responses from left triceps brachii collected during a series of 60 falls, in which subject falls forward until movement is arrested by outstretched arms. Records are centered about the moment of impact. Upper traces in each panel are rectified EMG. Lower traces are of vertical force exerted against a platform. Panel A shows averaged responses to first 20 falls, Panel B, the response to the last 20 falls in the sequence.

From Dietz et al.


Figure 37.

Vibration of the soleus muscle in the decerebrate cat prevents reflex compensation for muscle yield. Longitudinal tendon vibration was used to block the stretch response of primary endings to demonstrate the importance of the dynamic response in the transient phase of stiffness regulation. The initial force of the normal reflex response was augmented to match that developed in the presence of vibration with a cross‐extensor reflex. The difference between reflex and vibration traces is attributed mainly to primary endings, whereas the difference between vibration and mechanical traces is attributed mainly to secondary endings, although tendon organ inhibition may limit the magnitude of this component. Mechanical trace is an estimate, based on stretch of muscle stimulated electrically at 8 pulses/s via the ventral roots. Reflex and vibration responses are ensemble averages.

From Houk, Rymer, and Crago


Figure 38.

Lack of dependence of EMG and force of the soleus on stretch velocity. Records show averaged response to 10 mm stretch, applied at three velocities, 1, 10, and 100 mm/s. Force output, measured at ramp end, shows approximately a 2‐fold increase for a 100‐fold increase in stretch velocity. EMG increment measured at the same point is slightly larger, but increase is still modest in comparison with increase in velocity. Dashed traces represent the mechanical responses.

From Houk


Figure 39.

Movements made by a normal human subject and by an analogue model of the limb. A: position and velocity records of movements made by subject during performance of visually guided step tracking task. B: analogous traces obtained from the model in which movements were produced by a step change in resting spring constant. C: a representation of a model in which the static position of a limb is treated as the point of equilibrium of opposing springs of variable stiffness. D: phase plane plots of movements obtained from human subject and from model. In the model, different movement amplitudes were produced by varying the size of the step in spring constant.

From Cooke
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James C. Houk, W. Zev Rymer. Neural Control of Muscle Length and Tension. Compr Physiol 2011, Supplement 2: Handbook of Physiology, The Nervous System, Motor Control: 257-323. First published in print 1981. doi: 10.1002/cphy.cp010208