Abstract
The stiffness of the human elbow joint was investigated during targeted, 1.0-rad voluntary flexion movements at speeds ranging from slow (1.5 rad/s) to very fast (6.0 rad/s). A torque motor produced controlled step position errors in the execution of the movements. The steps began at the onset of movement, rose to an amplitude of 0.15 rad in 100 ms, and had a duration equal to movement duration. The net joint torque (muscle torque) resisting the step perturbation was computed from the applied torque, the joint acceleration, and the limb inertia. Subjects resisted the imposed step changes with approximately step changes in the net muscle torque. The mean resistance torque divided by the step amplitude was computed and is referred to as the stiffness. The stiffness increased with the voluntary movement speed, over the range of speeds (1.5–6 rad/s). The stiffness increased linearly with the magnitude of the net muscle torque on the unperturbed trials (referred to as “background torque”). The stiffness changed by only 20% when the step amplitude ranged from 0.05 to 0.15 rad. The mechanical resonant frequency (f r), estimated from the average stiffness estimates, ranged from 0.8 to 3.0 Hz. The resonant frequency approximately equaled the principal frequency component of the movement f m. On average: f r = 0.96 f m+0.46. During the fixed, 100-ms rise time of the step, the resistance was not linearly related to the background torque. At slower speeds the resistance was relatively greater during this rise time. However, when the imposed step perturbation was modified so that its rise time occurred in a time proportional to the movement duration (rather than in the fixed, 100-ms, time), the muscle torque resisting the motor during this rise time was proportional to the background torque. When these modified step responses were plotted on a time scale normalized to the movement duration, they all had approximately the same shape. Apparently the muscle viscosity scaled with the stiffness so as to maintain the constant response shape (constant damping ratio). The observed “tuning” of the mechanical properties to the movement speed is suggested to be important in the robust generation of smooth stereotyped voluntary movements.
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References
Akazawa K, Milner TE, Stein RB (1983) Modulation of reflex EMG and stiffness in response to stretch of human finger muscle. J Neurophysiol 49: 16–27
Amis A, Prochazka A, Short D, Trend PST, Ward A (1987) Relative displacements in muscle and tendon during human arm movements. J Physiol (Lond) 389: 37–44
Atkeson CG, Hollerbach JM (1985) Kinematics features of unrestrained vertical arm movements. J Neurosci 5: 2318–2330
Bawa P, Stein RB (1976) Frequency response of human soleus muscle. J Neurophysiol 39: 788–793
Bennett DJ (1991) Dynamic scaling in human elbow joint movements (abstract). Third IBRO World Congress of Neuroscience, IBRO, Montreal
Bennett DJ (1993) Electromyographic responses to constant position errors imposed during voluntary elbow joint movement in human. Exp Brain Res 95:499–508
Bennett DJ (1993) Stretch reflex responses in the human elbow joint during a voluntary movement. J Physiol (Lond) (in press)
Bennett DJ, Hollerbach JM, Xu Y, Hunter IW (1992) Time-varying stiffness of human elbow joint during cyclic voluntary movement. Exp Brain Res 88: 433–442
Cannon SC, Zahalak GI (1982) The mechanical behaviour of active human skeletal muscle in small oscillations. J Biomech 15: 111–121
Gottlieb GL, Agarwal GC (1979) Response to sudden torques about ankle in man: myotatic reflex. J Neurophysiol 42: 91–106
Hill AV (1938) The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond [Biol] 126: 136–195
Hoffer JA, Andreassen S (1981) Regulation of soleus muscle stiffness in premammillary cat: intrinsic and reflexive components. J Neurophysiol 45: 267–285
Houk JC, Rymer WZ, Crago PE (1981) Dependence of dynamic response of spindle receptors on the muscle length and velocity. J Neurophysiol 46: 143–166
Joyce GC, Rack PMH, Westbury DR (1969) The mechanical properties of cat soleus muscle during controlled lengthening and shortening movements. J Physiol (Lond) 204: 461–474
Latash ML (1992) Virtual trajectories, joint stiffness, and changes in the limb natural frequency during single-joint oscillatory movements. Neurosci 49: 209–220
MacNeil JB, Kearney RE, Hunter IW (1992) Identification of timevarying biological systems from ensemble data. IEEE Trans Biomed Eng 39: 1213–1225
Matthews PBC, Stein RB (1969) The sensitivity of the muscle spindle afferents to small sinusoidal changes in length. J Physiol (Lond) 200: 723–743
Matthews PBC, Watson JDG (1981) Effect of vibrating agonist or antagonist muscle on the reflex response to sinusoidal displacement of the human forearm. J Physiol (Lond) 321: 297–316
Milner TE (1993) Dependence of elbow viscoelastic behavior on speed and loading in voluntary movements. Exp Brain Res 93: 177–180
Nichols TR, Houk JC (1976) Improvement in linearity and regulation of stiffness that results from actions of stretch reflex. J Neurophysiol 39: 119–142
Rack RMH, Ross HF (1984) The tendon of flexor pollicis longus: its effects on the muscular control of force and position at the human thumb. J Physiol (Lond) 351: 99–110
Rack PMH, Westbury DR (1974) The short range stiffness of active mammalian muscle and its effect on mechanical properties. J Physiol (Lond) 240: 331–350
Sinkjaer T, Toft E, Andreassen S, Hornemann BC (1988) Muscle stiffness in human ankle dorsiflexors: intrinsic and reflex components. J Neurophysiol 60: 1110–1121
Soechting JF, Dufresne JR, Lacquaniti F (1981) Time-varying properties of the myotatic response in man during some simple motor tasks. J Neurophysiol 46: 1226–1243
Stein RB, Cody FWJ, Capaday C (1988) The trajectories of human wrist movements. J Neurophysiol 59: 1814–1830
Walsh EG, Wright GW (1987) Inertia, resonant frequency, stiffness and kinetic energy of the human forearm. Q J Exp Physiol 72: 161–170
Weiss PL, Hunter IW, Kearney RE (1988) Human ankle joint stiffness over the full range of muscle activation levels. J Biomech 21: 539–544
Zahalak GI, Pramod R (1985) Myoelectric response of the human triceps brachii to displacement controlled oscillations of the forearm. Exp Brain Res 58: 305–317
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Bennett, D.J. Torques generated at the human elbow joint in response to constant position errors imposed during voluntary movements. Exp Brain Res 95, 488–498 (1993). https://doi.org/10.1007/BF00227142
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DOI: https://doi.org/10.1007/BF00227142