Abstract
A phenomenological theory of muscle dynamics has been elaborated on the basis of data obtained in experiments on hind limb extensor muscles of narcotized cat. Functional dependence of muscle length on external load was explored in conditions of a constant frequency of the efferent stimulation. It was shown that the system under study could be presented for a rather wide class of input signals as a system with nonlinear statics and linear dynamics. The nonlinear statics was shown to be determined mainly by the hysteretical effects of muscle contraction, whereas dynamic element was described by the first order linear differential equation corresponding to the traditional three-component mechanical model of the muscle. A hypothesis was proposed to explain the hysteresis in active muscle on the basis of functioning of the troponin-tropomyosin regulatory complex. Elaborated mathematical model of muscle dynamics can be used to predict and evaluate changes in the muscle length evoked by arbitrary changes in the external load.
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References
Abbot BC, Aubert XM (1952) The force exerted by active striated muscle during and after change of length. J Physiol 117:77–86
Curtin NA, Davies RE (1972) Chemical and mechanical changes during stretching of activated skeletal muscle. Cold Spring Harbor Symp Quant Biol 37:619–626
Deshcherevsky VI (1977) Mathematical models of muscle contraction. Nauka, Moscow
Edman KAP, Elzinga C, Noble MIM (1978) Enhancement of mechanical performance by stretch during tetanic contractions of vertebrate skeletal muscle fibres. J Physiol 281:139–155
Gurfinkel' VS, Levik YuS (1985) Skeletal muscle, structure and function. Nauka, Moscow
Hill AV (1970) First and last experiments in muscle mechanics. Univ. Press, Cambridge
Huxley AF (1974) Muscular contraction. J Physiol 243:1–43
Joyce GC, Rack PMH (1969) Isotonic lengthening and shortening movements of cat soleus muscle. J Physiol 204:475–491
Kostyukov AI (1985a) Dynamics of efferent control of muscular contraction. Determination of transient responses: external load-muscle length. Neurophysiology 17:334–343
Kostyukov AI (1985b) Dynamics of efferent control of muscular contraction. Determination of transient responses: efferent stimulation frequency-muscle length. Neurophysiology 17:468–475
Kostyukov AI (1986a) Hysteretical properties of muscle contraction under conditions of continuous and intermittent stimulation of efferents. Neurophysiology 18:696–699
Kostyukov AI (1986b) Indeterminacy of the equilibrium value of joint angle and its connection with hysteretical properties of muscle contraction. Neurophysiology 18:699–701
Kostyukov AI, Korneev VV, Ivanov AE (1986) Indetermination of the equilibrium length in the active muscle. Neurophysiology 18:561–563
Rack PMH, Westbury DR (1969) The effects of length and stimulus rate on tension in the isometric cat soleus muscle. J Physiol 204:443–460
Rack PMH, Westbury DR (1974) The short range stiffness of active mammalian muscle and its effect on mechanical properties. J Physiol 240:331–350
Stein RB (1974) The peripheral control of movement. Physiol Rev 54:215–243
Stephenson DG, Wendt IR (1984) Length dependence of changes in sarcoplasmic calcium concentration and myofibrillar calcium sensitivity in striated muscle fibres. J Muscle Res Cell Motillity 5:243–272
Talbot SA, Gessner U (1973) Systems physiology. Wiley, New York London Sydney Toronto
Weber A, Murray JM (1973) Molecular control mechanisms in muscle contraction. Physiol Rev 53:612–673
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Kostyukov, A.I. Muscle dynamics: Dependence of muscle length on changes in external load. Biol. Cybernetics 56, 375–387 (1987). https://doi.org/10.1007/BF00319517
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DOI: https://doi.org/10.1007/BF00319517