A myocybernetic control model of skeletal muscle

A mathematical model of skeletal muscle is presented which contains the two physiological control parameters stimulation rate and motor unit recruitment. The model is complete in the sense that it adequately describes all possible contractive states normally occurring in living muscle. The modelling procedure relies entirely on established myo-physiological facts and each assumption made is substantiated by experimental data. Extensive simulation studies reveal that the model is capable of correctly predicting practically all known phenomena of the muscular force-output. A simplified version of the model is also presented, particularly suitable for inclusion as the driving structure in complex musculoskeletal link systems. This version was successfully tested in the prediction of an optimal human motion. The present control model is believed to fill a gap in the literature on models of muscle, and may be expected to provide a sound basis for research into the optimal control aspects of muscular contraction, and to stimulate such research.

[1]  R. Close Dynamic properties of mammalian skeletal muscles. , 1972, Physiological reviews.

[2]  D. Jacobson,et al.  Studies of human locomotion via optimal programming , 1971 .

[3]  T T Soong,et al.  A stochastic model for biological tissue elasticity in simple elongation. , 1973, Journal of biomechanics.

[4]  Archibald Vivian Hill,et al.  A discussion on muscular contraction and relaxation: their physical and chemical basis - Introduction , 1950, Proceedings of the Royal Society of London. Series B - Biological Sciences.

[5]  R. Stein,et al.  Tremor and other oscillations in neuromuscular systems , 2004, Biological Cybernetics.

[6]  F H NORRIS,et al.  Isometric relaxation of striated muscle. , 1961, The American journal of physiology.

[7]  An Analysis of Oscillations in NeuroMuscular Systems * , 2003 .

[8]  S. Walker,et al.  Potentiation and hysteresis induced by stretch and subsequent release of papillary muscle of the dog. , 1960, The American journal of physiology.

[9]  A. Huxley,et al.  The variation in isometric tension with sarcomere length in vertebrate muscle fibres , 1966, The Journal of physiology.

[10]  A V HILL The series elastic component of muscle. , 1950, Proceedings of the Royal Society of London. Series B, Biological sciences.

[11]  G. Falk,et al.  Linear electrical properties of striated muscle fibres observed with intracellular electrodes , 1964, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[12]  D. Wilkie Measurement of the series elastic component at various times during a single muscle twitch , 1956, The Journal of physiology.

[13]  O. Lippold,et al.  Motor unit activity in the voluntary contraction of human muscle , 1954, The Journal of physiology.

[14]  H. Sugi,et al.  Tension changes during and after stretch in frog muscle fibres , 1972, The Journal of physiology.

[15]  R. H. Adrian,et al.  The kinetics of mechanical activation in frog muscle , 1969, The Journal of physiology.

[16]  A Eberstein,et al.  Slow and fast twitch fibers in human skeletal muscle. , 1968, The American journal of physiology.

[17]  J. Gillis,et al.  The site of action of calcium in producing contraction in striated muscle , 1969, The Journal of physiology.

[18]  R. Stein,et al.  Predictions and ecperimental tests of a visco-elastic muscle model using elastic and inertial loads , 2004, Biological Cybernetics.

[19]  A. Bahler,et al.  Modeling of mammalian skeletal muscle. , 1968, IEEE transactions on bio-medical engineering.

[20]  A. F. Huxley,et al.  Local activation of striated muscle fibres , 1958 .

[21]  T. L. Hill,et al.  Theoretical formalism for the sliding filament model of contraction of striated muscle. Part I. , 1974, Progress in biophysics and molecular biology.

[22]  F. Zajac,et al.  A study of the coordination of cat hindlimb muscles during a maximal vertical jump , 1975, 1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.

[23]  Frank,et al.  A study of controllability of body motion in a biped by a linearized model , 1974 .

[24]  C T Dragomir,et al.  On the nature of the forces acting between myofilaments in resting state and under contraction. , 1970, Journal of theoretical biology.

[25]  F. G. Evans,et al.  Strength of biological materials , 1970 .

[26]  René Thom,et al.  Structural stability and morphogenesis , 1977, Pattern Recognit..

[27]  S. A. A. G. Antz A CONSTITUTIVE EQUATION FOR THE PASSIVE PROPERTIES OF MUSCLE * , 2003 .

[28]  G Falk,et al.  Predicted delays in the activation of the contractile system. , 1968, Biophysical journal.

[29]  Lawrence Stark,et al.  Neurological Control Systems: Studies in Bioengineering , 1995 .

[30]  R. Stein,et al.  Changes in firing rate of human motor units during linearly changing voluntary contractions , 1973, The Journal of physiology.

[31]  D. Wilkie The relation between force and velocity in human muscle , 1949, The Journal of physiology.

[32]  R. Ramsey,et al.  The isometric length‐tension diagram of isolated skeletal muscle fibers of the frog , 1940 .

[33]  J. Délèze,et al.  The mechanical properties of the semitendinosus muscle at lengths greater than its length in the body , 1961, The Journal of physiology.

[34]  B. R. Jewell,et al.  The mechanical properties of relaxing muscle , 1960, The Journal of physiology.

[35]  H. Hatze A model of skeletal muscle suitable for optimal motion problems , 1974 .

[36]  R. Natori,et al.  Excitability of isolated myofibrils. , 1962 .

[37]  E. Geoffrey Walsh Physiology of the nervous system , 1957 .

[38]  A. Crowe A mechanical model of muscle and its application to the intrafusal fibres of the mammalian muscle spindle. , 1970, Journal of biomechanics.

[39]  R. Stein,et al.  Synchronization of human motor units: possible roles of exercise and supraspinal reflexes. , 1975, Electroencephalography and clinical neurophysiology.

[40]  H. Hatze The complete optimization of a human motion , 1976 .

[41]  R. S. Alexander,et al.  MUSCLE STRETCH AND THEORIES OF CONTRACTION. , 1965, The American journal of physiology.

[42]  S. Lowey,et al.  Substructure of the myosin molecule. II. The light chains of myosin. , 1971, Journal of molecular biology.

[43]  Lee D. Peachey,et al.  THE SARCOPLASMIC RETICULUM AND TRANSVERSE TUBULES OF THE FROG'S SARTORIUS , 1965, The Journal of cell biology.

[44]  A. Bahler,et al.  Series elastic component of mammalian skeletal muscle. , 1967, The American journal of physiology.

[45]  A. Bahler,et al.  The Active State of Mammalian Skeletal Muscle , 1967, The Journal of general physiology.

[46]  S. Lowey,et al.  Substructure of the myosin molecule. I. Subfragments of myosin by enzymic degradation. , 1969, Journal of molecular biology.

[47]  R B Stein,et al.  The orderly recruitment of human motor units during voluntary isometric contractions , 1973, The Journal of physiology.

[48]  D. G. Green A note on modelling muscle in physiological regulators , 2006, Medical and biological engineering.

[49]  A. Huxley Muscle structure and theories of contraction. , 1957, Progress in biophysics and biophysical chemistry.

[50]  F. Julian,et al.  The effect of calcium on the force‐velocity relation of briefly glycerinated frog muscle fibres , 1971, The Journal of physiology.

[51]  W. Parmley,et al.  Series Elasticity in Heart Muscle: Its Relation To Contractile Element Velocity And Proposed Muscle Models , 1967, Circulation research.

[52]  A. Hodgkin,et al.  Potassium contractures in single muscle fibres , 1960, The Journal of physiology.

[53]  J. Desmedt,et al.  Kinetics of Myofilament Activation in Potentiated Contraction: Staircase Phenomenon in Human Skeletal Muscle , 1968, Nature.

[54]  Y C Fung,et al.  Mathematical representation of the mechanical properties of the heart muscle. , 1970, Journal of biomechanics.

[55]  R. J. Podolsky,et al.  Evidence for Depolarization of the Internal Membrane System in Activation of Frog Semitendinosus Muscle , 1966, Nature.

[56]  H Hatze,et al.  A theory of contraction and a mathematical model of striated muscle. , 1973, Journal of theoretical biology.

[57]  A. Huxley,et al.  LOCAL ACTIVATION OF MUSCLE , 1959, Annals of the New York Academy of Sciences.

[58]  P. Rack,et al.  The effects of length and stimulus rate on tension in the isometric cat soleus muscle , 1969, The Journal of physiology.

[59]  R. W. Little,et al.  A constitutive equation for collagen fibers. , 1972, Journal of biomechanics.

[60]  B. Katz,et al.  Biophysical aspects of neuro-muscular transmission. , 1956, Progress in biophysics and biophysical chemistry.

[61]  Dorothy S. Russell,et al.  Pathology of Tumours of the Nervous System , 1972 .

[62]  A. Bahler,et al.  The Dynamic Properties of Mammalian Skeletal Muscle , 1968, The Journal of general physiology.

[63]  A. Huxley,et al.  Proposed Mechanism of Force Generation in Striated Muscle , 1971, Nature.

[64]  B. R. Jewell,et al.  An analysis of the mechanical components in frog's striated muscle , 1958, The Journal of physiology.

[65]  F. Jöbsis,et al.  Calcium release and reabsorption in the sartorius muscle of the toad. , 1966, Biochemical and biophysical research communications.

[66]  C D Marsden,et al.  Isolated single motor units in human muscle and their rate of discharge during maximal voluntary effort. , 1971, The Journal of physiology.

[67]  S. Ebashi,et al.  Calcium ion and muscle contraction. , 1968, Progress in biophysics and molecular biology.

[68]  D. Wilkie,et al.  The dynamics of muscular contraction , 1958, The Journal of physiology.

[69]  F. Buchthal,et al.  The rheology of the cross striated muscle fibre, with particular reference to isotonic conditions , 1951 .

[70]  L. Hefner,et al.  Elastic components of cat papillary muscle. , 1967, The American journal of physiology.

[71]  G. Brindley,et al.  THE UNDERSTANDING OF THE BRAIN , 1973 .

[72]  R. Woledge,et al.  The thermoelastic effect of change of tension in active muscle , 1961, The Journal of physiology.

[73]  R. Stein,et al.  An analysis of oscillations in neuro-muscular systems , 1975 .

[74]  W. J. Williams,et al.  An electronic muscle simulator for demonstration and neuromuscular systems modelling , 1970, Medical and biological engineering.