Energy-optimal controls in the mammalian neuromuscular system

The hypothesis is advanced that the specific patterns of motor unit recruitment and stimulation frequencies observed in mammalian skeletal muscle under static isometric contractions are determined by a minimum-energy principle. By performing a constrained energy optimization based on a control model of skeletal muscle comprising three different fibre types, and appropriate expressions for the energy rates, it is indeed possible to obtain detailed predictions of recruitment and stimulation frequency patterns which agree well with the experimentally observed functions, thereby providing strong support for the minimum-energy hypothesis. Since the orderly recruitment sequence determined by the size principle is also, independently, predicted by the minimum-energy principle, it is concluded that there exists a relationship between motor unit size and the myoenergetic properties of the recruited unit. It is suggested that this relationship, together with the possibility of adjusting the relative proportions of the fibre types present in a muscle, constitutes an optimal adaptation of the neuromuscular system for practically all types of muscular performances normally encountered. For various types of muscles, the energy rates as functions of the force output are also discussed.

[1]  E. Adrian,et al.  The discharge of impulses in motor nerve fibres , 1929, The Journal of physiology.

[2]  E. Adrian,et al.  The discharge of impulses in motor nerve fibres , 1928, The Journal of physiology.

[3]  D W Bronk The energy expended in maintaining a muscular contraction , 1930, The Journal of physiology.

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

[5]  B. C. Abbott The heat production associated with the maintenance of a prolonged contraction and the extra heat produced during large shortening , 1951, The Journal of physiology.

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

[7]  F H NORRIS,et al.  Action potentials of single motor units in normal muscle. , 1955, Electroencephalography and clinical neurophysiology.

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

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

[10]  J. Hannerz,et al.  Recruitment order of motor units on voluntary contraction: changes induced by proprioceptive afferent activity. , 1968, Journal of neurology, neurosurgery, and psychiatry.

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

[12]  E. Henneman,et al.  Orderly recruitment of muscle action potentials. , 1968, Archives of Neurology.

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

[14]  W. Mommaerts Energetics of muscular contraction. , 1969, Physiological reviews.

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

[16]  H P Clamann,et al.  Activity of single motor units during isometric tension , 1970, Neurology.

[17]  R. Fletcher,et al.  A New Approach to Variable Metric Algorithms , 1970, Comput. J..

[18]  F. Buchthal,et al.  Contraction times and fibre types in intact human muscle. , 1970, Acta physiologica Scandinavica.

[19]  Roger C. Woledge,et al.  Heat Production and chemical change in muscle , 1971 .

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

[21]  R. E. Burke,et al.  Mammalian Motor Units: Physiological-Histochemical Correlation in Three Types in Cat Gastrocnemius , 1971, Science.

[22]  Gillies Jd Motor unit discharge patterns during isometric contraction in man. , 1972 .

[23]  C. Gibbs,et al.  Energy production of rat soleus muscle. , 1972, The American journal of physiology.

[24]  R. Person,et al.  Discharge frequency and discharge pattern of human motor units during voluntary contraction of muscle. , 1972, Electroencephalography and clinical neurophysiology.

[25]  J. Gillies Motor unit discharge patterns during isometric contraction in man. , 1972, The Journal of physiology.

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

[27]  C. Gibbs,et al.  Energy production of rat extensor digitorum longus muscle. , 1973, The American journal of physiology.

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

[29]  A. Gydikov,et al.  Physiological Characteristics of the Tonic and Phasic Motor Units in Human Muscles , 1973 .

[30]  R. Stein Peripheral control of movement. , 1974, Physiological reviews.

[31]  D. Jones,et al.  Heat production and chemical changes during isometric contractions of the human quadriceps muscle. , 1975, The Journal of physiology.

[32]  R. Fletcher An Ideal Penalty Function for Constrained Optimization , 1975 .

[33]  J Daniels,et al.  Skeletal muscle enzymes and fiber composition in male and female track athletes. , 1976, Journal of applied physiology.

[34]  Dimitri P. Bertsekas,et al.  Multiplier methods: A survey , 1975, at - Automatisierungstechnik.

[35]  A. Thorstensson,et al.  Force-velocity relations and fiber composition in human knee extensor muscles. , 1976, Journal of applied physiology.

[36]  H. Hatze A teleological explanation of Weber's Law and the motor unit size law. , 1979, Bulletin of mathematical biology.

[37]  H. Hatze,et al.  A myocybernetic control model of skeletal muscle , 1977, Biological Cybernetics.

[38]  G. Bolstad,et al.  Energy metabolism in different human skeletal muscles during voluntary isometric contractions , 1978, European Journal of Applied Physiology and Occupational Physiology.

[39]  H. Hatze The relative contribution of motor unit recruitment and rate coding to the production of static isometric muscle force , 2004, Biological Cybernetics.

[40]  A. M. Wani,et al.  A model for gradation of tension-recruitment and rate coding , 1975, Medical and biological engineering.