A simple model of force generation by skeletal muscle during dynamic isometric contractions

The force that an isometric skeletal muscle will produce in response to time-varying stimulation ("dynamic isometric" force) is important both for understanding muscle function and for designing neuroprostheses. The paper reports a model for predicting the force produced by an isometric skeletal muscle at rest length in response to a wide range of stimulation patterns. The model consists of two linear, first-order systems separated by a static nonlinearity. The rate constant of the second first-order system varies with force level. The model was validated using three cat soleus and three cat plantaris muscles. The following whole-nerve stimulation trains were used: single pulses (twitches), 2-4 pulses, constant rates, triangularly modulated interpulse intervals, and randomly modulated interpulse intervals. The model reproduced most responses accurately. The model shows that a force-dependent rate constant is essential for model validity, and could be used in the control of neuroprostheses.

[1]  L. Vodovnik,et al.  Electrical stimulation of skeletal muscle—A study of muscle as an actuator , 1967, Medical and biological engineering.

[2]  R. Stein,et al.  Nonlinear summation of contractions in cat muscles. I. Early depression , 1981, The Journal of general physiology.

[3]  T Gordon,et al.  Temperature dependence of mammalian muscle contractions and ATPase activities. , 1982, Biophysical journal.

[4]  W. Durfee,et al.  Methods for estimating isometric recruitment curves of electrically stimulated muscle , 1989, IEEE Transactions on Biomedical Engineering.

[5]  M. Solomonow,et al.  Frequency response model of skeletal muscle: effect of perturbation level, and control strategy , 1989, Medical and Biological Engineering and Computing.

[6]  H P Clamann,et al.  Force output of cat motor units stimulated with trains of linearly varying frequency. , 1989, Journal of neurophysiology.

[7]  F. Zajac,et al.  Properties of stimulus trains producing maximum tension-time area per pulse from single motor units in medial gastrocnemiu muscle of the cat. , 1980, Journal of neurophysiology.

[8]  R. Stein,et al.  Determination of the frequency response of isometric soleus muscle in the cat using random nerve stimulation , 1973, The Journal of physiology.

[9]  A. Hill.  The heat of shortening and the dynamic constants of muscle , 1938 .

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

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

[12]  R B Stein,et al.  The kinetics relating calcium and force in skeletal muscle. , 1988, Biophysical journal.

[13]  H. Hatze.  A general myocybernetic control model of skeletal muscle , 1978, Biological Cybernetics.

[14]  L. A. Bernotas,et al.  A Discrete-Time Model of Electrcally Stimulated Muscle , 1986, IEEE Transactions on Biomedical Engineering.

[15]  R. Stein,et al.  Nonlinear summation of contractions in cat muscles. II. Later facilitation and stiffness changes , 1981, The Journal of general physiology.

[16]  F. Zajac,et al.  The effect of activation history on tension production by individual muscle units , 1976, Brain Research.

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

[18]  G. Shue,et al.  Muscle-joint models incorporating activation dynamics, moment-angle, and moment-velocity properties , 1995, IEEE Transactions on Biomedical Engineering.

[19]  H.J. Chizeck,et al.  Recursive parameter identification of constrained systems: an application to electrically stimulated muscle , 1991, IEEE Transactions on Biomedical Engineering.

[20]  A. Schultz,et al.  A simple Hill element-nonlinear spring model of muscle contraction biomechanics. , 1991, Journal of applied physiology.

[21]  L. A. Bernotas,et al.  Adaptive Control of Electrically Stimulated Muscle , 1987, IEEE Transactions on Biomedical Engineering.

[22]  K. Edman,et al.  Laser diffraction studies of sarcomere dynamics during ‘isometric’ relaxation in isolated muscle fibres of the frog , 1982, The Journal of physiology.

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

[24]  F. Zajac.  Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. , 1989, Critical reviews in biomedical engineering.

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

[26]  C. P. Taylor,et al.  Isometric muscle contraction and the active state: an analog computer study. , 1969, Biophysical journal.

[27]  W S Levine,et al.  An optimal control model for maximum-height human jumping. , 1990, Journal of biomechanics.

[28]  P. Crago.  Muscle input-output model: the static dependence of force on length, recruitment, and firing period , 1992, IEEE Transactions on Biomedical Engineering.

[29]  L D PARTRIDGE,et al.  MODIFICATIONS OF NEURAL OUTPUT SIGNALS BY MUSCLES: A FREQUENCY RESPONSE STUDY. , 1965, Journal of applied physiology.

[30]  R. Stein,et al.  A linear time-varying model of force generation in skeletal muscle , 1993, IEEE Transactions on Biomedical Engineering.

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