Muscle–Tendon Model with Length History-Dependent Activation–Velocity Coupling

We developed muscle–tendon models incorporating Hill-type structure and length-dependent coupling between activation and velocity. The models were evaluated in electrically stimulated cat soleus muscles. Dynamic model parameters were estimated by a nonlinear parameter estimation algorithm from input–output data obtained during simultaneous random stimulation and length changes. Static parameters were estimated from the length–tension curve. A model with length history-dependent activation–velocity coupling predicted the behavior of the muscle under a wide variety of conditions, including during random perturbations and during isovelocity movements, where it captured short range stiffness and length history-dependent postyielding behavior. Furthermore, the model predicted twitch responses. The generality of this fixed parameter model makes it especially suitable for simulation and feedforward control, where muscle responses are not available for on-line parameter adaptation.

[1]  G. Zahalak.  A comparison of the mechanical behavior of the cat soleus muscle with a distribution-moment model. , 1986, Journal of biomechanical engineering.

[2]  Michel A. Lemay,et al.  External Control of Limb Movements Involving Environmental Interactions , 1990 .

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

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

[5]  P. Crago,et al.  Feedback control of electrically stimulated muscle using simultaneous pulse width and stimulus period modulation , 1991, IEEE Transactions on Biomedical Engineering.

[6]  G. Loeb,et al.  Mechanical properties of aponeurosis and tendon of the cat soleus muscle during whole‐muscle isometric contractions , 1995, Journal of morphology.

[7]  P. Rack,et al.  Elastic properties of the cat soleus tendon and their functional importance. , 1984, The Journal of physiology.

[8]  J. Winters.  Hill-Based Muscle Models: A Systems Engineering Perspective , 1990 .

[9]  J J Abbas,et al.  New control strategies for neuroprosthetic systems. , 1996, Journal of rehabilitation research and development.

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

[12]  P. Rack,et al.  The short range stiffness of active mammalian muscle and its effect on mechanical properties , 1974, The Journal of physiology.

[13]  P. Crago,et al.  Feedback control methods for task regulation by electrical stimulation of muscles , 1991, IEEE Transactions on Biomedical Engineering.

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

[15]  F.E. Zajac,et al.  Restoring unassisted natural gait to paraplegics via functional neuromuscular stimulation: a computer simulation study , 1990, IEEE Transactions on Biomedical Engineering.

[16]  W. Rymer,et al.  Muscle stiffness during transient and continuous movements of cat muscle: perturbation characteristics and physiological relevance , 1994, IEEE Transactions on Biomedical Engineering.

[17]  John E. Dennis,et al.  Algorithm 573: NL2SOL—An Adaptive Nonlinear Least-Squares Algorithm [E4] , 1981, TOMS.

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

[19]  D. Morgan,et al.  Quantitative analysis of sarcomere non-uniformities in active muscle following a stretch , 1996, Journal of Muscle Research & Cell Motility.

[20]  G. Zahalak.  A distribution-moment approximation for kinetic theories of muscular contraction , 1981 .

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

[22]  G. C. Joyce,et al.  The mechanical properties of cat soleus muscle during controlled lengthening and shortening movements , 1969, The Journal of physiology.