Summary
In a recent work the mammalian neuro-muscular system has been investigated by the authors from the physiological point of view. This system is described by a nonlinear differential-difference equation. In the present work we analyse the differential-difference equation and investigate the oscillations pertaining to the neuro-muscular system. The dependence of these oscillations on the muscular and neural feedback parameters has been studied systematically. Several simple relationships are described which can be compared with experimental results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Armstrong, C. F., Huxley, A. F., Julian, F. J.: Oscillatory responses in frog skeletal muscle fibres. J. Physiol. (London) 186, 26–27 P (1966).
Bawa, P., Stein, R. B.: Properties of human soleus muscle and the associated feedback loop. J. Physiol. (London) in press.
Bawa. P., Mannard. A., Stein, R. B.: a) Effects of elastic loads on the contractions of cat muscles. J. Physiol. (London) in press, b) Predictions and experimental tests of a visco-elastic muscle using elastic and inertial loads. J. Physiol. (London) in press.
Bellman, R., Cooke, K. L.: Differential-Difference Equations. New York-London: Academic Press 1963.
Bronk, D. W., Ferguson, L. K.: The nervous control of intercostal respiration. Am. J. Physiol. 110, 700–707 (1935).
Gurfinkel, V. S., Osovets, S. M.: Mechanism of generation of oscillation in the tremor form of Parkinsonism. Biophysics 18, 731–738 (1973).
Hill, A. V.: The heat of shortening and the dynamic constants of muscle. Proc. Roy. Soc. (London) B 126. 136–195 (1938).
Joyce, G. C., Rack, P. M. H.: The effects of load and force on tremor at the normal human elbow joint. J. Physiol. 240, 375–396 (1974).
Julian, E. J., Sollins, K. R., Sollins, M. R.: A model for the transient and steady-state mechanical behaviour of contracting muscle. Biophys. J. 14, 546–561 (1974).
Levin, B. Ja.: Distributions of Zeros of Entire Functions. Providence, Rhode Island: Amer. Math Soc. 1964.
Mannard, A., Stein, R. B.: Determination of the frequency response of isometric soleus muscle in the cat using random nerve stimulation. J. Physiol. (London) 229, 275–296 (1973).
Matthews, P. B. C., Stein, R. B.: Sensitivity of muscle spindle afferents to small simusoidal changes in length. J. Physiol. (London) 200, 723–743 (1969).
Myshkis, A. D.: Lineare Differentialgleichungen mit nacheilendem Argument. Berlin: Deutscher Verlag der Wiss. 1955.
Oguztöreli, M. N.: Time-Lag Control Systems. New York-London: Academic Press 1966.
Oguztöreli, M. N., Stein, R. B.: Tremor and other oscillations in neuromuscular systems. J. Physiol. (London) in press.
Padsha, S. M., Stein, R. B.: The bases of tremor during a maintained posture. In: Control of Posture and Locomotion (Stein, R. B., Pearson, K. G., Smith, R. S., Redford, J. B., eds.), pp. 415–419. New York: Plenum Press 1973.
Pinney, E.: Differential-Difference Equations. Berkeley, Los Angeles: University of California Press 1958.
Podolsky, R. J., Nolan, A. C., Zaveler, S. A.: Cross-bridge properties derived from muscle isotonic velocity transients. Proc. Nat. Acad. Sci. U.S.A. 64, 504–511 (1969).
Pontryagin, L. S.: On the zeros of some elementary transcendental functions. Izv. Akad. Nauk SSR, Ser. Mat. 6, 115–134 (1942).
Author information
Authors and Affiliations
Additional information
This work was partly supported by the National Research Council of Canada Grant NRC-A4345 and by the Medical Research Council of Canada Grant MRC-MA-3307 through the University of Alberta.
Rights and permissions
About this article
Cite this article
O<guztöreli, M.N., Stein, R.B. An analysis of oscillations in neuro-muscular systems. J. Math. Biology 2, 87–105 (1975). https://doi.org/10.1007/BF00275922
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00275922