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Feedback and delays in neurological diseases: A modeling study using gynamical systems

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Abstract

Numerous regulatory mechanisms in motor control involve the presence of time delays in the controlled behavior of the system. Experimentally, we have shown that an increase of the time delay in visual feedback induces different oscillations in control subjects and in patients with neurological diseases during the performance of a simple compensatory tracking task. A preliminary model is proposed to describe the oscillations observed in control subjects and in patients with neurological diseases. The influence of delays in two feedback loops are the main components of the motor control circuitry involved in this task and are studied from an analytical and physiological perspective. We analytically determine the influence in the model of each of these delays on the stability of the finger position. In addition, the influence of stochastic elements (“noise”) in the modeling equation is seen to contribute qualitatively to a more accurate reproduction of experimental traces in patients with Parkinson's disease but not in patients with cerebellar disease.

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Literature

  • Alexander, G. E., M. D. Crutcher and M. R. DeLong. 1990. Basal ganglia-thalamocortical circuits: Parallel substrates for motor, oculomotor, “prefrontal” and “limbic” functions.Prog. Brain Res. 85, 119–146.

    Article  Google Scholar 

  • Bélair, J. and M. C. Mackey. 1989. Consumer memory and price fluctuations in commodity markets: An integrodifferential model.J. Dyn. diff. Eq. 1, 3, 299–325.

    Article  Google Scholar 

  • Beppu, H., M. Nagaoka and R. Tanaka. 1987. Analysis of cerebellar motor disorders by visually-guided elbow tracking movement.Brain 110, 1–18.

    Google Scholar 

  • Beuter, A., D. Larocque and L. Glass. 1989a. Complex oscillations in a human motor system.J. Motor Behav. 21, 277–289.

    Google Scholar 

  • Beuter, A., J. G. Milton, C. Labrie and L. Glass. 1989b. Complex motor dynamics and control in multi-looped negative feedback systems.Proceedings of the 1989 IEEE International Conference on Systems, Man and Cybernetics, Cambridge, MA, 14–17 November, p. 899.

  • Beuter, A., C. Labrie and L. Glass. 1990a. Analysis of complex dynamics during a visuomotor task in patients with neurological diseases.Proceedings of the 12th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Philadelphia, PE, 1–4 November 1990, pp. 992–993.

  • Beuter, A., J. G. Milton, C. Labrie, L. Glass and S. Gauthier. 1990b. Effects of delayed visual feedback on motor control in patients with Parkinson's disease.Exp. Neurol. 110, 228–235.

    Article  Google Scholar 

  • Beuter, A., C. Labrie and K. Vasilakos. 1991. Transient dynamics in motor control of patients with Parkinson's disease.Chaos 1(3), 279–286.

    Article  MATH  Google Scholar 

  • Beuter, A., C. Labrie and J. G. Milton. 1992. Delayed visual feedback and movement control in patients with cerebellar disease. Submitted.

  • Cooke, K. L. and Z. Grossman. 1982. Discrete delay, distributed delay and stability switches.J. math. Anal. Appl. 86, 592–627.

    Article  MATH  MathSciNet  Google Scholar 

  • Flament, D. and J. Hore. 1986.J. Neurophysiol. 55, 1221–1233.

    Google Scholar 

  • Flament, D., T. Vilis and J. Hore. 1984. Dependence of cerebellar tremor on proprioceptive but not visual feedback.Exp. Neurol. 84, 314–325.

    Article  Google Scholar 

  • Glass, L. 1990. Is cardiac chaos normal or abnormal?J. Cardiovasc. Electrophysiol. 1, 481–482.

    Google Scholar 

  • Glass, L. and M. C. Mackey. 1979. Pathological conditions resulting from instabilities in physiological control systems.Ann. NY Acad. Sci. 316, 214–235.

    MATH  Google Scholar 

  • Glass, L. and M. C. Mackey. 1988.From Clocks to Chaos: The Rhythms of Life. Princeton, NJ: Princeton University Press.

    MATH  Google Scholar 

  • Glass, L., A. Beuter and D. Larocque. 1988. Time delays, oscillations and chaos in physiological control systems.Math. Biosci. 90, 111–125.

    Article  MATH  MathSciNet  Google Scholar 

  • Goldberger, A. and B. West. 1987. Application of nonlinear dynamics to clinical cardiology.Ann. NY Acad. Sci. 504, 195–213.

    Google Scholar 

  • Guevara, M. R., L. Glass and A. Shrier. 1981. Phase locking, period-doubling bifurcation, and irregular dynamics in periodically stimulated cardiac cells.Science 214, 1350–1353.

    Google Scholar 

  • Haken, H., J. A. S. Kelso and H. Bunz. 1985. A theoretical model of phase transitions in human hand movements.Biol. Cyb. 51, 347–356.

    Article  MATH  MathSciNet  Google Scholar 

  • Hoehn, M. M. and M. D. Yahr. 1967. Parkinsonism: Onset, progression and mortality.Neurology 17, 427–442.

    Article  Google Scholar 

  • Houk, J. C. 1987. Model of the cerebellum as an array of adjustable pattern generators. In:Cerebellum and Neuronal Plasticity, M. Glickstein and J. Stein (Eds), NATO Advanced Research Workshop on Cerebellum and Behavioral Plasticity (1986), pp. 249–260. New York: Plenum Press.

    Google Scholar 

  • Houk, J. C. and A. R. Gibson. 1987. Sensory processing through the cerebellum. In:New Concepts in Cerebellar Neurobiology, pp. 387–416. New York: Alan R. Liss, Inc..

    Google Scholar 

  • Kaplan, D. T. and L. Glass. 1992. Direct test for determinism in a time series.Phys. Rev. Lett. 68 (4), 427–430.

    Article  Google Scholar 

  • Kelso, J. A. S., E. Saltzman and B. Tuller. 1986. The dynamical perspective on speech production: data and theory.J. Phonet. 14, 29–59.

    Google Scholar 

  • Mackey, M. C. and J. G. Milton. 1987. Dynamical diseases.Ann. NY Acad. Sci. 504, 16–32.

    Google Scholar 

  • Mackey, M. C. and J. G. Milton. 1990. Feedback, delays and the origin of blood cell dynamics.Comments theor. Biol. 1 (5), 299–327.

    Google Scholar 

  • Mallet-Paret, J. 1988. Morse decompositions for delay differential equations.J. diff. Eq. 72, 270–315.

    Article  MATH  MathSciNet  Google Scholar 

  • May, R. 1976. Simple mathematical models with very complicated dynamics.Nature 261, 459–467.

    Article  Google Scholar 

  • Merton, P. A., H. B. Morton and C. Rashbass. 1967. Visual feedback in hand tremor.Nature (London) 216, 583–584.

    Article  Google Scholar 

  • Miall, R. C., D. J. Weir and J. F. Stein. 1985. Visuomotor tracking with delayed visual feedback.Neuroscience 16, 511–520.

    Article  Google Scholar 

  • Pool, R. 1989. Is it noise, or is it just noise? and Is it healthy to be chaotic?Science 243, 25–28 and 604–607.

    Google Scholar 

  • Sheridan, M. R. and K. A. Flowers. 1990. Movement variability and bradykinesia in Parkinson's disease.Brain 113, 1149–1161.

    Google Scholar 

  • Skarda, C. A. and W. J. Freeman. 1987. How brains make chaos in order to make sense of the world.Behav. Brain Sci. 10, 161–195.

    Article  Google Scholar 

  • Stech, H. W. 1985. Hopf bifurcation calculations for functional differential equations.J. math. Anal. Appl. 109, 472–491.

    Article  MATH  MathSciNet  Google Scholar 

  • Stein, J. F., R. C. Miall and D. J. Weir. 1987. The role of the cerebellum in the visual guidance of movement. In:Cerebellum and Neuronal Plasticity, M. Glickstein and J. Stein (Eds), NATO Advanced Research Workshop on Cerebellum and Behavioral Plasticity (1986), pp. 249–260. New York: Plenum Press.

    Google Scholar 

  • Thelen, E., J. A. S. Kelso and A. Fogel. 1987. Self-organizing systems and infant motor development.Devel. Rev. 7, 39–65.

    Article  Google Scholar 

  • Vasilakos, K. and A. Beuter. 1992. Effects of noise on a delayed visual feedback system. Submitted.

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Author notes

  1. Anne Beuter, Jacques Bélair, Christiane Labrie & Jacques Bélair

    Present address: Centre for Nonlinear Dynamics in Physiology and Medicine, McGill University, H3G 1Y6, Montréal, Canada

Authors and Affiliations

  1. Département de Kinanthropologie, Université du Québec à Montréal, C.P. 8888-A, H3C 3P8, Montréal, Canada

    Anne Beuter, Jacques Bélair & Christiane Labrie

  2. Département de Mathématiques et Statistique, Université de Montréal, C.P. 6128-A, H3C 3J7, Montréal, Canada

    Jacques Bélair

Authors
  1. Anne Beuter
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  2. Jacques Bélair
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  3. Christiane Labrie
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  4. Jacques Bélair
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Beuter, A., Bélair, J., Labrie, C. et al. Feedback and delays in neurological diseases: A modeling study using gynamical systems. Bltn Mathcal Biology 55, 525–541 (1993). https://doi.org/10.1007/BF02460649

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  • DOI: https://doi.org/10.1007/BF02460649

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