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A mathematical model of the respiratory center

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Abstract

The signal that drives the respiratory muscles is assumed to be caused by the mutual interaction of two neural networks in the respiratory center. These nets are considered to be spatially homogeneous with all the neurones firing simultaneously so that their dynamical characteristics depend upon the process of temporal summation. A mathematical model of this phenomenon leads to a description of the behavior of the respiratory center consisting of a nonlinear, Volterra-type integral equation equivalent to a second-order, nonlinear autonomous differential equation, which is proved to exhibit, under some conditions, a limit cycle from which stems the basic respiratory drive. It is suggested that the frequency of this drive is controlled by chemical or central influences by varying the central facilitation of the neurones at rest.

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Literature

  • Beurle, R. L. 1957. “Properties of a Mass of Cells Capable of Regenerating Pulses.”Phil. Trans. Roy. Soc. (London),A240, 55–94.

    Google Scholar 

  • Burns, B. D. and G. C. Salmoiraghi. 1960. “Repetitive Firing of Respiratory Neurons during their Burst Activity.”J. Neurophysiol.,23, 27–46.

    Google Scholar 

  • Fulton, J. F. 1955.Textbook of Physiology. Philadelphia and London: W. B. Saunders Co.

    Google Scholar 

  • Griffith, J. S. 1963. “A Field Theory of Neural Nets: I. Derivation of Field Equations.”Bull. Math. Biophysics,25, 111–120.

    MATH  MathSciNet  Google Scholar 

  • —, 1965. “A Field Theory of Neural Nets: II. Properties of the Field Equations.”Ibid.,27, 187–195.

    MATH  MathSciNet  Google Scholar 

  • Guyton, A. C. 1961.Textbook of Medical Physiology. Philadelphia and London: W. B. Saunders Co.

    Google Scholar 

  • Salmoiraghi, G. C. 1962. “Cardiovascular Neurons in Brain-Stem of Cat.”J. Neurophysiol.,25, 182–197.

    Google Scholar 

  • —, 1963. “Functional Organization of Brain-Stem Respiratory Neurons.”Ann. N. Y. Acad. of Sci.,109, 571–585.

    Google Scholar 

  • — and R. von Baumgarten. 1961. “Intracellular Potentials from Respiratory Neurons in Brain-Stem of Cat and Mechanisms of Rhythmic Respiration.”J. Neurophysiol.,24, 203–218.

    Google Scholar 

  • — and B. D. Burns. 1960a. “Localization and Patterns of Discharge of Respiratory Neurons in Brain-Stem of Cat.”Ibid.,23, 2–13.

    Google Scholar 

  • ——. 1960b. “Notes on the Mechanisms of Rhythmic Respiration.”Ibid.,23, 14–26.

    Google Scholar 

  • Tricomi, F. G. 1961.Differential Equations. New York: Hafner Publishing Co.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, University of Leeds, Leeds, England

    J. E. Rubio

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  1. J. E. Rubio
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Rubio, J.E. A mathematical model of the respiratory center. Bulletin of Mathematical Biophysics 29, 719–736 (1967). https://doi.org/10.1007/BF02476923

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  • DOI: https://doi.org/10.1007/BF02476923

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