Nonlinear Dynamics of a Model of the Central Respiratory Pattern Generator
Recently, several models have computationally explored the network hypothesis of central respiratory rhythm generation.1, 2 One characteristic common to these models is the perfectly periodic nature of their outputs. This is not consistent with the impression that the respiratory rhythm is considerably more variable. This impression was recently quantified,3 and the data supports the notion that lightly anesthetized vagotomized animals exhibit rhythmic behavior consistent with perfectly periodic limit cycle oscillations. However, animals with an intact vagus consistently displayed more irregular respiratory patterns. The dynamical features of these patterns were quantitated by computing the correlation dimension of the corresponding time series.4 The vagotomized animals produced time series whose correlation dimension was equal to one, whereas the presence of an intact vagus, rather than stabilizing the rhythm, produced time series with non-integer correlation dimensions significantly greater than unity. The presence of a non-integer correlation dimension is consistent with a process exhibiting chaotic dynamics.4 Thus, the breath by breath variability in the ventilatory pattern may be explainable as a fundamental component of the process generating the respiratory rhythm, and not the product of intrinsic or extrinsic noise, or overwhelming system dimensionality. We hypothesized that our model of the central respiratory pattern generator, when appropriately modified to include vagal feedback from the pulmonary stretch receptors, would exhibit chaotic dynamics.
KeywordsLyapunov Exponent Bifurcation Diagram Chaotic Dynamic Correlation Dimension Respiratory Rhythm
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- 1.M.D. Ogilvie, A. Gottschalk, K. Anders, D.W. Richter and A.I. Pack, A network model of respiratory rhythmogenesis. Am. J. Physiol. (In Review)Google Scholar
- 4.G. Mayer-Kress (ed), “Dimensions and Entropies in Chaotic Systems,” Springer Verlag, New York (1989).Google Scholar
- 5.D.W. Richter, D. Ballantyne and J.E. Remmers, How is the respiratory rhythm generated? A model. NIPS 1:109–112 (1986).Google Scholar
- 8.C. von Euler, Brainstem mechanisms for generation and control of breathing pattern, in: “Handbook of Physiology. The Respiratory System II,” Am. Physiol. Soc., Washington, (1986).Google Scholar
- 9.J.L. Feldman, Neurophysiology of breathing in mammals, in: “Handbook of Physiology. The Nervous System IV,” Am. Physiol. Soc., Washington (1986).Google Scholar
- 11.F.J. Clark and C. von Euler, On the regulation of depth and rate of breathing. J. Physiol. (Lond) 222:267–95 (1972).Google Scholar
- 13.P. Berge, Y. Pomeau and C. Vidal, “Order Within Chaos-Towards a Deterministic Approach to Turbulence,” John Wiley & Sons, New York (1984).Google Scholar