Journal of Computational Neuroscience

, Volume 30, Issue 3, pp 607–632 | Cite as

Interacting oscillations in neural control of breathing: modeling and qualitative analysis

  • Jonathan E. Rubin
  • Bartholomew J. Bacak
  • Yaroslav I. Molkov
  • Natalia A. Shevtsova
  • Jeffrey C. Smith
  • Ilya A. Rybak
Article

Abstract

In mammalian respiration, late-expiratory (late-E, or pre-inspiratory) oscillations emerge in abdominal motor output with increasing metabolic demands (e.g., during hypercapnia, hypoxia, etc.). These oscillations originate in the retrotrapezoid nucleus/parafacial respiratory group (RTN/pFRG) and couple with the respiratory oscillations generated by the interacting neural populations of the Bötzinger (BötC) and pre-Bötzinger (pre-BötC) complexes, representing the kernel of the respiratory central pattern generator. Recently, we analyzed experimental data on the generation of late-E oscillations and proposed a large-scale computational model that simulates the possible interactions between the BötC/pre-BötC and RTN/pFRG oscillations under different conditions. Here we describe a reduced model that maintains the essential features and architecture of the large-scale model, but relies on simplified activity-based descriptions of neural populations. This simplification allowed us to use methods of dynamical systems theory, such as fast-slow decomposition, bifurcation analysis, and phase plane analysis, to elucidate the mechanisms and dynamics of synchronization between the RTN/pFRG and BötC/pre-BötC oscillations. Three physiologically relevant behaviors have been analyzed: emergence and quantal acceleration of late-E oscillations during hypercapnia, transformation of the late-E activity into a biphasic-E activity during hypercapnic hypoxia, and quantal slowing of BötC/pre-BötC oscillations with the reduction of pre-BötC excitability. Each behavior is elicited by gradual changes in excitatory drives or other model parameters, reflecting specific changes in metabolic and/or physiological conditions. Our results provide important theoretical insights into interactions between RTN/pFRG and BötC/pre-BötC oscillations and the role of these interactions in the control of breathing under different metabolic conditions.

Keywords

Neural oscillations Respiratory central pattern generator Pre-Bötzinger Complex Parafacial respiratory group Coupled oscillators Phase plane analysis 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Jonathan E. Rubin
    • 1
  • Bartholomew J. Bacak
    • 2
  • Yaroslav I. Molkov
    • 2
  • Natalia A. Shevtsova
    • 2
  • Jeffrey C. Smith
    • 3
  • Ilya A. Rybak
    • 2
  1. 1.Department of MathematicsUniversity of PittsburghPittsburghUSA
  2. 2.Department of Neurobiology and AnatomyDrexel University College of MedicinePhiladelphiaUSA
  3. 3.Cellular and Systems Neurobiology Section, National Institute of Neurological Disorders and StrokeNational Institutes of HealthBethesdaUSA

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