A network model of respiratory rhythmogenesis

A mathematical model of the three-phase respiratory network proposed by Richter et al. (News Physiol. Sci. 1: 109-112, 1986) is developed and its properties are examined. The model reproduces the experimentally determined trajectories of membrane potential for the five physiologically distinct types of neurons included. Stepwise parameter changes can produce a respiratory rhythm with only two separate electrophysiological phases, result in apnea, or produce more complex patterns of firing. The phase-resetting behavior of the model was obtained with perturbing stimuli and is comparable to experimentally determined phase-resetting data. There is reasonable agreement between model predictions and experimental results. In the model, the properties of the phase singularity make termination of the respiratory rhythm by an appropriately timed perturbation virtually impossible, which is in agreement with experimental observations. The rhythm can be stopped by alterations that simulate the effect of input from the superior laryngeal nerve; the rhythm is locked in the postinspiratory phase. We conclude that our results are consistent with the concept of a network oscillator as the source of the respiratory rhythm.