Phase resetting and fixed-delay stimulation of a simple model of respiratory rhythm generation

In a previous study (Lewis et al., 1990), the response of the respiratory rhythm to a perturbing stimulus was investigated using two different stimulus protocols: phase resetting and fixed-delay stimulation. The first protocol consists of measuring the effects of perturbing an oscillator at different phases of the cycle on the duration of the perturbed cycle. The resulting phase response curves (PRCs) can be used to characterize the properties of the oscillator (Winfree, 1980). A second protocol, fixed-delay stimulation, involves perturbing an oscillator at a fixed latency from the onset of the cycle, repeated every n-th cycle. If a single stimulus produces an effect that lasts longer than a single cycle, complicated responses can be expected from fixed-delay stimulation (Lewis et al., 1987). A simple three-phase model for respiratory rhythm generation based on a hypothesis by Richter and coworkers (1982, 1983, 1986) was investigated in the context of these experimental studies. Phase resetting and fixed-delay stimulation protocols were simulated in the model. PRCs of the model resemble those obtained experimentally: a phase-dependent prolongation or shortening of the inspiratory phase depending on the stimulus magnitude, and a slight prolongation of the expiratory phase. Stimuli delivered to the model repetitively during successive inspiratory periods at a fixed-delay produced various combinations of shortened and prolonged cycles, similar to those observed in the experiments. However, the marked increases in cycle duration observed in the experiments during, as well as after, stimulation were not evident in the model. These comparisons suggest that (1) PRCs may not be an adequate way to evaluate certain models of rhythmogenesis, and (2) to improve the present simplified formulation of the three-phase model of the respiratory oscillator, time-varying stimulus dependent effects should be incorporated.