A mathematical model of the central neural mechanisms of respiratory rhythm generation is developed. This model assumes that the respiratory cycle consists of three phases: inspiration, post-inspiration, and expiration. Five respiratory neuronal groups are included: inspiratory, late-inspiratory, post-inspiratory, expiratory, and early-inspiratory neurons. Proposed interconnections among these groups are based substantially on previous physiological findings. The model produces a stable limit cycle and generally reproduces the features of the firing patterns of the 5 neuronal groups. When simulated feedback from pulmonary stretch receptors is made to excite late-inspiratory neurons and inhibit early-inspiratory neurons, the model quantitatively reproduces previous observations of the expiratory-prolonging effects of pulses and steps of vagal afferent activity presented in expiration. In addition the model reproduces expected respiratory cycle timing and amplitude responses to change of chemical drive both in the absence and in the presence of simulated stretch receptor feedback. These results demonstrate the feasibility of generating the respiratory rhythm with a simple neural network based on observed respiratory neuronal groups. Other neuronal groups not included in the model may be more important for shaping the waveforms than for generating the basic oscillation.

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