Bifurcations of the respiratory pattern produced with phasic vagal stimulation in the rat

Geometric methods from nonlinear dynamics are employed to evaluate dynamic processing of vagal afferent information by the respiratory central pattern generator (RCPG). While measuring airflow and diaphragm EMG, we applied brief electrical stimuli (40- to 130-ms duration) to one afferent vagus of bilaterally vagotomized urethan-anesthetized rats during every breath at various phases of the respiratory cycle. Stimuli applied during early or late inspiration of every breath evoke highly predictable one-dimensional responses: reversible (graded inhibition) or irreversible (off-switching) inhibition of inspiratory activity, respectively. Stimulation during midinspiration produces higher-dimensional oscillations that wander unpredictably over a continuum of graded inhibition and off-switching; "spiral" attractors and "horseshoe" return maps at this phase are characteristic of Silnikov's bifurcation. Stimuli applied during early expiration always prolonged expiratory duration, but those delivered during midexpiration evoked unpredictable wandering between prolongations and shortening of expiratory duration. A narrow time window surrounds the expiratory-inspiratory (E-I) transition, where stimuli elicit either breaths of short duration and low amplitude (irreversible E-I transition, decreased total respiratory cycle duration) or transient bursts of inspiratory activity at the E-I transition followed by a prolonged breath (reversible E-I transition, increased total respiratory cycle duration). We conclude that RCPG "gating" of and adaptation to vagal feedback combine to produce complex breath-to-breath dynamics in the rat that are consistent with low-dimensional chaos.