A simple model of dynamic interactions between respiratory centers

There is a general consensus that neurons responsible for the generation of a respiratory rhythm are located in the rostral ventrolateral medulla. However, there is still controversy regarding the necessary components for respiratory rhythm generation. Both inspiratory neurons in the preBotzinger complex (preBOtC) and pre-inspiratory neurons located more rostrally to this anatomical structure referred to as the parafacial respiratory group (pFRG) have been proposed to be essential for respiratory rhythmogenesis. To study the dynamical interactions between preBOtC and pFRG neurons, we use a canonical model that describes each neuron population as a phase oscillator. We assume that the oscillators are weakly coupled with pFRG neurons providing stimulation to preBOtC neurons and preBOtC neurons providing inhibitory drive to pFRG neurons. In our mathematical study, we explore plausible mechanisms that may account for the complex interactions between I and pre-I neuron. In particular, we show that reduced excitability of inspiratory in preBOtC may lead to the phenomena known as "quantal slowing"