The mathematics of respiration: it's all in your head
Jonathan Rubin (Department of Mathematics, University of Pittsburgh)
(April 6, 2008 10:30 AM - 11:30 AM)
In mammals, the respiratory rhythm is maintained under a wide range of conditions, depending on age, metabolic demand, and environmental factors. This rhythm is driven by a pacemaker system in the brainstem. Hence, a central question is, how does this pacemaker system generate such robust, adaptable rhythms? One component of the respiratory pacemaker system is the pre-Botzinger complex (pBC), a collection of neurons that can exhibit bursts of activity under appropriate conditions and that are coupled with synaptic excitation. I will discuss the mathematical analysis of the mechanisms by which synaptic coupling and heterogeneity can promote rhythmic activity in a model pBC network. This analysis incorporates fast-slow decomposition, bifurcation analysis, reduction of differential equations to maps, and a bit of graph theory.