Modeling the Dynamics of Central Pattern Generators and Anesthetic Action

This thesis contains two parts. Part 1 of this thesis has two goals. The first is to understand the phase response properties of half-center oscillators (HCOs) using idealized models. The second is to begin developing an understanding of the phase-locking mechanisms between coupled half-center oscillators using numerical simulations and the theory of weakly coupled oscillators. This work is a starting point towards a greater understanding of the mechanisms underlying coordinated limb movement during locomotion in the crayfish swimmeret system. The analysis is compared to experimental data from the crayfish swimmeret system and possible experiments are suggested.;The goal of Part 2 of this thesis is to build mathematical models to study the effects of volatile anesthetic on neural networks in the spinal cord. The network under consideration is composed of excitatory interneurons in the lamprey central pattern generator (CPG), a spinal cord neuronal network responsible for generating rhythmic locomotor movement in vertebrates such as swimming or walking. It is thought that the excitatory interneurons of the CPGs are the main target of the volatile anesthetic isoflurane, leading to immobility under anesthesia. We model these interneurons and incorporate the most relevant effects of the volatile anesthetic isoflurane on intracellular conductances using bifurcation analysis and numerical simulations.