Georgia Institute of Technology College of Sciences

Sleep and wake states are driven by interactions of neuronal populations in many areas of the human brain, such as the brainstem, midbrain, hypothalamus, and basal forebrain. The timing of human sleep is strongly modulated by the 24 h circadian rhythm and the homeostatic sleep drive, the need for sleep that depends on the history of prior awakening. The parameters dictating the evolution of the homeostatic sleep drive may vary with development or interindividual characteristics and have been identified as important parameters for generating the transition from multiple sleeps to a single sleep episode per day. Features of the mean firing rate of the neurons in the suprachiasmatic nucleus (SCN), the central pacemaker in humans, may differ with seasonality. In this talk, I will present our analysis of changes in sleep patterning under variation of homeostatic and circadian parameters using a mathematical model for human sleep-wake regulation. I will also talk about the fundamental tools we employ to understand the dynamics of the model, such as the construction of a circle map that captures the timing of sleep onsets on successive days. Analysis of the structure and bifurcations in the map reveals changes in the average number of sleep episodes per circadian day in a period-adding-like structure caused by the separate or combined effects of circadian and homeostatic variation. Time permitting, I will talk about some of our current work on modeling sleep patterns in early childhood using experimental data.