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A Mathematical Model of the Human Sleep/Wake Cycle
by
Lisa Rogers
Rensselaer Polytechnic Institute
Coauthors: Mark Holmes (Rensselaer Polytechnic Institute)
Most living organisms exhibit daily biological rhythms. One of the most curious and difficult to understand is the sleep/wake cycle. Although there is little discussion about the importance of the wake phase, the reasons for sleep are not well understood. In this talk a model of the human sleep/wake cycle will be presented that consists of a system of nonlinear integro-differential equations that describe the behavior of inhibitory and excitatory neurons contributing to sleep and wake. Specifically, the model is based on recent experimental studies identifying the brain circuitry and neurotransmitters that regulate the sleep and wake states. We utilize inherent properties of the REM/NREM cycle as well as stability theory and computational methods to analyze the system. A correlation is shown between the model’s output and experimental data taken from sleep studies. The consequences of qualitative and quantitative analysis are utilized to shed light on the various physiological implications that arise from the mathematical structure of the human sleep and wake processes.
Date received: May 1, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawd-47.