Abstract
This study explores the intricate relationship between sleep stages and brain oscillations, utilizing quantitative EEG analysis and mathematical models. We examine the distinct EEG characteristics of light sleep, deep sleep, and REM sleep, focusing on power spectral density (PSD), coherence, and phase synchronization analyses. The Ising model and Kuramoto model provide frameworks for understanding the synchronization dynamics and phase relationships of neuronal populations across sleep stages. Our findings highlight significant variations in oscillatory activity, coherence, and phase synchronization, offering insights into the neural mechanisms underlying sleep regulation. Additionally, we discuss the implications of these findings for sleep disorders such as insomnia, sleep apnea, and narcolepsy, demonstrating how mathematical models can predict therapeutic outcomes and guide targeted interventions. This comprehensive analysis contributes to the understanding of sleep architecture and the development of novel treatments for sleep disorders.
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