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Related Experiment Videos

A circle map model of human circadian rhythms.

H Sakai1, M Nakao, M Yamamoto

  • 1Laboratory of Neurophysiology and Bioinformatics, Graduate School of Information Sciences, Tohoku University, Sendai, Japan.

Frontiers of Medical and Biological Engineering : the International Journal of the Japan Society of Medical Electronics and Biological Engineering
|June 4, 1999
PubMed
Summary

This study introduces a new mathematical model for human circadian rhythms, explaining the complex interactions between sleep-wake cycles and body temperature. The model reveals how these rhythms synchronize or desynchronize, offering a unified framework for understanding circadian dynamics.

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Area of Science:

  • Chronobiology
  • Mathematical Biology
  • Human Physiology

Background:

  • The interplay between the sleep-wake cycle and the body's temperature rhythm is complex, exhibiting states like internal synchronization, desynchronization, and phase trapping during free-run conditions.
  • Characterizing these behavioral states relies on understanding the periods of both rhythms and their phase relationships.

Purpose of the Study:

  • To propose mathematical interpretations for observed sleep-wake and temperature rhythm dynamics.
  • To develop a novel circadian system model based on these interpretations.
  • To provide a systematic framework for understanding human circadian rhythms.

Main Methods:

  • Development of a mathematical model comprising two coupled circle maps, representing sleep-onset and wake-onset phases relative to the temperature rhythm.

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  • Unique estimation of model parameters using experimental data.
  • Analysis of model dynamics, particularly bifurcation phenomena, to explain synchronized and desynchronized states.

    • Main Results:

    • A new mathematical model was developed, with sleep-onset dynamics primarily governing wake-onset behavior.
    • Model parameters were uniquely determined from experimental results.
    • Diverse behaviors of the sleep-wake cycle, including synchronized and desynchronized states, were explained as bifurcation phenomena controlled by a single parameter.

    Conclusions:

    • The proposed model offers a novel mathematical framework for systematically understanding human circadian rhythms.
    • Bifurcation analysis of the model provides insights into the complex dynamics of sleep-wake and temperature rhythms.
    • This work advances the comprehension of internal synchronization, desynchronization, and phase trapping in circadian systems.