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Revised Limit Cycle Oscillator Model of Human Circadian Pacemaker

Circadian, Neuroendocrine and Sleep Disorders Section, Division of Endocrinology, Department of Medicine, Harvard Medical School, Brigham and Women's Hospital, Boston, MA 02115

Daniel B. Forger

Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138

Richard E. Kronauer

Circadian, Neuroendocrine and Sleep Disorders Section, Division of Endocrinology, Department of Medicine, Harvard Medical School, Brigham and Women's Hospital, Boston, MA 02115; Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138

In 1990, Kronauer proposed a mathematical model of the effects of light on the human circadian pacemaker. This study presents several refinements to Kronauer's original model of the pacemaker that enable it to predict more accurately the experimental results from a number of different studies of the effects of the intensity, timing, and duration of light stimuli on the human circadian pacemaker. These refinements include the following: The van der Pol oscillator from Kronauer’s model has been replaced with a higher order limit cycle oscillator so that the system’s amplitude recovery is slower near the singularity and faster near the limit cycle; the phase and amplitude of the circadian rhythm in sensitivity to light from Kronauer’s model has been refined so that the peak sensitivity to light on the limit cycle now occurs 4 h before the core body temperature minimum (CBT_min) and is three times as great as the minimum sensitivity on the limit cycle; the critical phase (at which type 1 phase response curves [PRCs] can be distinguished from type 0 PRCs) that occurs at CBT_min now corresponds to 0.8 h after the minimum of x (x_min) in this refined model rather than to the exact timing of x_min as in Kronauer’s model; a direct effect of light on circadian period was incorporated into the model such that as light intensity increases, the period decreases, which is in accordance with Aschoff’s rule.

Key Words: biological rhythms • mathematical model • bright light • amplitude • van der Pol oscillator • human circadian pacemaker

Journal of Biological Rhythms, Vol. 14, No. 6, 493-500 (1999)
DOI: 10.1177/074873049901400608


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