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Am J Physiol Endocrinol Metab 279: E669-E683, 2000;
0193-1849/00 $5.00
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Vol. 279, Issue 3, E669-E683, September 2000

A statistical model of the human core-temperature circadian rhythm

Emery N. Brown1, Yong Choe1, Harry Luithardt1, and Charles A. Czeisler2

1 Statistics Research Laboratory, Department of Anesthesia and Critical Care, Massachusetts General Hospital, and Division of Health Sciences and Technology, Harvard Medical School-Massachusetts Institute of Technology, Boston 02114-2696; and 2 Circadian, Neuroendocrine and Sleep Disorders Section, Division of Endocrinology, Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts 02115

We formulate a statistical model of the human core-temperature circadian rhythm in which the circadian signal is modeled as a van der Pol oscillator, the thermoregulatory response is represented as a first-order autoregressive process, and the evoked effect of activity is modeled with a function specific for each circadian protocol. The new model directly links differential equation-based simulation models and harmonic regression analysis methods and permits statistical analysis of both static and dynamical properties of the circadian pacemaker from experimental data. We estimate the model parameters by using numerically efficient maximum likelihood algorithms and analyze human core-temperature data from forced desynchrony, free-run, and constant-routine protocols. By representing explicitly the dynamical effects of ambient light input to the human circadian pacemaker, the new model can estimate with high precision the correct intrinsic period of this oscillator (~24 h) from both free-run and forced desynchrony studies. Although the van der Pol model approximates well the dynamical features of the circadian pacemaker, the optimal dynamical model of the human biological clock may have a harmonic structure different from that of the van der Pol oscillator.

biological clock; dynamical system; harmonic regression; perturbation expansion; thermoregulation; van der Pol equation


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