A Simpler Model of the Human Circadian Pacemaker

Abstract

Numerous studies have used the classic van der Pol oscillator, which contains a cubic nonlinearity, to model the effect of light on the human circadian pacemaker. Jewett and Kronauer demonstrated that Aschoff's rule could be incorporated into van der Pol type models and used a van der Pol type oscillator with higher order nonlinearities. Kronauer, Forger, and Jewett have proposed a model for light preprocessing, Process L, representing a biochemical process that converts a light signal into an effective drive on the circadian pacemaker. In the paper presented here, the authors use the classic van der Pol oscillator with Process L and Jewett and Kronauer's model of Aschoff's rule to model the human circadian pacemaker. This simpler cubic model predicts the results of a three-pulse human phase response curve experiment and a two-pulse amplitude reduction study with as much, or more, accuracy as the models of Jewett and Kronauer and Kronauer, Forger, and Jewett, which both employ a nonlinearity of degree 7. This suggests that this simpler cubic model should be considered as a potential alternative to other models of the human circadian system currently available.

Quantitative modelling of sleep dynamics

“…The total excitatory drive D to the VLPO comprises C and H , where C can be interpreted as the SCN firing rate and H is a firing rate change due to somnogenic effects; in both cases only the products n vc C and n vh H influence D. When simple entrainment can be assumed, C ≈ c 0 + cos(Ut), where c 0 is a constant offset, U = 2p/(24 h), and the amplitude of C is absorbed into n vc . In other cases, such as jetlag and modelling chronotype, C is modelled using the oscillator model of Forger et al [27], which includes (i) a light processing component (process L), and (ii) a van der Pol oscillator component (process P). In process L, retinal …”

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