Mathematical models of regulatory mechanisms of sleep-wake rhythms

Nakao, Mitsuyuki; Karashima, Akihiro; Katayama, N.

doi:10.1007/s00018-007-6534-z

Cited by 12 publications

(14 citation statements)

References 46 publications

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“…Here, similarity between the phase oscillator model and two‐process model is shown in terms of a circle map. The two‐process model is still one of the most popular models though 20 or more years have passed since it was developed 12,13 . The two‐process model consists of periodic C processes and an exponentially rising–decaying S process.…”

Section: Similarity Between the Phase Oscillator Model And The Two‐prmentioning

confidence: 99%

“…Because a sleep–wake rhythm is not directly controlled by the SCN oscillator, Osc I, obtaining the circle map of the sleep‐onset phase with regard to phase of the SCN oscillator is a complicated task under the phase oscillator model. For this purpose, the model is reduced into a coupled oscillator with unidirectional connection from Osc I to II by identifying Osc SW as Osc II and ignoring the opposite connection from Osc II to I 13 . The reduced model is shown at the top of Figure 5.…”

Section: Similarity Between the Phase Oscillator Model And The Two‐prmentioning

confidence: 99%

“… The simplified phase oscillator model (upper panel) and its circle map for varied C 12 = 0.30, 0.50, 0.77 (from top to bottom, lower panel) 13 …”

Section: Similarity Between the Phase Oscillator Model And The Two‐prmentioning

confidence: 99%

“…On the other hand, for the delaying case, they are changed rapidly under the schedule. The effect of Osc I on Osc II through C 13 and C 32 overcomes that through C 12 , which enables the delaying reentrainment.…”

Section: Simulations Of Non-photic Entrainment Of the Human Circadianmentioning

confidence: 99%

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Top-down modeling of hierarchical biological clock mechanisms

Nakao

Okayama

Karashima

et al. 2010

Sleep and Biological Rhythms

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The behavior of human circadian rhythms could be interpreted within the two-oscillator regime: one for the circadian pacemaker driving temperature/plasma melatonin rhythm and the other for the sleep-wake rhythm, tentatively called the SCN (suprachiasmatic nucleus) oscillator and non-SCN oscillator, respectively. Recently, the existence of the non-SCN oscillator was demonstrated through showing the possibility of non-photic entrainments by the shifted sleep schedule, and its interactions with the SCN oscillator were disclosed through analyzing the re-entrainment processes. Based on these experimental results at the behavioral level, we developed a phase oscillator model consisting of mutually coupled SCN and non-SCN oscillators, and an extra-oscillator representing an overt sleep-wake rhythm. Our model successfully reproduced the experimental results of the non-photic entrainments. In addition, our phase oscillator model and the widely accepted twoprocess model were shown to share a possible mechanism underlying interactions found between the SCN and non-SCN oscillators during the re-entrainment processes. Therefore, it was suggested that the interactions indicated essential dynamics of the SCN and non-SCN oscillators. Then, a possible mechanism underlying the interactions at the behavioral level was reduced into the conditions of coupling strength and intrinsic angular velocity in the coupled realistic oscillators. These conditions led us to the hypothesis at the organ level that a part of the SCN oscillator is non-photically entrained through being coupled with the non-SCN oscillator. Of course, its reality should be assessed further. This top-down approach is one of practical strategies for modeling the hierarchical biological system.

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Section: Similarity Between the Phase Oscillator Model And The Two‐prmentioning

confidence: 99%

Section: Similarity Between the Phase Oscillator Model And The Two‐prmentioning

confidence: 99%

“… The simplified phase oscillator model (upper panel) and its circle map for varied C 12 = 0.30, 0.50, 0.77 (from top to bottom, lower panel) 13 …”

Section: Similarity Between the Phase Oscillator Model And The Two‐prmentioning

confidence: 99%

Section: Simulations Of Non-photic Entrainment Of the Human Circadianmentioning

confidence: 99%

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Top-down modeling of hierarchical biological clock mechanisms

Nakao

Okayama

Karashima

et al. 2010

Sleep and Biological Rhythms

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“…The sleep–waking cycle is produced through the interplay of two mechanisms. The first is circadian and is governed by the hypothalamic suprachiasmatic nucleus, and consists of heterogeneous coupled oscillators that receive input from multiple areas of the brain (Indic et al 2007), while the second, homeostatic, strives to maintain the length of sleep and is involved in energy balance via still poorly understood feedbacks (Phillips & Robinson, 2007; Nakao et al 2007; McCauley et al 2009). In addition, other inputs from within the body arising, for example, from the respiratory and circulatory systems can lead to switching from sleep to wakefulness and vice versa.…”

mentioning

confidence: 99%

Influence of arousal threshold and depth of sleep on respiratory stability in man: analysis using a mathematical model

Longobardo

Evangelisti

Cherniack

2009

Experimental Physiology

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We examined the effect of arousals (shifts from sleep to wakefulness) on breathing during sleep using a mathematical model. The model consisted of a description of the fluid dynamics and mechanical properties of the upper airways and lungs, as well as a controller sensitive to arterial and brain changes in CO 2 , changes in arterial oxygen, and a neural input, alertness. The body was divided into multiple gas store compartments connected by the circulation. Cardiac output was constant, and cerebral blood flows were sensitive to changes in O 2 and CO 2 levels. Arousal was considered to occur instantaneously when afferent respiratory chemical and neural stimulation reached a threshold value, while sleep occurred when stimulation fell below that value. In the case of rigid and nearly incompressible upper airways, lowering arousal threshold decreased the stability of breathing and led to the occurrence of repeated apnoeas. In more compressible upper airways, to maintain stability, increasing arousal thresholds and decreasing elasticity were linked approximately linearly, until at low elastances arousal thresholds had no effect on stability. Increased controller gain promoted instability. The architecture of apnoeas during unstable sleep changed with the arousal threshold and decreases in elasticity. With rigid airways, apnoeas were central. With lower elastances, apnoeas were mixed even with higher arousal thresholds. With very low elastances and still higher arousal thresholds, sleep consisted totally of obstructed apnoeas. Cycle lengths shortened as the sleep architecture changed from mixed apnoeas to total obstruction. Deeper sleep also tended to promote instability by increasing plant gain. These instabilities could be countered by arousal threshold increases which were tied to deeper sleep or accumulated aroused time, or by decreased controller gains.

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