Quantitative modelling of sleep dynamics

Robinson, P. A.; Phillips, Andrew J. K.; Fulcher, Ben D.; Puckeridge, Max; Roberts, James A.

doi:10.1098/rsta.2011.0120

Cited by 37 publications

(33 citation statements)

References 53 publications

(97 reference statements)

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“…This approach leads to so-called neural field models and is used in this issue by Bojak et al [38], Fleshner et al [39] and Robinson et al [40]. It ignores the precise firing times of neurons, which can be a reasonable approximation in neural populations for processes that are slow compared with that of the spike dynamics.…”

Section: The Complex Dynamics Of the Sleeping Brainmentioning

confidence: 99%

“…There the activity of the specific neural populations involved in sleep regulation is modelled by coupled nonlinear ordinary differential equations that can produce limit cycles, show hysteresis effects and undergo bifurcations. In this issue, Fleshner et al [39] concentrate on the interaction between the circadian and the homeostatic regulatory mechanisms by modelling the neurotransmitter-mediated interactions between the corresponding neural populations, whereas Robinson et al [40] focus on the reaction of the regulatory dynamics to external influences, such as auditory stimuli, sleep deprivation or caffeine.…”

Section: (B) the Nonlinear Dynamics Of Sleep Regulationmentioning

confidence: 99%

“…Both Robinson et al [40] and Fleshner et al [39] model homeostasis in the framework of the adenosinergic system. In these models, the homeostatic component, however, has no link to neuronal substrates generating slow waves and thus has no relation to slow-wave activity.…”

Section: (B) the Nonlinear Dynamics Of Sleep Regulationmentioning

confidence: 99%

“…by analysing the linear response of the stationary solution to stochastic perturbations. Robinson et al [48] formulated a neural field model of the thalamocortical system during sleep (reviewed also briefly in this issue [40]), which reproduced spectral characteristics of the sleep EEG in the different sleep stages. They related the different sleep oscillations to corresponding Hopf bifurcations in the model, with normal awake and sleep stages being located in the region where the fixed point is stable.…”

Section: (A) Sleep Oscillationsmentioning

confidence: 99%

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The sleeping brain as a complex system

Olbrich

Achermann

Wennekers

2011

Phil. Trans. R. Soc. A.

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'Complexity science' is a rapidly developing research direction with applications in a multitude of fields that study complex systems consisting of a number of nonlinear elements with interesting dynamics and mutual interactions. This Theme Issue 'The complexity of sleep' aims at fostering the application of complexity science to sleep research, because the brain in its different sleep stages adopts different global states that express distinct activity patterns in large and complex networks of neural circuits. This introduction discusses the contributions collected in the present Theme Issue. We highlight the potential and challenges of a complex systems approach to develop an understanding of the brain in general and the sleeping brain in particular. Basically, we focus on two topics: the complex networks approach to understand the changes in the functional connectivity of the brain during sleep, and the complex dynamics of sleep, including sleep regulation. We hope that this Theme Issue will stimulate and intensify the interdisciplinary communication to advance our understanding of the complex dynamics of the brain that underlies sleep and consciousness.

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Section: The Complex Dynamics Of the Sleeping Brainmentioning

confidence: 99%

Section: (B) the Nonlinear Dynamics Of Sleep Regulationmentioning

confidence: 99%

Section: (B) the Nonlinear Dynamics Of Sleep Regulationmentioning

confidence: 99%

Section: (A) Sleep Oscillationsmentioning

confidence: 99%

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The sleeping brain as a complex system

Olbrich

Achermann

Wennekers

2011

Phil. Trans. R. Soc. A.

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“…Obviously, the transition from wakefulness to sleep and vice versa, and the transitions between NREM and REM sleep are state changes. Saper and co-workers [41,42] have proposed a 'putative flipflop' for wake-sleep as well as for NREM-REM sleep transitions (see also [43]). …”

Section: (A) Principal Component Analysismentioning

confidence: 99%

The multiple time scales of sleep dynamics as a challenge for modelling the sleeping brain

Olbrich

Claussen

Achermann

2011

Phil. Trans. R. Soc. A.

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A particular property of the sleeping brain is that it exhibits dynamics on very different time scales ranging from the typical sleep oscillations such as sleep spindles and slow waves that can be observed in electroencephalogram (EEG) segments of several seconds duration over the transitions between the different sleep stages on a time scale of minutes to the dynamical processes involved in sleep regulation with typical time constants in the range of hours. There is an increasing body of work on mathematical and computational models addressing these different dynamics, however, usually considering only processes on a single time scale. In this paper, we review and present a new analysis of the dynamics of human sleep EEG at the different time scales and relate the findings to recent modelling efforts pointing out both the achievements and remaining challenges.

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Mathematical modeling of circadian rhythms

Asgari-Targhi

Klerman

2018

WIREs Mechanisms of Disease

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Circadian rhythms are endogenous~24-hr oscillations usually entrained to daily environmental cycles of light/dark. Many biological processes and physiological functions including mammalian body temperature, the cell cycle, sleep/wake cycles, neurobehavioral performance, and a wide range of diseases including metabolic, cardiovascular, and psychiatric disorders are impacted by these rhythms. Circadian clocks are present within individual cells and at tissue and organismal levels as emergent properties from the interaction of cellular oscillators. Mathematical models of circadian rhythms have been proposed to provide a better understanding of and to predict aspects of this complex physiological system. These models can be used to: (a) manipulate the system in silico with specificity that cannot be easily achieved using in vivo and in vitro experimental methods and at lower cost, (b) resolve apparently contradictory empirical results, (c) generate hypotheses, (d) design new experiments, and (e) to design interventions for altering circadian rhythms. Mathematical models differ in structure, the underlying assumptions, the number of parameters and variables, and constraints on variables. Models representing circadian rhythms at different physiologic scales and in different species are reviewed to promote understanding of these models and facilitate their use. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models K E Y W O R D S biological oscillators, circadian clock, circadian rhythms, dynamic systems, mathematical modeling, statistical modeling BOX 1 CIRCADIAN MODELINGCircadian clocks are present within individual cells, and communication among multiple cells gives rise to emergent properties at the tissue level. In mammals, both the master circadian clock in the suprachiasmatic nucleus and tissuelevel peripheral clocks have major effects at the organism level on numerous key physiological functions, including sleep/wake cycles, metabolism, cardiovascular function, reproduction, immune function, neurobehavioral performance, and mood. Misalignment between the master clock and peripheral clocks within an organism, or misalignment between an organism's clocks and its external environment, has adverse physiological consequences. When circadian interventions are needed to improve physiological function, a multiscale understanding of circadian rhythmicity therefore is essential to accurately manipulate this complex oscillatory system. Mathematical modeling is an essential tool to study and analyze complex physiological systems. It has been used to provide insight into the circadian system at multiple levels (i.e., organism, multi-cellular, cellular, molecular, genetic), to design new experiments, and to manipulate and control the components of the system in silico with specificity that

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Quantitative modelling of sleep dynamics

Cited by 37 publications

References 53 publications

The sleeping brain as a complex system

The sleeping brain as a complex system

The multiple time scales of sleep dynamics as a challenge for modelling the sleeping brain

Mathematical modeling of circadian rhythms

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