Speaker
Description
Insomnia is one of the most prevalent sleep disorders, associated with increased risk of conditions ranging from diabetes to heart disease \cite{b23}. Yet, much about its physiological causes and processes is still far from understood.
Mathematical modelling has had an important role to play in understanding the process of sleep itself. Some of the most important of these contributions have been the two-process model, composing sleep as interacting circadian and homeostatic drives \cite{b82}, the flip-flop model, inspired by neurological processes to model a ‘natural’ switch between the sleeping and waking state \cite{s01}, and physiology-inspired network models, incorporating REM and non-REM sleep states through physically realistic networks \cite{f08}.
In this talk our new three-process model for insomnia-like awakenings will be presented, introducing a new wakefulness drive to the two-process model of sleep. This will include sensitivity analysis of the original model and an exploration of its dynamical regimes, and the new insights these provide into the mechanisms by which insomnia can arise. These results will be further contextualised with dynamical analysis of key existing sleep models, demonstrating the need for this new approach to incorporate insomnia.
Finally, a new framework for mathematically representing insomnia based on this model will be discussed, including its implications for further modelling developments to understand more insomnia features.
Bibliography
@article{b23,
title = {Diurnal rhythms of wrist temperature are associated with future disease risk in the {UK} {Biobank}},
volume = {14},
issn = {2041-1723},
url = {https://www.nature.com/articles/s41467-023-40977-5},
doi = {10.1038/s41467-023-40977-5},
abstract = {Abstract
Many chronic disease symptomatologies involve desynchronized sleep-wake cycles, indicative of disrupted biorhythms. This can be interrogated using body temperature rhythms, which have circadian as well as sleep-wake behavior/environmental evoked components. Here, we investigated the association of wrist temperature amplitudes with a future onset of disease in the UK Biobank one year after actigraphy. Among 425 disease conditions (range
n
= 200-6728) compared to controls (range
n
= 62,107-91,134), a total of 73 (17\%) disease phenotypes were significantly associated with decreased amplitudes of wrist temperature (Benjamini-Hochberg FDR q {\textless} 0.05) and 26 (6.1\%) PheCODEs passed a more stringent significance level (Bonferroni-correction α {\textless} 0.05). A two-standard deviation (1.8° Celsius) lower wrist temperature amplitude corresponded to hazard ratios of 1.91 (1.58-2.31 95\% CI) for NAFLD, 1.69 (1.53-1.88) for type 2 diabetes, 1.25 (1.14-1.37) for renal failure, 1.23 (1.17-1.3) for hypertension, and 1.22 (1.11-1.33) for pneumonia (phenome-wide atlas available at
http://bioinf.itmat.upenn.edu/biorhythm\_atlas/
). This work suggests peripheral thermoregulation as a digital biomarker.},
language = {en},
number = {1},
urldate = {2026-03-15},
journal = {Nature Communications},
author = {Brooks, Thomas G. and Lahens, Nicholas F. and Grant, Gregory R. and Sheline, Yvette I. and FitzGerald, Garret A. and Skarke, Carsten},
month = aug,
year = {2023},
pages = {5172},
}
@article{b82,
title = {A two process model of sleep regulation},
volume = {1},
issn = {0721-9075},
abstract = {Presents a model of sleep regulation based on experimental studies. It is proposed that 2 processes play a dominant role in sleep regulation: a sleep-dependent process (Process S) and a sleep-independent circadian process (Process C). The time course of Process S was derived from the spectral analysis of slow wave activity in the human EEG. Its level shows an exponential decline during sleep and an increase during waking. The level of Process S at sleep onset is therefore considered to be a function of prior waking time. Process C is reflected by the rhythmic variation of sleep propensity during prolonged sleep deprivation and is assumed to be controlled by a circadian oscillator. In the model, sleep propensity and the duration of sleep are determined by the combined action of the 2 processes. The model is able to stimulate the variations of sleep duration as a function of sleep onset time. (103 ref) (PsycINFO Database Record (c) 2016 APA, all rights reserved)},
number = {3},
journal = {Human Neurobiology},
author = {Borbély, A. A.},
year = {1982},
keywords = {Human Biological Rhythms, Sleep, Models},
pages = {195--204},
}
@article{s01,
title = {The sleep switch: hypothalamic control of sleep and wakefulness},
volume = {24},
copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
issn = {01662236},
shorttitle = {The sleep switch},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0166223600020026},
doi = {10.1016/S0166-2236(00)02002-6},
language = {en},
number = {12},
urldate = {2026-03-15},
journal = {Trends in Neurosciences},
author = {Saper, Clifford B and Chou, Thomas C and Scammell, Thomas E},
month = dec,
year = {2001},
pages = {726--731},
}
@article{f08,
title = {Modeling the impact of impulsive stimuli on sleep-wake dynamics},
volume = {78},
copyright = {http://link.aps.org/licenses/aps-default-license},
issn = {1539-3755, 1550-2376},
url = {https://link.aps.org/doi/10.1103/PhysRevE.78.051920},
doi = {10.1103/PhysRevE.78.051920},
language = {en},
number = {5},
urldate = {2026-03-15},
journal = {Physical Review E},
author = {Fulcher, B. D. and Phillips, A. J. K. and Robinson, P. A.},
month = nov,
year = {2008},
pages = {051920},
}
