Sleep and circadian rhythms
Our lives have an approximately daily (circadian) rhythm of wake and sleep, feeding and fasting. These rhythms are part of a complex, hierarchical, coupled oscillator system with rhythmicity generated within nearly every cell of our bodies and coordinated by the so-called 'master' clock in the suprachiasmatic nucleus of the brain. There is increasing evidence that disrupting our biological rhythms is bad for our health and a contributory factor to obesity, cardiovascular disease, mood disorders and cognitive decline.
We use mathematical models at many different scales to help understand the structure of this complex system – from detailed models of gene transcription/translation cycles at the molecular level through to human scale models of the sleep/wake cycle.
The impact of the modern light environment on sleep
Anne Skeldon with Derk-Jan Dijk (Surrey Sleep Research Centre) are using mathematical modelling to assess the impact of the modern light environment on sleep and the consequent impact on health and wellbeing. Traditionally, humans experienced bright light during the day and very low levels of light after sunset. The use of bright artificial lighting has had a profound effect on our light environment, giving us much greater choice over when we work and socialise. But with what impact? Light pollution at night disrupts the behaviour of wildlife and is correlated with poor sleep quality and reduced sleep duration in humans.
During waking hours, our lifestyles mean that we spend the majority of time indoors and expose ourselves to artificial light long after sunset. The net effect is that we have a greatly reduced exposure to the natural cycle of light and dark, resulting in delayed circadian rhythms, later sleep timing, social jet-lag and difficulties maintaining 24-hour rhythmicity. These issues are further exacerbated by the increased use of lighting in the evening with an enhanced-blue component.
In a recent paper with Andrew Phillips (Harvard Medical School), mathematical modelling is used to understand how light, individual physiological differences and social constraints such as getting up for work or school interact. The work was featured in the UK parliamentary debate 'school should start at 10am because teenagers are too tired'. The team has a particular interest in the impact of our light environment on sleep, including the impact of permanent DST (PDF).
Analysis of mathematical models of sleep/wake regulation: Non-smooth dynamics and bifurcations
The most influential model of sleep/wake regulation is the two process model. This model postulates that sleep and wake occur as a result of the interaction of two oscillators, one describing circadian rhythmicity (the body clock) and one describing sleep homeostasis (sleep need). This model has formed the theoretical framework for sleep researchers for the last 30 years, and forms the backbone of recent `physiological' models of sleep. The two process model is an interesting example of a non-smooth dynamical system.
Anne Skeldon and Gianne Derks, with PhD student Matt Bailey, are investigating the bifurcations and dynamics of the two process model, which can be represented as a circle map. In collaboration with Paul Glendinning (University of Manchester), they have also analysed a broader class of `threshold models' of which the two process model is an example.
We are interested in developing interactive tools to help explain the interactions of sleep, light and social rhythms. Take a look at an early example of this work from Anne Skeldon.
Sleep, maths and technology
Anne Skeldon and Derk-Jan Dijk are interested in developing new data analytics/mathematical modelling techniques for extracting meaning from data, particularly in the context of sleep and circadian rhythms. Some of their work is funded by the Dementia Research Institute, which aims to develop technological solutions to help people live in their own homes as long as possible. They also collaborate with researchers in the Centre for Vision Speech and Signal Processing.
Biomathematical models of fatigue
When people are sleep deprived, they make poorer decisions, are slower to react and are more at risk of having accidents. In the workplace, employers have a duty to manage fatigue risk – a particular issue for shift work. Anne Skeldon, Derk-Jan Dijk and Steven Lockley (Surrey Sleep Research Centre) develop and apply biomathematical models of fatigue. Read a report on fatigue, alertness and risk prediction for shift workers from a recent collaboration with TFL.