Method to determine whether sleep phenotypes are driven by endogenous circadian rhythms or environmental light by combining longitudinal data and personalised mathematical models
Authors: Skeldon Anne C. , Rodriguez Garcia Thalia , Cleator Sean F. , della Monica Ciro , Ravindran Kiran K.G. , Revell Victoria L. , Dijk Derk-Jan 
Published: June 2023

Sleep timing varies between individuals and can be altered in mental and physical health conditions. Sleep and circadian sleep phenotypes, including circadian rhythm sleep-wake disorders, may be driven by endogenous physiological processes, exogeneous environmental light exposure along with social constraints and behavioural factors. Identifying the relative contributions of these driving factors to different phenotypes is essential for the design of personalised interventions.

The timing of the human sleep-wake cycle has been modelled as an interaction of a relaxation oscillator (the sleep homeostat), a stable limit cycle oscillator with a near 24-hour period (the circadian process), man-made light exposure and the natural light-dark cycle generated by the Earth’s rotation. However, these models have rarely been used to quantitatively describe sleep at the individual level. Here, we present a new Homeostatic-Circadian-Light model (HCL) which is simpler, more transparent and more computationally efficient than other available models and is designed to run using longitudinal sleep and light exposure data from wearable sensors. We carry out a systematic sensitivity analysis for all model parameters and discuss parameter identifiability.

We demonstrate that individual sleep phenotypes in each of 34 older participants (65-83y) can be described by feeding individual participant light exposure patterns into the model and fitting two parameters that capture individual average sleep duration and timing. The fitted parameters describe endogenous drivers of sleep phenotypes.

We then quantify exogenous drivers using a novel metric which encodes the circadian phase dependence of the response to light. Combining endogenous and exogeneous drivers better explains individual mean mid-sleep (adjusted R-squared 0.64) than either driver on its own (adjusted R-squared 0.08 and 0.17 respectively).

Critically, our model and analysis highlights that different people exhibiting thesamesleep phenotype may havedifferentdriving factors and opens the door to personalised interventions to regularize sleep-wake timing that are readily implementable with current digital health technology.

Author summary

Disrupted sleep has long term health consequences and affects our day-to-day ability to function physically, mentally and emotionally. But what determines when and how long we sleep?

It is well-known that daily light exposure patterns determine the timing of the body clock. However, creating mathematical models that can take realistic light exposure patterns and predict plausible sleep timing has been challenging. Furthermore, nearly all previous studies have focused on developing models for average behaviour, yet sleep timing and duration are highly individual.

In this paper, we present a simple model that combines sleep regulatory and circadian processes. The model can take individual light exposure patterns and, by fitting physiologically plausible parameters, describe individual mean sleep timing and duration. We test our model on data collected from 34 older participants. Our modelling approach suggests that some of the participants slept late because of physiological factors, while for other individuals, late sleep was a consequence of their light environment.

This approach of combining a model with longitudinal data could be implemented in digital health technology such that your smart watch could tell you not only how you slept last night, but also how to change your light environment to sleep better tomorrow.