To be clear, we’re not making a crack about math problems “sending you to sleep” or anything. It’s actually much cooler than that: a new study from researchers at the University of Surrey has found that the so-called “two-process model” of sleep – the usual framework through which we understand the phenomenon – can be modeled mathematically.
“This work shows how math can bring clarity to something as complex and personal as sleep,” Derk-Jan Dijk, co-author of the study and director of the Surrey Sleep Research Center at the University of Surrey, said in a statement this week. “With the right data and models, we can give more tailored advice and develop novel interventions to improve sleep patterns for those whose rest is affected by modern routines, aging, or health conditions.”
The patterns behind your sleep pattern
How can math explain our sleep patterns? Well, the first thing to understand is the two-process model of sleep itself: it’s the widely used framework that places our sleep patterns as the product of two independent factors (hence the name, really). The first, homeostatic sleep drive or “sleep pressure”, builds up steadily while we’re awake and reduces while we’re asleep – you can think of it as like the charges on a credit card building up until they get paid off at the end of the month. The second is your circadian rhythm – the 24-hour-ish cycle held in check by external stimuli like the sunlight or mealtimes.
While it’s easy to describe in vague terms like this, the two-process model of sleep “consists of mathematical equations with a precise meaning,” write the researchers – and that “means it has quantitative predictive power.” It also means that sleep patterns can be modeled and investigated theoretically – and when the team did so, they saw something interesting.
“The two-process model […] falls within the wider class of coupled oscillator models,” they explain in the paper. Basically, it’s a complicated system, but only because it’s a sum of simpler ones: it comes from the sleep-wake cycles that our bodies naturally want to follow, but kept in check – a process called “entrainment” – by our inner body clocks, which take their cues from food, hormones, and so on, and the pattern of light and dark which reaches our brains through our eyes.
These three inputs all interact together to create our individual rhythms of sleepiness and wakefulness – a lovely, predictable mathematical system. Scientists have previously used this structure to explain how the body reacts to things like sleep deprivation, time isolation, and continuous bed rest – so perhaps, the team thought, could it also help us understand sleep disorders and disruption?
Turns out, yes, it can.
The math of sleep
So, what did the team learn? Well, turns out viewing sleep patterns through this mathematical lens sheds some light on longstanding puzzles and patterns. For example, we know that generally, sleep phenotypes change as we age – and that, the team suggests, “may be a consequence of changes in circadian amplitude and/or sleep homeostasis and not changes in circadian period.”
Take babies, for example. As any new parent can tell you, those guys sleep a lot – and often, too, taking as many as six naps throughout their day. Eventually, though, that evens out to the now-standard “one sleep per day” model – a change which the team says “could be explained by physiological changes that lead to a gradual lengthening of the natural-sleep wake period rather than a change in the circadian process.”
But – and again, as any new parent can tell you – that process is far from gradual. What parents know as “sleep regressions” may also be explained by this mathematical interpretation of the two-process model: “the theoretical structure predicts that periods of relatively regular sleep patterns followed by periods of transition,” they write.
A similar mathematical accounting can explain why teens sleep in and elderly people rise with the sun, the team believes. Rather than a gradual maturing of the circadian system, as is sometimes assumed, the reason may be that sleep pressure increases more slowly with age. The length of a day, on the other hand, doesn’t change – or at least, not perceptibly so – so the net effect is that the circadian minimum, when your body is at its sleepiest, moves from late to early over the years.
Altogether, the work is a “challenge [to] our pre-conceptions on what causes phenotypes or phenotypic change in humans,” the team writes.
Go to bed!
Of course, the fact that you’re older than you were last week probably isn’t entirely why your sleep schedule is out of whack. It’s well-known at this point that the main driver of the human circadian rhythm is light – and so that third oscillator, the light-dark cycle, has an outsized effect on the system. The result is something that likely won’t surprise you: “[If] there is insufficient contrast between light that is available during the day and light that is available during the night, then only a small range of intrinsic circadian periods close to 24h can be entrained,” the team write. “The stronger the forcing, the larger the range of circadian periods that can be entrained.”
In other words? If you extend the amount of time you spend in light – whether because you happen to live at an extreme latitude or, more likely, because you own at least one lightbulb – then your circadian rhythm is going to be easier to disrupt. It’s hardly news, we know, but it certainly adds fuel to the advice Hozier’s love interest keeps giving about getting to bed before the sunlight.
“By using math, we can see how small changes in light, routine, or biology shift our sleep, and test practical ways to support better sleep for everyone,” explained Anne Skeldon, Head of the School of Mathematics at the University of Surrey and lead author of the study.
“This model gives us hope that sleep problems can be better understood and tackled,” Skeldon said. “It’s a step toward more personalized, effective solutions that improve people’s daily lives.”
The study is published in the journal npj Biological Timing and Sleep.
Source Link: Why Is Your Sleep Schedule So Messed Up? Math Has The Answer!
