Maths and apps promise help for sleepless nights

Researchers concerned about disruptions in the body’s day/night cycle, often called its circadian rhythm, are increasingly turning from the sleep lab to mathematics to work out thorny problems in how best to handle jetlag, shift work, and weekend lifestyle patterns.

The research draws on known factors influencing circadian rhythms and sleep, such as the effect of light, caffeine, napping, and even an increasingly sophisticated understanding of the body’s circadian pacemaker, a group of about 20,000 nerve cells in the hypothalamus, a tiny region of the brain that controls a number of important metabolic processes.

One early application of such modelling, says Elizabeth Klerman, a sleep researcher at Brigham and Women’s Hospital in Boston, Massachusetts, US, was by NASA, when it wanted to shift astronaut’s circadian rhythms so they would be at peak alertness for a 2am shuttle launch.

“It was one of the first times modelling had been used,” Klerman recently told a meeting of the Society for Industrial and Applied Mathematics (SIAM) in Portland, Oregon.

“Astronauts actually demanded that lighting be added to their pre-launch rooms.”

Models can also be used to help adjust as efficiently as possible to jet lag. Olivia Walch, an applied mathematician at the University of Michigan, has developed a free smartphone app called Entrain, that tells users when to seek light or avoid it in order to most rapidly adjust to any time-zone change.

In exchange, users are encouraged to submit their own lighting history, travel schedules, and jetlag ratings, in order to improve the model and fuel the next generation of research.

More recently, she realised that if people are willing to share movement and heart rate data from devices such as an Apple Watch, it’s possible to track their sleep patterns, including when they are in deep REM sleep or lighter non-REM sleep.

“People are walking around with sophisticated devices on their arms all the time,” she explains. “Entrain has gone from a jetlag project to a potential way to collect sleep data from around the world.”

Modelling can also help researchers design lab protocols for future circadian rhythm studies, says Nora Stack, a graduate student at Colorado School of Mines in Golden, Colorado.

These studies, she says, are often done by subjecting experimental subjects to a series of mini-days and nights, possibly as short as four hours each. Such protocols are used because they allow many such cycles in the course of a few days, rather than using longer cycles that require research subjects to live with them over the course of weeks or months.

But what’s the best cycle, she asks. Four hours? Five? Seven? And what’s the best time of day to begin the study? Noon? Early afternoon? Late morning? Modelling work such as Stack’s, says Klerman, helps researchers design experiments without having to work through every possible variant just to see which is best.

Circadian modelling can also be used to help people be alert for other important tasks, even if they aren’t as dramatic as a space shuttle launch.

For example, suppose you have to miss a night’s sleep but still be alert for an important event about the time you’d normally go to sleep on the second day? Circadian rhythm models, Klerman says, can help you help figure out the optimum timing of a bright light, caffeine, and maybe a nap, to put you at your peak abilities at the right time, rather than having you asleep on your feet.

Such research, she adds, can also be used to optimise the schedules of medical residents, well known for having horrible work shifts.

But the biggest benefits are for public health. Medical researchers are increasingly aware that jetlag and night shift can be detrimental to health, says Klerman, “[and] there is increasing evidence that ‘social jetlag’ [from weekend late nights] is also detrimental.”

Not that our lives are ever going to return to pre-industrial days.

“We know we need people to do shift work, because we need things to function 24 hours a day,” says Stack’s dissertation advisor, Cecilia Diniz Behn, also of the Colorado School of Mines.

The goal, she says, is to take what we are learning and find ways to use it to help people adjust to such schedules with minimum harm to their health.

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