A report in LiveScience, in partnership with the National Science Foundation, attempts to understand sleep via mathematics. Janet Best, a mathematician at Ohio State University, has spent the past decade studying sleep-wake cycles using mathematical models.
“To understand sleep, we try to reformulate biological questions in terms of mathematics, typically systems of differential equations,” said Best in a LiveScience publication. “Sleep is both regular and random. It’s regular in that we go to sleep generally at the same time of day. The randomness occurs in infants who seem to have no pattern to their sleep cycles and in the variability of when we might wake up during the night. I’ve been investigating how neural structures in the brain affect the random and regular transitions between sleep and wake.”
The report from Ivy F. Kupec of the National Science Foundation describes the work of Best through equations involving the properties of neurons involved in sleep-wake brain circuitry. “Best develops mathematical models that represent ways in which neurons interact and influence each other,” writes Kupec. “She validates her models by checking their predictions against data that biologists gather in studies involving both humans and rats. Once validated, Best’s models can be used to test ideas about sleep and wake patterns.”
“The idea is to see how people sleep normally, so we can understand when things go wrong,” said Best. “Throughout the night we experience ‘bouts’ of sleep and wakefulness. There’s variability that we’re aware of, but actually even more variability is occurring – we only recall longer wake episodes. However, both short and long episodes occur, and that’s something I’m trying to understand. Experimentalists collect data on these wake/sleep bouts. Since the length of sleep and wake bouts and the transitions between them show some regular and some random behavior, the differential equations must capture both of these facets.”
