Why Your Sleep Is Disrupted: The Math Solution!

Understanding Sleep Through Mathematical Models

There are numerous factors that influence how and when we sleep—our mood, the level of activity during the day, various drugs or illnesses, and even external disturbances like someone screaming in the middle of the night. However, a new study from researchers at the University of Surrey has introduced an unexpected element: mathematics. This research reveals that the two-process model of sleep, which is widely used to explain our sleep patterns, can be accurately described using mathematical equations.

Derk-Jan Dijk, co-author of the study and director of the Surrey Sleep Research Center, emphasized the importance of this discovery. “This work shows how math can bring clarity to something as complex and personal as sleep,” he stated. He added that with the right data and models, scientists can provide more tailored advice and develop innovative interventions to improve sleep for those affected by modern lifestyles, aging, or health conditions.

The Two-Process Model of Sleep

The two-process model of sleep is based on two key factors: homeostatic sleep drive, often referred to as "sleep pressure," and the circadian rhythm. The sleep pressure builds up while we are awake and decreases during sleep, similar to a credit card balance that accumulates until it is paid off. The circadian rhythm, on the other hand, follows a 24-hour cycle influenced by external cues such as sunlight and meal times.

These two processes interact to determine our sleep-wake cycles. According to the researchers, the two-process model is not just a conceptual framework but consists of precise mathematical equations that allow for quantitative predictions. This means that sleep patterns can be modeled and studied theoretically, leading to deeper insights into how our bodies regulate sleep.

Mathematical Insights into Sleep Patterns

By applying mathematical analysis to the two-process model, the research team discovered some fascinating findings. For instance, they found that changes in sleep patterns as we age may result from shifts in circadian amplitude or sleep homeostasis rather than changes in the circadian period itself.

Take babies, for example. They typically sleep a lot and take multiple naps throughout the day. As they grow, their sleep patterns evolve into the standard one-sleep-per-day model. The researchers suggest this shift could be due to physiological changes that gradually lengthen the natural sleep-wake period rather than alterations in the circadian process.

Additionally, the study explains phenomena like "sleep regressions" in infants. These periods of disrupted sleep may be linked to the theoretical structure of the two-process model, which predicts regular sleep patterns followed by transitional phases.

Sleep Changes Across the Lifespan

The mathematical model also helps explain why teenagers tend to sleep in and older adults rise early. Rather than a gradual maturation of the circadian system, the researchers propose that sleep pressure increases more slowly with age. Since the length of a day remains constant, the circadian minimum—the time when the body is most sleepy—shifts earlier over time.

This finding challenges previous assumptions about the causes of phenotypic changes in humans, offering a new perspective on how our sleep patterns evolve throughout life.

The Role of Light in Sleep Regulation

While aging plays a role in sleep disruption, light remains the primary driver of the human circadian rhythm. The researchers noted that insufficient contrast between daytime and nighttime light can limit the range of circadian periods that can be entrained. In other words, if you spend too much time in artificial light, your internal clock becomes more susceptible to disruption.

“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, lead author of the study. She added that this model offers hope for better understanding and addressing sleep problems, paving the way for personalized solutions that improve daily life.

Conclusion

The study, published in the journal npj Biological Timing and Sleep, highlights the power of mathematics in unraveling the complexities of sleep. By providing a clearer framework for understanding sleep patterns, it opens the door to more effective strategies for improving sleep quality across different stages of life.