Why can't I fall asleep? Will this new medication keep me up all night? Can I sleep off this cold? Despite decades of research, answers to these basic questions about one of our most essential bodily functions remain exceptionally difficult to answer. In fact, researchers still don't fully understand why we even sleep at all. In an effort to better understand the sleep-wake cycle and how it can go awry, researchers at Rensselaer Polytechnic Institute are taking a different approach than the traditional brain scans and sleep studies. They are using mathematics.
Professor of Mathematics Mark Holmes and his graduate student Lisa Rogers are using math to develop a new computer model that can be easily manipulated by other scientists and doctors to predict how different environmental, medical, or physical changes to a person's body will affect their sleep. Their model will also provide clues to the most basic dynamics of the sleep-wake cycle.
"We wanted to create a very interdisciplinary tool to understand the sleep-wake cycle," Holmes said. "We based the model on the best and most recent biological findings developed by neurobiologists on the various phases of the cycle and built our mathematical equations from that foundation. This has created a model that is both mathematically and biologically accurate and useful to a variety of scientists.
"This is also an important example of how applied mathematics can be used to solve real issues in science and medicine," Holmes continued.
To create the model, the researchers literally rolled up their sleeves and took to the laboratory before they put pencil to paper on the mathematical equations. Rogers spent last summer with neurobiologists at Harvard Medical School to learn about the biology of the brain. She investigated the role of specific neurotransmitters within the brain at various points in the sleep-wake cycle. The work taught the budding mathematician how to read EEG (electroencephalography) and EMG (electromyography) data on the brainwaves and muscle activity that occur during the sleep cycle. This biologic data would form the foundation of their mathematic calculations.
She also learned about the role of light and the sleep-wake cycle, a process known as a circadian rhythm. "There are many connections between the sleep-wake cycle and circadian rhythms," Rogers said. "But scientists have come to realize that the basic parts of the sleep-wake cycle are not light dependent. People will sleep in a dark cave or in constant bright sun. We used this to develop the first mathematical model that is not predicated on daylight or the absence of daylight."