such as "Introduction", "Conclusion"..etc
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
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
biological data would form the foundation of their mathematical
This research foundation allowed the team to develop a massive
11-equation model of the sleep-wake cycle. They are now working to
input those differential equations into an easy-to-use graphic computer
model for biologists and doctors to study.
"We have developed a model that can serve other researchers as a
benchmark of the ideal, healthy sleep-wake cycle," Holmes said.
"Scientists will be able to take this ideal model and predict how
different disturbances such as caffeine or jet lag will impact that
ideal cycle. This is a very non-invasive way to study the brain and
sleep that will provide important clues on how to overcome these
disturbances and allow patients to have better and more undisturbed
Rogers will continue her work on the program after receiving her
doctoral degree in applied mathematics from Rensselaer this spring. Her
work on the mathematics of the sleep-wake cycle has already garnered
attention within the scientific community, earning her a postdoctoral
research fellowship from the National Science Foundation (NSF). With
the fellowship, Rogers will continue her work at New York University
and begin to incorporate other aspects of the sleep-wake cycle in the
model such as the impacts of circadian rhythms.
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