University of Pittsburgh
February 25, 1998


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PITTSBURGH, Feb. 26 -- A mathematical model of the mechanisms by which brain waves change based on our activity levels, from fully alert to sleeping, is the subject of new research by Pitt mathematician Bard Ermentrout published in the Feb. 27 issue of the prestigious journal Science.

This computational neuroscience modeling looks directly at the origins of certain brain waves in the thalamus, the portion of the human brain that relays information from our senses to the cerebral cortex, the main part of the brain where we do most of our thinking. The brain has a certain set of rhythms that vary according to our consciousness level. These rhythms originate in the thalamus and have a lower frequency, or occur less often, when we're sleeping and have higher frequencies when we're alert.

What Ermentrout, along with John Rinzel of New York University, David Terman of Ohio State University and Xiao Jing Wang of Brandeis University have discovered is that certain waves originating in the thalamus are not the kind of smooth continuous waves you would expect, but waves that "jump" as if interrupted along their way.

"If you think about a 'wave' at a football game," said Ermentrout, "you'll see that its movement is continuous. Imagine what that wave would look like if the crowd got up and sat down all together, only one section at a time. Then the wave would appear to jump from position to position. That's similar to what we are seeing in our computational models." Waves with this jumpy type of behavior are found in experiments on certain parts of the thalamus in animals.

This is happening, Ermentrout and his colleagues think, because of a type of neuron, or brain cell, in the thalamus that can be inhibited, or shut off, by other connected neurons. "When the inhibition stops, these neurons seem to 'turn on' in large groups which could be the cause of a non-smooth 'lurching' brain wave to move across the thalamus into the cortex," said Ermentrout.

Because of the far-reaching implications of the thalamus' role in controlling sleep and other sensory inputs, researchers want to understand the mechanisms by which these brain waves from the thalamus change. "This is a really rich area for mathematicians to mine," said Ermentrout. "Because neurobiology has become increasingly quantitative, there is a need for computational models. Furthermore, these models can sometimes have a direct impact on people's lives. For example, models for epileptic rhythms have been used to suggest possible new drug treatments."

It's not unusual to find mathematicians working on problems in neuroscience and using computer models and analysis of equations to suggest experiments to physiologists. "We've been working in brain modeling at Pitt for 15 years, starting with an interdisciplinary program back in 1991," said Ermentrout. "To me this seems like one of the last really interesting and useful areas of mathematics, trying to understand how the different parts of the brain 'talk' rhythmically to each other and how the thalamus interacts with other parts of the brain via rhythms and waves."