News Release
Mathematics Helps Unlock
Secrets of the Nervous System
For further information, contact:
Professor Nancy Kopell, Boston University
e-mail: nk@math.bu.edu
telephone: 617-353-5210
fax: 617-353-8100
December 9, 1999
PROVIDENCE, RI--- The mammalian nervous system is extraordinarily complex and
not yet well understood scientifically. Technology has evolved to the point
where it is possible to make minutely detailed measurements of neurological
activity and generate masses of data. But the data often end up being nearly
as complicated and as perplexing as the system itself.
In such situations, mathematics can serve as an important tool for stripping
away confusing detail and highlighting important structures. In the enclosed
article, mathematician Nancy Kopell describes three case studies in which
mathematics has deepened understanding of aspects of the nervous system.
One of the case studies involves mysterious and controversial rhythms in
electrical activity in the brain, called gamma and beta rhythms. Some
researchers believe these rhythms are associated with key cognitive states,
such as attention and perception, as well as with memory. There is also
tantalizing new evidence that pathologies in these rhythms are associated with
thought disorders such as schizophrenia.
The rhythms are produced through self-organization in collections of brain
cells and are not the result of outside coordination, as by an orchestra
conductor. Just how the cells coordinate their activity to produce these
rhythms is a puzzle.
Mathematics has now helped to solve some parts of this puzzle. Using
experimental data and an arsenal of mathematical tools, Kopell and her
co-workers formulated a set of mathematical models of a collection of cells
producing these rhythms. The mathematics revealed that the gamma and beta
rhythms achieve coherence in different ways, and that the beta rhythm is able
to create precise synchronization between neurons separated by a much longer
conduction delay. The mathematics also helps to explain data suggesting that
the nervous system uses the beta frequency for long-distance coherence, and the
gamma rhythm for more local communication.
The work described in this article focuses on collections of cells that are
small enough to be tractable; the next challenge is to see whether these ideas
can work in larger and more realistic, but messier, circumstances. "This may
involve statistical and probabilistic notions, a kind of statistical mechanics
for neurons," Kopell predicts in the article. "I believe it will be critical
for such a theory to respect the structure of the smaller idealized building
blocks, not simply mimic the concepts developed for statistical physics."
The article, "We Got Rhythm:
Dynamical Systems of the Nervous System,"
appears in the January 2000 issue of the Notices of the AMS.
Founded in 1999 to further mathematical research and scholarship, the
30,000-member AMS fulfills its mission through programs and services that
promote mathematical research and its uses, strengthen mathematical education,
and foster awareness and appreciation of mathematics and its connections to
other disciplines and to everyday life.
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