Signal Propagation Along Non-Uniform Axon
MBI Summer Project –
2003
Group
Leader: Avner Friedman
Team members: Stephen Clark, Yevgeniy Gokun, Hsiu-Tsun Hsieh,
Prasanna Karunanayaka, Namyong Lee, Mike Martin
Group Photo
In the summer of 2003, the Mathematical Biosciences Institute hosted
their first educational summer program. The theme of the program
was on neuronal rythyms. A select goup of faculty, graduate
students, and undergraduate students took in
very stimulating lectures on the requisite mathematics and the
neurobiology that they
model. The mathematical and computer simulation lectures were
delivered
by David Terman and those on the neurosciences aptly given by Brian
Smith. Participants also had the opportunity to visit several
research labs on the Ohio State University campus. After a week
of lectures, the participants were divided
into four groups, each with a different project and focus.
This page is devoted to one of those groups whose study concerned
signal propagation at abrupt changes in the diameter of an axon.
Avner Friedman, our group leader and MBI director, charged the group
with investigating these properties both numerically and
analytically. We reviewed a great abundance of literature,
realizing that a lot of work has been done in the area, but there are
still many open questions. Our simulations utilized the
Fitzhugh-Nagumo, Morris-Lecar, and Hodgkin-Huxley models for action
potentials along the length of an axon. Using the first two of
these models we observed signal transmission, signal blocking, signal
reflection, and hybridizations of these phenomena. Our work on
the Hodgkin-Huxley system is ongoing as well as our pursuit of
existence proofs for these phenomena. Work in the area has
potential applications for amyotrophic lateral sclerosis (ALS),
diseased cardiac tissue, and mechanisms of "pain."
By creating and maintaining this page, we intend to share our work and
resources with others, continue our work on the project (by giving
pointers to our subsequent endeavors), provide an avenue for continued
communications, and promote the important mission of the relatively
young Mathematical Biosciences Institute.
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