Grambling State University
Title:
Modeling Electrophysiological Processes in Excitable Tissue
Director(s):
Brett Sims
Email:
simsb@gram.edu
Dates of Program: June 5 - July 14, 2006
Summary:
This program will give four undergraduate students the opportunity to
study and perform an interdisciplinary research at the crossroads of
Mathematics, Computational Analysis, and Biology with application to
modeling bioelectric processes in neural and heart tissue. Students
will also participate in writing code (C++) for simulations. Student
research will be supported by short lectures on special topics that
under gird their research. The lectures will be given by the PI. The
students will learn how electrical properties of neural and excitable
tissue are quantified and will participate in developing deterministic
models for action potential propagation and biomagnetic fields at the
tissue level. Existing models involving various bioelectric current
distributions such as current dipoles and spiral waves responsible for
bioelectric fields will be studied and discussed. Hodgkin-Huxley and
Fitzhugh-Nagumo type models will be studied and compared. Action
potential models containing piecewise linear source terms for membrane
dynamics will also be considered. Investigative studies will include a
theoretical analysis of solutions, eigenvalues, and eigenvectors for
various wave propagation models of the form:
Biological applications of wave
propagation will be
investigated via numerical simulations. Two students will be selected
to present their research at a mathematics conference.
Student Researchers Supported by MAA:
- Charles Bethea.
Major: Mathematics
- Kemmerly Walker. Major: Biology
- Patrick Harris. Major: Mathematics
- Stanley Drinks. Major: Mathematics
Program Contacts:
Bill Hawkins
MAA SUMMA
bhawkins@maa.org
202-319-8473
Michael Pearson
MAA Programs & Services
pearson@maa.org
202-319-8470