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NREUP Programs

Grambling State University

Title: Modeling Electrophysiological Processes in Excitable Tissue

Director(s): Brett Sims


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

Michael Pearson
MAA Programs & Services