P293 Numerical Analysis of AP Propagation Parameter Thresholds Under Varied Space and Time Discretization
Lucas Swanson*1, Erin Munro Krull1, Laura Zittlow1
1Mathemarical Sciences Department, Ripon College, Ripon, WI, US
*Email: swansonl@ripon.edu
Introduction
There is a lot known about how discretization affects the numerical solution to PDEs. However, little is known about how these discretization affects finding a parameter threshold for a PDE. In particular, there is the sodium conductance propagation threshold (gNaT), which is the the threshold for AP propagation when varying g̅_Na. Preliminary results show that this threshold, if known for simple morphologies, may be used to predict the gNaT of other, more complex morphologies.
Methods
We modeled cells using the Hodgkin-Huxley type model with parameters for a rat neocortical L5 pyramidal cell axon [1], on the NEURON software. Using a binary search, we were able to calculate the gNaT of any morphology from a given stimulus to a given AP propagation test site. We explored the effects of the discretization parameters, for time and space,dtanddx, on the gNaT of 10 randomly generated morphologies. We varieddtfrom 2⁻⁸ms to 2⁻⁵ms, anddxfrom 2⁻⁸λto 2⁻⁴λ, whereλis the electrotonic length.
Results
Our results show that increaseddtleads to increased gNaT values, regardless of morphology anddx; and that increasingdxcan cause gNaT values to diverge sporadically, especially in morphologies with short, or tightly spaced branches.
Discussion
Further investigation should be done to find the true nature ofdx’s effects on gNaT, since the sporadic divergence of gNaT seen in our results could be attributed to the locations of branches being re-discretized, and/or short branches having significantly different behaviors. That is, our results show that the accuracy of calculated parameter thresholds may be linked to morphology.
Acknowledgements
I would like to thank the faculty of the Ripon College math department, which includes my mentor for this project, Professor Erin Munro Krull, all of whom gave me advice and counsel. I would also like to thank the organizers of Ripon College's Summer Opportunities for Advanced Research (SOAR) program, as well as the many donors of the college who helped fund the program.
References
● Traub, R. D., Contreras, D., Cunningham, M. O., Murray, H., LeBeau, F. E., Roopun, A., Bibbig, A., Wilent, W. B., Higley, M. J., & Whittington, M. A. (2005). Single-column thalamocortical network model exhibiting gamma oscillations, sleep spindles, and epileptogenic bursts.Journal of neurophysiology,93(4), 2194. doi.org/10.1152/jn.00983.2004
