The study of cardiac action potentials has many medical applications. Dr. Dennis Noble first used mathematical models to study cardiac action potentials in the 1960s. We begin our study of cardiac action potentials with one form of the Fitzhugh-Nagumo partial differential equation. We use the non-classical method to produce a closed form solution for the decoupled Fitzhugh Nagumo equation. Using voltage recording data of action potentials in a cardiac myocyte and in purkinje fibers, we estimate parameter values for the closed form solution with standard linear and non-linear regression methods. Results are limited, thus leading us to perturb the solution to obtain a better fit. We turn to singular perturbation theory to justify our pole-based approach. Finally, we test our model on independent action potential data sets to evaluate our model and to draw conclusions on how our model can be applied.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:honors-1156 |
| Date | 01 May 2011 |
| Creators | Brooks, Jeremy |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Undergraduate Honors Theses |
| Rights | Copyright by the authors., http://creativecommons.org/licenses/by-nc-nd/3.0/ |
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