University Honors, Honors in Mathematics
Date of Award
Thesis Professor Department
Mathematics and Statistics
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.
Honors Thesis - Open Access
Brooks, Jeremy, "A Singular Perturbation Approach to the Fitzhugh-Nagumo PDE for Modeling Cardiac Action Potentials." (2011). Undergraduate Honors Theses. Paper 152. https://dc.etsu.edu/honors/152
Copyright by the authors.