Final Project:Megan L. Matthews, Jasmin Imran Alsous-Dynamics of the Fitzhugh-Nagumo Model: A Model for Cardiac Electrical Activity

We investigated the Fitzhugh-Nagumo System as a model for cardiac electrophysiology in multiple dimensions. In a 0D model of a single cell, we were able to capture the dynamics of the depolarization block that occurs as a result of increasing the external stimulus. This change in the dynamics of the system is captured in a 2D phase portrait of the nullclines of the system. In the 1D model, we were able to simulate a propagating trigger wave using the Winfree mechanism, on a ring and to reproduce the dispersion curve that illustrates the smallest ring size for which a traveling wave can be sustained. Furthermore, we investigated the effect of diffusion on the speed of a propagating wave as a model to account for the blockage of propagation that occurs in damaged tissues as a result of cardiac infarctions. Finally, we expanded our model to a 2D model to investigate the effects of heterogeneity in refractoriness on the formation and sustainability of spiral waves. This was studied in the context of functional reentry waves, which contribute to arrhythmia and tachycardia. The PDEs were solved using the Crank-Nicolson and Alternating Direction Implicit (ADI) methods, and all simulations were performed in Matlab.

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