Author Archives: mlmatth2

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.

Project Idea: Investigation of Traveling Waves in the Belousov-Zhabotinskii (BZ) Reaction, Jasmin Imran Alsous, Megan Matthews [Weinberg]

We are planning on looking at traveling wave solutions in the Belousov-Zhabotinskii (BZ) reaction, and in the Fitzhugh Nagumo (FHN) system. This will first include finding the traveling wave solutions in 1D, estimating the traveling wave velocities obtained for a traveling front and trigger waves, and determining the dispersion wave relation for a propagating pulse on a ring. This is interesting because there is a minimum size for the system below which propagating waves cannot be sustained on a periodic 1D domain (or a ring). This is of biological importance because it allows us to determine whether conditions such as fibrillations are possible for hearts of a certain size (e.g. humans can have fibrillations, but cats cannot). If time allows we plan to study these systems in 2D, by investigating the conditions that allow for spiral wave solutions. By studying these two systems, for which solutions are already known, we can become confident in our analysis of such coupled-PDE systems, and we hope/plan to use this knowledge in the analysis of our future research projects, such as examining the evolution of actin dynamics in migrating cells.

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Megan Matthews, North Carolina State University

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