Abstract
The determination of the mechanisms of spiral breakup in excitable media is still an open problem for researchers. In the context of cardiac electrophysiological activities, spiral breakup exhibits complex spatiotemporal pattern known as ventricular fibrillation. The latter is the major cause of sudden cardiac deaths all over the world. In this paper, we numerically study the instability of periodic planar traveling wave solution in two dimensions. The emergence of stable spiral pattern is observed in the considered model. This pattern occurs when the heart is malfunctioning (i.e., ventricular tachycardia). We show that the spiral wave breakup is a consequence of the transverse instability of the planar traveling wave solutions. The alternans, that is, the oscillation of pulse widths, is observed in our simulation results. Moreover, we calculate the widths of spiral pulses numerically and observe that the stable spiral pattern bifurcates to an oscillatory wave pattern in a one-parameter family of solutions. The spiral breakup occurs far below the bifurcation when the maximum and the minimum excited states become more distinct, and hence the alternans becomes more pronounced.
Highlights
Cardiovascular diseases and sudden cardiac deaths are major issues nowadays facing researchers in the fields of medical sciences and mathematical physiology throughout the globe, especially in the industrialized world
We have studied the different phenomenon of spiral wave solutions in an excitable FHN-type of reaction-diffusion system
We observed in our numerical results that the process of spiral breakup is a consequence of the transverse instability of the planar traveling wave solutions
Summary
Cardiovascular diseases and sudden cardiac deaths are major issues nowadays facing researchers in the fields of medical sciences and mathematical physiology throughout the globe, especially in the industrialized world. Fifteen million [1] individuals die every year in the universe because of cardiovascular diseases. Per annum, these diseases, in the United States alone, have nearly one million deaths, which is over 40% of all deaths [1]. The most irregular, life threatening, and deadly case of cardiac arrhythmia is known as ventricular fibrillation, which occurs when the heart is not able to pump oxygen-rich blood to the body and results in death of body cells and heart cells [2]
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