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Published on: February 22, 2018
Annihilation and reflection of spiral waves at a boundary for the Beeler-Reuter model
Daniel Olmos1, Bernie D Shizgal
1Institute of Applied Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1. daniel@iam.ubc.ca
Abstract:
We employ a reaction diffusion equation with local dynamics specified by the Beeler-Reuter model to study the meandering of spiral waves. With the appropriate choice for the conductances of sodium and calcium channels, the trajectory of the tip of a spiral wave lies on a straight line. The phenomenon of annihilation or reflection of a spiral at the boundaries of the domain is studied. This phenomenon is analyzed in terms of the variable j , which controls the reactivation of the sodium channel in the Beeler-Reuter model. The results presented can have potential applications in the study of cardiac arrhythmias by providing insight on the interaction between spiral waves and obstacles in the heart.
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