Mathematics Colloquia and Seminars

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Each beat of our heart is triggered by a wave of electrical activity, called an action potential, that propagates through our heart tissue. Usually, when a propagated cardiac action potential interacts with a local tissue heterogeneity such as an abrupt change in geometry or a region of depressed excitability, either the action potential is blocked and annihilated or it successfully propagates across the heterogeneity. However, in some cases, action potentials can successfully cross the heterogeneity and then give rise to a reflected action potential, i.e., an action potential that propagates in the retrograde direction. These reflected pulses are thought to lead to the onset of life-threatening arrhythmias. The mechanisms that generate reflected pulses are not well understood, but their existence has been linked to the existence of an unstable spatiotemporal periodic orbit that has been referred to as a one-dimensional (1D) spiral wave. 1D spiral waves are 'source defects' that consist of a non-excited core that sheds anti-phase counter-propagating pulses. The link between reflection, 1D spiral waves, and the induction of cardiac arrhythmias make it crucial to clarify the underlying mechanisms that give rise to 1D spiral waves and to identify conditions for which they exist.

In this talk, I will briefly explain the mathematics of action potential propagation in cardiac tissue, and I will give an overview of our work that elucidates the bifurcation scenario leading to the existence of 1D spirals.