School of Mathematical Sciences Colloquium: Traveling waves, reflections, and the onset of cardiac arrhythmias

School of Mathematical Sciences Colloquium
Traveling waves, reflections, and the onset of cardiac arrhythmias

Dr. Stephanie Dodson
Krener Assistant Professor
Department of Mathematics
University of California, Davis

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Abstract:
When propagated action potentials in cardiac tissue interact with local heterogeneities, reflected waves can sometimes be induced. These reflected waves have been associated with the onset of cardiac arrhythmias, and while their generation is not well understood, their existence is linked to that of one-dimensional (1D) spiral waves. Thus, understanding the existence and stability of 1D spirals plays a crucial role in determining the likelihood of the unwanted reflected pulses. Mathematically, we probe these issues by viewing the 1D spiral as a time-periodic antisymmetric source defect pattern that arises in a reaction-diffusion system. Through a combination of root-finding and continuation methods, we numerically solve for the 1D spiral wave pattern to investigate its existence and stability and determine how the system's propensity for reflections are influenced by system parameters. Our results support and extend a previous hypothesis that the 1D spiral is an unstable periodic orbit that emerges through a global rearrangement of heteroclinic orbits and we identify key parameters and physiological processes that promote and deter reflection behavior.

Speaker Bio:
Stephanie is currently a Krener Visiting Assistant Professor in the Department of Mathematics at UC Davis. Previously, she received her PhD in Applied Mathematics from Brown University, where she was advised by Bjorn Sandstede and was a recipient of an NSF Graduate Fellowship. Stephanie's research spans the fields of dynamical systems, nonlinear waves, and mathematical biology. In the fall, Stephanie will start as a tenure-track Assistant Professor in the Mathematics Department at Colby College.

Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.

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