Wave Reflections in a Biophysically Detailed Model of Cardiac Tissue

Author (Your Name)

Grace Moberg, Colby CollegeFollow

Date of Award

2025

Document Type

Honors Thesis (Open Access)

Department

Colby College. Mathematics and Statistics Dept.

Advisor(s)

Stephanie Dodson

Second Advisor

Stephanie Taylor

Abstract

Regular heart rhythms are governed by the coordinated spread of action potentials through cardiac tissue. The interaction of an action potential with a tissue heterogeneity may lead to a reflection, where both a retrograde and an anterograde wave propagate off of the initial impulse. Reflections have been experimentally linked to cardiac arrhythmias, but their mechanisms of generation are not well-understood. Mathematically, reflections in phenomenological models of cardiac tissue have been linked to an unstable periodic orbit. These models typically sacrifice detail about the variety of ionic currents and processes involved in action potential propagation in favor of mathematical simplicity. Biophysically detailed models provide more insight into the currents and processes that generate reflections in cardiac tissue. However, reflections have not been studied at length in these models. We investigate the existence of reflections in a biophysically detailed, conductance-based model of cardiac tissue. Using numerical methods, we seek to determine how the likelihood of reflections is impacted by modifications to the system parameters. Our results suggest that an unstable periodic orbit underlies reflections in the biophysically detailed model, extending previous work that connected the unstable periodic orbit to reflections in phenomenological models. We also identify key physiological parameters and processes that reduce the system's propensity for reflections.

Keywords

cardiac arrhythmia, wave reflections, ten Tusscher, one-dimensional spiral waves

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