  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. Through a
combination of direct numerical simulation and continuation methods, we
investigate existence and stability of a 1D spiral wave in a qualitative ionic
model to determine how the systems 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.
