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When propagated action potentials in cardiac tissue interact with local heterogeneities, counter propagating or "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 it’s appearance in a qualitative ionic model and determine how the spiral's existence is influenced by system parameters. Our results support and extend a previous hypothesis that the 1D spiral emerges through a global rearrangement of heteroclinic orbits.