Memory in an Excitable Medium: A Mechanism for Spiral Wave Breakup in the Low-Excitability Limit

The electrophysiology of cardiac tissue is altered during acute myocardial ischemia, making the tissue less excitable but, nonetheless, more susceptible to tachyarrythmias which frequently degenerate to fibrillation within several seconds. The transition from tachycardia to fibrillation is associated with the breakup of spiral waves into multiple offspring, and has been linked to steep restitution $(\mathrm{slope}>1\mathrm{})$ of action potential duration (APD). However, restitution curves become so flat during ischemia that this mechanism does not apply. We found that when the response of APD to recent activations is included in a model of excitable media, spiral breakup can occur even when the slope in APD restitutions is $<1\mathrm{}$.