This study investigates ultra-low-energy defibrillation protocols using a simple two-dimensional model of cardiac tissue. We find that, rather counter-intuitively, a single, properly timed, biphasic pulse can be more effective in defibrillating the tissue than low energy antitachycardia pacing (LEAP), which employs a sequence of such pulses, succeeding where the latter approach fails. Furthermore, we show that, with the help of adjoint optimization, it is possible to reduce the energy required for defibrillation even further, making it three orders of magnitude lower than that required by LEAP. Finally, we establish that this dramatic reduction is achieved through exploiting the sensitivity of the dynamics in vulnerable windows to promote the annihilation of pairs of nearby phase singularities.
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