  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
annihilation of pairs of nearby phase singularities.
