Electrical turbulence in cardiac tissue is associated with arrhythmias such as the life-threatening ventricular fibrillation. The application of a high-energy electrical shock constitutes an effective defibrillation, but also causes severe side effects. Recent experimental studies have shown that a sequence of low energy electrical far-field pulses is able to terminate fibrillation more gently than a single pulse. During this low-energy antifibrillation pacing (LEAP) only tissue near sufficiently large conduction heterogeneities, such as large coronary arteries, is activated. In order to understand and potentially optimize LEAP, we performed extensive simulations of cardiac tissue perforated by blood vessels. We checked three alternative cellular models that exhibit qualitatively different electrical turbulence. LEAP may operate if and only if the spectrum of this chaotic activity is characterized by a narrow peak around a dominant frequency. For each of 100 initial conditions, we tested different electrical field strengths, pulse shapes, numbers of pulses, and periods between the pulses. It turned out that the optimal period matches the dominant period of the chaotic activity while both over-and underdrive pacing lead to a considerably smaller success probability and higher field strength for reliable defibrillation. An optimal LEAP protocol, which minimizes the required total energy for successful defibrillation, consists of five or six pulses. Compared to a single bi-phasic defibrillation pulse, it reduces the total energy by about 86%, corresponding to an energy reduction of 97 -98% per pulse.PACS numbers: ... Keywords: cardiac modeling, excitable media, defibrillation, low-energy antifibrillation pacing (LEAP)In ventricular fibrillation, the heart is quivering instead of pumping, a condition which leads to cardiac arrest and ultimately to death. This loss of synchronous contraction stems from disorganized electrical activity in the ventricles. Emergency defibrillation is achieved by the application of a strong electrical shock which is accompanied by severe side effects such as tissue damage and trauma. Recently, an alternative treatment using a sequence of low energy pulses has been suggested in which each electrical pulse excites only localized tissue sites at the large heterogeneities -such as blood vessels -instead of the entire tissue. In laboratory experiments in vitro and in vivo, this so-called low-energy antifibrillation pacing (LEAP) with five pulses achieves defibrillation with an energy reduction of 80 -90 % per pulse in comparison with standard single shock treatment. Here, we perform an extensive numerical study of LEAP employing far field pacing at the major blood vessels. We have tested three alternative electrophysiological models that exhibit qualitatively different spatiotemporally chaotic activity. LEAP operates if and only if the spectrum of this chaotic activity is characterized by a narrow peak around a dominant frequency. In this case, a resonant pacing with the same frequency and a ...