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Polarization of individual cells ("sawtooth") has been proposed as a mechanism for field stimulation and defibrillation. To date, the modeling work has concentrated on the myocardium with periodic spatial structure; this paper investigates potentials arising in cardiac fibers with random spatial structure. Ten different random fibers consisting of cells with varying length (lc=100±50 μm), diameter (dc 20 ± 10 μm), thickness of extracellular space (te=1.18±0.59 μm), and junctional resistance (Rj=2±1 MΩ) are studied. Simulations demonstrate that randomizing spatial structure introduces to the field-induced potential (Vm) a randomly varying baseline, which arises due to polarization of groups of cells. This polarization appears primarily in response to randomizing te; Rj, lc, and dc have less influence. The maximum Vm increases from 3.5 mV in a periodic fiber to 20.5±4.7 mV in random fibers (1 V/cm field applied for 5 ms). Field stimulation threshold Eth decreases from 6.9 to 1.59±0.43 V/cm, which is within the range of experimental measurements. Thresholds for normal and reversed field polarities are statistically equivalent: 1.59±0.43 versus 1.44±0.41 V/cm, (p value = 0.453). Thus, Vm arising due to random structure of the myocardium may play an important role in field stimulation and defibrillation.