Ventricular tachycardia, a life-threatening regular and repetitive fast heart rhythm, frequently occurs in the setting of myocardial infarction. Recently, the peri-infarct zones surrounding the necrotic scar (termed gray zones) have been shown to correlate with ventricular tachycardia inducibility. However, it remains unknown how the latter is determined by gray zone distribution and size. The goal of this study is to examine how tachycardia circuits are maintained in the infarcted heart and to explore the relationship between the tachycardia organizing centers and the infarct gray zone size and degree of heterogeneity. To achieve the goals of the study, we employ a sophisticated high-resolution electrophysiological model of the infarcted canine ventricles reconstructed from imaging data, representing both scar and gray zone. The baseline canine ventricular model was also used to generate additional ventricular models with different gray zone sizes, as well as models in which the gray zone was represented as different heterogeneous combinations of viable tissue and necrotic scar. The results of the tachycardia induction simulations with a number of high-resolution canine ventricular models (22 altogether) demonstrated that the gray zone was the critical factor resulting in arrhythmia induction and maintenance. In all models with inducible arrhythmia, the scroll-wave filaments were contained entirely within the gray zone, regardless of its size or the level of heterogeneity of its composition. The gray zone was thus found to be the arrhythmogenic substrate that promoted wavebreak and reentry formation. We found that the scroll-wave filament locations were insensitive to the structural composition of the gray zone and were determined predominantly by the gray zone morphology and size. The findings of this study have important implications for the advancement of improved criteria for stratifying arrhythmia risk in post-infarction patients and for the development of new approaches for determining the ablation targets of infarct-related tachycardia.