After myocardial infarction, the evolution of the cardiac scar and the remodeling of the border zone play a critical role in the generation of life-threatening ventricular tachycardias. Three-dimensional and anatomically realistic biventricular models can help understand the mechanisms underlying reentrant arrhythmias in such circumstances. In the present work, personalized models of infarcted hearts are built from late gadolinium enhancement cardiac magnetic resonance images. The electrical activity of these hearts is simulated under different remodeling scenarios of the scar border zone. After applying the same stimulation protocol applied by clinicians to the virtual heart of a patient presenting ventricular tachycardia (VT) and to a patient presenting no tachycardia, we could replicate the arrhythmogenic behavior of these hearts for specific conditions of structural remodeling of the border zone. Our simulations reproduced realistic patterns of reentry consistent with those obtained in the clinic, providing a better understanding of the mechanisms underlying VT.