Spiral or scroll waves of electrical excitation in the myocardium can cause cardiac arrhythmias. It is known that the structural and functional heterogeneity of myocardial tissue is one of the key factors affecting the drift of the scroll waves. In this paper, we studied the dynamics of scroll waves in realistic anatomical models of the left ventricle (LV) of a human heart depending on the geometry of the LV and the depth of the postinfarction scar in the LV wall. Based on ultrasound data, we built two models of LV geometry with averaged parameters observed for normal heart and for the heart of patients with dilated cardiomyopathy. In both models, we formed postinfarction scars of various sizes and varied the transmural depth of the scar in the LV wall. In the absence of myocardial infarction, scroll waves were stable and independent of the LV geometry. In LV models with postinfarction scar, the geometry of the LV influenced the dynamics of the scroll waves. In case of normal geometry, the scroll waves disappeared with a depth of 2/3 or fully transmural scar. In the LV model with dilated cardiomyopathy geometry, at all depths of the scar, a scroll wave break-up (LV fibrillation) was observed after 10-15 seconds of the simulation.