In this paper, we present a method to simulate and visualize blood flow through the human heart, using the reconstructed 4D motion of the endocardial surface of the left ventricle as boundary conditions. The reconstruction captures the motion of the full 3D surfaces of the complex features, such as the papillary muscles and the ventricular trabeculae. We use visualizations of the flow field to view the interactions between the blood and the trabeculae in far more detail than has been achieved previously, which promises to give a better understanding of cardiac flow. Finally, we use our simulation results to compare the blood flow within one healthy heart and two diseased hearts.