Patients with blood-contacting medical devices have an increased risk of thrombosis, which can lead to serious complications such as stroke and death. There is a need for a computational model for predicting thrombosis risk in these patients. In this thesis, we explore the use of finite time Lyapunov exponent (FTLE) fields and Lagrangian coherent structures (LCS) for modeling thrombosis for a variety of devices/conditions which alter the blood flow inside the left ventricle. LCS have been shown in previous studies to clearly identify the location of vortices inside the ventricle and have also been theorized to have links to platelet activation and thrombosis. The blood-contacting devices studied in this thesis are a left ventricular assist device (LVAD), LVAD inflow cannula, and a variety of mitral valve prostheses. Differences in FTLE values and LCS location in a dilated cardiomyopathy model suggest that with increased LVAD support, there is an increase in platelet activation at the apex of the ventricle. This suggests that blood which flows through the LVAD is predisposed to clotting even prior to being exposed to the high shear conditions inside of the pump. A simulated thrombus near the left ventricular outflow tract produces an attracting LCS suggesting that distal to the thrombus is a region of high stagnation, and a repelling LCS at the thrombus suggesting the thrombus increases platelet activation due to mechanical deformation of the platelets. Increases in cannula implantation depth are studied and show changes in the flow pattern due to the cannula. A bioprosthetic valve, bileaflet valve, and a tilting disc valve in both septum and free wall orientations are shown to produce very different flow patterns in the left ventricle when placed in the mitral valve position, as evidenced by changes in the LCS they produce. These findings suggest that FTLE/LCS analysis is a useful tool in modeling how different conditions affect the flow field in the left ventricle, and may also be a useful indictor of increased thrombosis risk. These studies are also the first to consider the effects of cannulation and LVAD support on FTLE fields in the left ventricle.