Single Ventricle congenital heart defects with cyanotic mixing between systemic and pulmonary circulations afflict 2 per 1000 live births. The total cavo-pulmonary connection (TCPC), where the superior and inferior vena cavae are sutured to the left and right pulmonary arteries, is the current procedure of choice. It is believed that reducing the fluid mechanical power losses in the TCPC will relieve strain on the single functional ventricle. It is hypothesized that a proposed idealized TCPC design, decreases power losses to a level below that of any other TCPC designs, while providing other advantages and increased flexibility. Physical models with slightly different geometries of the proposed design were created, and in vitro experiments carried out with particle image velocimetry (PIV), phase contrast magnetic resonance imaging (PC-MRI), and control volume flow analysis at physiological flow rates. Computational fluid dynamics (CFD) was used for numerical studies of the same geometries as in the physical models. Power losses were calculated using the control volume method and the viscous power dissipation function. The latter method incorporated registration of high-resolution PC-MRI velocity vectors to tetrahedral meshes followed by inverse interpolation of the vectors onto the meshes. Detailed flow structures were analyzed. Results show that the new design is more energy efficient than any other idealized models. Furthermore, a tool was developed to extract flow and vessel information from PC-MRI datasets obtained from patients with Fontan connections. The tool utilized a display algorithm, which was developed for optimal noise detection in PC-MRI images. This enabled accurate segmentation. Comparing PC-MRI images before and after this accurate segmentation showed that the standard deviations of the pixels at the perimeter of the segmented vessel were statistically significantly smaller after the segmentation in 94.1% of the datasets investigated. The developed tool was able to extract flow, flow in the quadrants of vessels, area of the segmented vessel, velocities and pulsatility indices. The velocity vectors were exported for use as CFD boundary conditions in models reconstructed from patient anatomies. A database was created with patient PC-MRI data from approximately 140 patients, which is probably the largest database in the world.