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Many flow visualization techniques, especially integration-based methods, are problematic when the measured data exhibit noise and discretization issues. Particularly, this is the case for flow-sensitive phase-contrast magnetic resonance imaging (PC-MRI) data sets which not only record anatomic information, but also time-varying flow information. We propose a novel approach for the visualization of such data sets using integration-based methods. Our ideas are based upon finite-time Lyapunov exponents (FTLE) and enable identification of vessel boundaries in the data as high regions of separation. This allows us to correctly restrict integration-based visualization to blood vessels. We validate our technique by comparing our approach to existing anatomy-based methods as well as addressing the benefits and limitations of using FTLE to restrict flow. We also discuss the importance of parameters, i.e., advection length and data resolution, in establishing a well-defined vessel boundary. We extract appropriate flow lines and surfaces that enable the visualization of blood flow within the vessels. We further enhance the visualization by analyzing flow behavior in the seeded region and generating simplified depictions.