Cardiovascular diseases, mostly related to atherosclerosis, are the major cause of death in industrial countries. It is observed that blood flow dynamics play an important role in the aetiology of atherosclerosis. Especially, the blood velocity distribution is an important indicator for predisposition regions. Today magnetic resonance imaging (MRI) delivers, in addition to the morphology of the cardiovascular system, blood flow patterns. However, the spatial resolution of the data is slightly less than 1 mm and owing to severe restrictions in magnetic field gradient switching frequencies and intensities, this limit will be very hard to overcome. In this paper, constrained fluid dynamics is applied within the smoothed particle hydrodynamics formalism to enhance the MRI flow data. On the one hand, constraints based on the known volumetric flow rate are applied. They prove the plausibility of the order of magnitude of the measurements. On the other hand, the higher resolution of the simulation allows one to determine in detail the flow field between the coarse data points and thus to improve their spatial resolution.