Blood flow properties in the heart can be examined non invasively by means of Phase Contrast MRI (PC MRI), an imaging technique that provides not only morphology images but also velocity information. We present a novel feature combination for level set segmentation of the heart's cavities in multidirectional 4D PC MRI data. The challenge in performing the segmentation task successfully in this context is first of all the bad image quality, as compared to classical MRI. As generally in heart segmentation, the intra and inter subject variability of the heart has to be coped with as well. The central idea of our approach is to integrate a set of essentially differing sources of information into the segmentation process to make it capable of handling qualitatively bad and highly varying data. To the best of our knowledge our system is the first to concurrently incorporate a flow measure as well as a priori shape knowledge into a level set framework in addition to the commonly used edge and curvature information. The flow measure is derived from PC MRI velocity data. As shape knowledge we use a 3D shape of the respective cavity. We validated our system design by a series of qualitative performance tests. The combined use of shape knowledge and a flow measure increases segmentation quality compared to results obtained by using only one of those features. A first clinical study was performed on two 4D datasets, from which we segmented the left ventricle and atrium. The segmentation results were examined by an expert and judged suitable for use in clinical practice.