1. A magnetic resonance imaging (MRI) system comprising: a magnet system configured to generate a polarizing magnetic field about at least a region of interest (ROI) in a subject arranged in the MRI system; a plurality of gradient coils configured to apply a gradient field to the polarizing magnetic field; a radio frequency (RF) system configured to apply an excitation field to the subject and acquire MR image data from a ROI; a computer system programmed to carry out steps of: a) performing a first pulse sequence that directs the MRI system to: i) apply at least one RF saturation pulse to a prescribed imaging slice to substantially suppress MR signals in the prescribed imaging slice; ii) apply at least one RF saturation pulse to a slice outside the prescribed imaging slice to suppress signal from spins flowing into the prescribed imaging slice from the slice outside the prescribed imaging slice through one of veins and arteries; iii) observe a first quiescent inflow time period (QITP) selected to allow a desired inflow of spins flowing into the prescribed imaging slice from the slice outside the prescribed imaging slice through the one of arteries and veins; iv) acquire a flow-dependent imaging data set from the prescribed imaging slice following the first QITP; b) performing a second pulse sequence that directs the MRI system to acquire a flow-independent imaging data set from the prescribed imaging slice; c) subtracting the flow-dependent imaging data and the flow-independent imaging data to create a difference image of the prescribed imaging slice; and a display configured to display the image of the prescribed imaging slice illustrating the at least one of the arteries and the veins as having a bright contrast and another of the arteries and veins as having a suppressed contrast.