(FRE) Flow related enhancement could be seen most for blood flow, but also for other liquids with some MR imaging techniques, as an increase in intensity due to the washout of saturated spins. FRE provides positive contrast ("bright blood") of vascular details in time of flight MRA as well as the physiologic characterization of blood flow.
If stationary spins within the scanned region experience only an incomplete T1 relaxation between the repeated radio frequency (RF) excitations, this results in fewer signal of the stationary tissue (compared to inflowing blood with completely relaxed spins). The degree of the flow related enhancement is proportional to the blood flow velocity and the used repetition time. The use of flow compensation (gradient moment nulling) improves the FRE especially in gradient echo sequences.

Quick Overview
Please note that there are different common names for this artifact.

The received radio frequency signal is too strong, parts of the signal get lost by converting from analog to digital, resulting in a washed out image.

Auto-prescanning usually adjusts the amplification at the receiver in a way, that the received signal could be processed without any loss. Else the receiver gain must be corrected manually.

See also Data Clipping Artifact, Artifact Overview and Artifacts Reduction Index.

(I MRA) In MR imaging, inflowing non-saturated fluid gives a higher signal intensity than stationary tissue. This effect makes it especially useful for imaging of flowing blood. Other factors such as susceptibility and spin saturation, can affect the signal of the blood within the vessels. Furthermore turbulence is part of normal blood flow and can decrease signal intensity.

See also Time of Flight Angiography.

(FAIR) In this sequence 2 inversion recovery images are acquired, one with a nonselective and the other with a slice selective inversion pulse. The z-magnetization in the first sequence is independent of flow. Inflowing spins give z-magnetization from second pulse. A major signal loss in FAIR is the T1 relaxation of tagged blood in transit to the imaging slice. Sharper edges of the inversion pulse give narrow spacing between the inversion edge and the 1st slice because reduced transit time gives lower T1 relaxation induced signal loss. The difference of the images in a consequence contains information proportional to flow (blood partition coefficient). Standard adiabatic inversion RF pulse does not have good slice-profile, because of power/SAR limitation. A c-shaped frequency offset corrected inversion (FOCI) RF pulse can help to increase the signal.
Perfusion imaging, e.g. myocardial, using tissue water as endogenous contrast is suggested.

(M2DMRA) The M2D technique can be used to image both fast and slow flow, due to good refreshment of flowing blood. Using overlapping slices can reduce staircase artifacts, which might be seen in projection of the slice thickness.

See also Time of Flight Angiography.