A rephasing or refocusing, which occurs when constant velocity spins return to the same starting phase they had directly after the initial exciting RF pulse, as a result of the application of an even number of gradient pulses. This may also result from the application of multiple gradient echo pulses following the RF pulse. The even echo rephasing phenomenon is one of the flow effects observed in MR imaging.

The FEER method was the first clinically useful flow quantification method using phase effects, from which all spin phase related flow quantification techniques currently in use are derived.
In this sequence a gradient echo is measured after a gradient with flow compensation. The measured signal phase should be zero for all pixels. A deviation from gradient symmetry by shifting the gradient ramp slightly away from the symmetry condition will impart a defined phase shift to the magnetization vectors associated with spins from pixels with flow.
Slight stable variations in the magnetic field across the imaging volume will prevent the phase angle from being uniformly zero throughout the volume in the flow-compensated image. The first image (acquired without gradient shift) serves as reference, defining the values of all pixel phase angles in the flow (motion) compensated sequence. Ensuing images with gradient phase shifts imparted in each of the 3 spatial axes will then permit measurement of the 3 components of the velocity vector v = (vx, vy, vz) by calculating the respective phases px, py and pz by simply subtracting the pixel phases measured in the compensated image from the 3 images with a well defined velocity sensitization.
The determination of all 3 components of the velocity vector requires the measurement of 4 images.
The phase quantification requires an imaging time four times longer than the simple measurement of a phase image and associated magnitude image. If only one arbitrary flow direction is of interest, it suffices to acquire the reference image plus one image velocity sensitized in the arbitrary direction of interest.

See also Flow Quantification.

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

Flow effects in MRI produce a range of artifacts, e.g. intravascular signal void by time of flight effects; turbulent dephasing and first echo dephasing, caused by flowing blood.
Through movement of the hydrogen nuclei (e.g. blood flow), there is a location change between the time these nuclei experience a radio frequency pulse and the time the emitted signal is received (because the repetition time is asynchronous with the pulsatile flow).
The blood flow occasionally produces intravascular high signal intensities due to flow related enhancement, even echo rephasing and diastolic pseudogating. The pulsatile laminar flow within vessels often produces a complex multilayered band that usually propagates outside the head in the phase encoded direction. Blood flow artifacts should be considered as a special subgroup of motion artifacts.

Artifacts can be reduced by reduction of phase shifts with flow compensation (gradient moment nulling), suppression of the blood signal with saturation pulses parallel to the slices, synchronization of the imaging sequence with the heart cycle (cardiac triggering) or can be flipped 90° by swapping the phase//frequency encoding directions.

See also Flow Related Enhancement and Flow Effects.

Flow compensation is based on the principle of even echo rephasing and a function of specific pulse sequences, wherein the application of strategic gradient pulses can compensate for the objectionable spin phase effects of flow motion. Gradient moment nulling of the first order of flow is another adjustment for the reduction of flow artifacts.
Gradient field changes can be configured in such a way that during an echo the magnetization signal vectors for all pixels have zero phase angle independent of velocities, accelerations etc. of the measured tissue. The simplest velocity-compensated pulse sequence is the symmetrical second echo of a spin echo pulse sequence.
Strategic gradient pulses are integrated in special sequences (e.g. CRISP, Complex Rephasing Integrated with Surface Probes) and for the most sequences flow compensation is an optional parameter.

The spins flow with the blood through a slice and experience a RF pulse. If they flow out of the slice by the time the signal is recorded (because the repetition time (TR) is asynchronous with the pulsatile flow), the flowing blood produces intravascular signal void by 'time of flight' effects, turbulent dephasing and first echo dephasing. The liquid flow occasionally produces an intravascular high signal intensity due to flow related enhancement, even echo rephasing and diastolic pseudogating.

See also Flow Artifact and Flow Effects.