(DE FGRE, Dual/FFE, DE FFE) Simultaneously acquired in and out of phase TE gradient echo images. To quantitatively measure the signal intensity differences between out of phase and in phase images the parameters should be the same except for the TE.
The chemical shift artifact appearing on the out-of-phase image allows for the detection of lipids in the liver or adrenal gland, such as diffuse fatty infiltration, focal fatty infiltration, focal fatty sparing, benign adrenocortical masses and intracellular lipids within a hepatocellar neoplasm, where spin echo and fat suppression techniques are not as sensitive. Specific pathologies that have been reported include liver lipoma, angiomyolipoma, myelolipoma, metastatic liposarcoma, teratocarcinoma, melanoma, haemorrhagic neoplasm and metastatic choriocarcinoma.

(DE - dual / double echo) Dual echo sequences include images with different weightings and / or echo times and are used to obtain both, proton density and T2 weighted images or in phase and out of phase gradient echo images, simultaneously without increasing the measurement time.

In MRI, an echo is the emission of energy in form of an electromagnetic resonance signal of a nuclei after its excitation. At this point spins are back in phase again and the signal is measured. The desired number of echoes is selectable. Often until eight echoes are permissible for 2D or 3D scans using spin echo, inversion recovery or MIX techniques. Two echoes are permissible for all other techniques. A multi echo imaging sequence is needed for simultaneous measurement of T2 and density weighted images.

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.