(PCA) With this method images of the blood flow-velocity (or any other movement of tissue) are produced. The MRI signal contains both amplitude and phase information. The phase information can be used with subtraction of images with and without a velocity encoding gradient. The signal will be directly proportional to the velocity because of the relation between blood flow-velocity and signal intensity.
This is the strength of PCA, complete suppression of stationary tissue (no velocity - no signal), the direct velocity of flow is being imaged, while in TOF (Inflow) angiography, tissue with short T1 (fat or methaemoglobin) might be visualized.
The strength of the gradient determines the sensitivity to flow. It is set by setting the aliasing or encoding velocity (VENC). Unfortunately, phase sensitization can only be acquired along one axis at a time. Therefore, phase contrast angiographic techniques tend to be 4 times slower than TOF techniques with the same matrix.

See also Phase Contrast Sequence, Magnetic Resonance Angiography, Contrast Enhanced Magnetic Resonance Angiography, Flow Effects and Flow Quantification.

(PC) Phase contrast sequences are the basis of MRA techniques utilizing the change in the phase shifts of the flowing protons in the region of interest to create an image. Spins that are moving along the direction of a magnetic field gradient receive a phase shift proportional to their velocity.
In a phase contrast sequence two data sets with a different amount of flow sensitivity are acquired. This is usually accomplished by applying gradient pairs, which sequentially dephase and then rephase spins during the sequence. Both 2D and 3D acquisition techniques can be applied with phase contrast MRA.
The first data set is acquired with a flow compensated sequence, i. e. without flow sensitivity. The second data set is acquired with a flow sensitive sequence. The amount of flow sensitivity is controlled by the strength of the bipolar gradient pulse pair, which is incorporated into the sequence. Stationary tissue undergoes no effective phase change after the application of the two gradients. Caused by the different spatial localization of flowing blood to stationary tissue, it experiences a different size of the second bipolar gradient compared to the first. The result is a phase shift.
The raw data from the two data sets are subtracted. By comparing the phase of signals from each location in the two sequences the exact amount of motion induced phase change can be determined to have a map where pixel brightness is proportional to spatial velocity.
Phase contrast images represent the signal intensity of the velocity of spins at each point within the field of view. Regions that are stationary remain black while moving regions are represented as grey to white.
The phase shift is proportional to the spin's velocity, and this allows the quantitative assessment of flow velocities. The difference MRI signal has a maximum value for opposite directions. This velocity is typically referred to as venc, and depends on the pulse amplitude and distance between the gradient pulse pair. For velocities larger than venc the difference signal is decreased constantly until it gets zero. Therefore, in a phase contrast angiography it is important to correctly set the venc of the sequence to the maximum flow velocity which is expected during the measurement. High venc factors of the PC angiogram (more than 40 cm/sec) will selectively image the arteries (PCA - arteriography), whereas a venc factor of 20 cm/sec will perform the veins and sinuses (PCV or MRV - venography).

See also Flow Quantification, Contrast Enhanced MR Venography, Time of Flight Angiography, Time Resolved Imaging of Contrast Kinetics.

Pulse sequences, designed to be insensitive to flow, e.g. at every even echo, a spin echo sequence is not flow sensitive. Velocity compensation is achieved by using gradients, which are either symmetrical around a 180° pulse and switched on twice as is the case for motion compensated spin echo pulse sequences, or two antisymmetrical gradient lobes without 180° pulse, which is the way to produce a velocity compensated gradient echo pulse sequence.
The signal of the second echo (and all other even echoes) is independent of the velocity of the object. Thus, velocity-based motion effects stemming from the entire voxel or from spins within a voxel (intravoxel incoherent motion) are suppressed with such pulse sequences.
If higher order motion is relevant, as it may be in turbulent jets across valves, acceleration and jerk effects can also be compensated for by the use of appropriate combinations of gradient- and radio frequency pulses.
With the increasingly stronger gradients, echo times in MR systems can be shortened to the point at which effects other than velocity effects hardly ever become relevant.

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.

Bipolar gradients are two gradients with the same magnitude but opposite gradient direction. A bipolar gradient pulse is produced if one of the bipolar gradients is switched e.g., in negative direction and then switched in the opposite direction for an equivalent amount of time.
Bipolar gradients are used e.g. in phase contrast and diffusion weighted sequences. A bipolar gradient pulse pair produces a phase shift, which depends on the velocity component along this gradient. Motion along a bipolar gradient pulse pair results in a flow-induced phase shift of the transverse magnetization. The bipolar gradient pulse pair will not affect stationary spins. The amount of phase shifts depends on the area of each gradient pulse, and distance between the pulses. An echo occurring after such a gradient is flow compensated for velocity. A slight shift in the balance of this gradient will introduce a defined flow sensitivity of the pulse sequence.