(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.

Flow phenomena are intrinsic processes in the human body. Organs like the heart, the brain or the kidneys need large amounts of blood and the blood flow varies depending on their degree of activity. Magnetic resonance imaging has a high sensitivity to flow and offers accurate, reproducible, and noninvasive methods for the quantification of flow. MRI flow measurements yield information of blood supply of of various vessels and tissues as well as cerebro spinal fluid movement.
Flow can be measured and visualized with different pulse sequences (e.g. phase contrast sequence, cine sequence, time of flight angiography) or contrast enhanced MRI methods (e.g. perfusion imaging, arterial spin labeling).
The blood volume per time (flow) is measured in: cm3/s or ml/min. The blood flow-velocity decreases gradually dependent on the vessel diameter, from approximately 50 cm per second in arteries with a diameter of around 6 mm like the carotids, to 0.3 cm per second in the small arterioles.

Different flow types in human body:
See also Flow Effects, Flow Artifact, Flow Quantification, Flow Related Enhancement, Flow Encoding, Flow Void, Cerebro Spinal Fluid Pulsation Artifact, Cardiovascular Imaging and Cardiac MRI.

Quantification relies on inflow effects or on spin phase effects and therefore on quantifying the phase shifts of moving tissues relative to stationary tissues.
With properly designed pulse sequences (see phase contrast sequence) the pixel by pixel phase represents a map of the velocities measured in the imaging plane. Spin phase effect-based flow quantification schemes use pulse sequences specifically designed so that the phase angle in a pixel obtained upon measuring the signal is proportional to the velocity. As the relation of the phase angle to the velocity is defined by the gradient amplitudes and the gradient switch-on times, which are known, velocity can be determined quantitatively on a pixel-by-pixel basis. Once, this velocity is known, the flow in a vessel can be determined by multiplying the pixel area with the pixel velocity. Summing this quantity for all pixels inside a vessel results in a flow volume, which is measured, e.g. in ml/sec.
Flow related enhancement-based flow quantification techniques (entry phenomena) work because spins in a section perpendicular to the vessel of interest are labeled with some radio frequency RF pulse. Positional readout of the tagged spins some time T later will show the distance D they have traveled.
For constant flow, the velocity v is obtained by dividing the distance D by the time T : v = D/T. Variations of this basic principle have been proposed to measure flow, but the standard methods to measure velocity and flow use the spin phase effect.
Cardiac MRI sequences are used to encode images with velocity information. These pulse sequences permit quantification of flow-related physiologic data, such as blood flow in the aorta or pulmonary arteries and the peak velocity across stenotic valves.

(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.

(VENC) A specialized technique used for encoding flow-velocities.
The velocity encoding value is given by:
VENC = pi / gamma DELTA M1.
Gamma is the gyromagnetic ratio, and DELTA M1 is the gradient moment and is proportional to the area of the flow encoding gradient waveform.

See also Phase Contrast Sequence, Phase Contrast Angiography, and Bipolar Gradient Pulse.