(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.

(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.

(3D MRA) The 3D angiography technique can be applied to focus on fast flowing (arterial) blood and to visualize small tortuous vessels. 3D TOF images are less sensitive to turbulent flow artifacts. The advantage of this approach is that the signal, acquired from the entire volume has an increased signal to noise ratio. Slices are defined by a second phase encoded axis, which divides the volume into 'partitions'. 3D TOF MRA is acquired with 3D FT slabs or multiple overlapping thin 3D FT slabs (MOTSA) depending on the coverage required and the range of flow-velocities under examination.
Such 3D techniques can provide equal spatial resolution along all three axes, i.e. be 'isotropic', or the partition thickness can be greater or less than the in plane spatial resolution in which case can be said to be 'anisotropic'. The circle of Willis, anatomy as well as its fast arterial flow, lends itself well to both 3D TOF and 2D or 3D phase contrast angiography.

Angiography means the imaging of veins and arteries. Magnetic resonance angiography (MRA) has a lower invasion than conventional angiography with catheter and X-ray contrast agent. Time of flight angiography (inflow) and phase contrast angiography works without contrast agents. Only in contrast enhanced magnetic resonance angiography is the use of contrast agents necessary, but the lack of side effects is an advantage of MRI contrast agents, just as the smaller dosage as used in X-ray angiography techniques.

See also the related poll result: 'MRI will have replaced 50% of x-ray exams by'