The phase shift is the loss of phase coherence in precessing spins. Vascular spins move at variable velocities; faster flow undergo a stronger phase shift than slower flowing spins.

The partial Fourier technique is a modification of the Fourier transformation imaging method used in MRI in which the symmetry of the raw data in k-space is used to reduce the data acquisition time by acquiring only a part of k-space data.
The symmetry in k-space is a basic property of Fourier transformation and is called Hermitian symmetry. Thus, for the case of a real valued function g, the data on one half of k-space can be used to generate the data on the other half.
Utilization of this symmetry to reduce the acquisition time depends on whether the MRI problem obeys the assumption made above, i.e. that the function being characterized is real.
The function imaged in MRI is the distribution of transverse magnetization Mxy, which is a vector quantity having a magnitude, and a direction in the transverse plane. A convenient mathematical notation is to use a complex number to denote a vector quantity such as the transverse magnetization, by assigning the x'-component of the magnetization to the real part of the number and the y'-component to the imaginary part. (Sometimes, this mathematical convenience is stretched somewhat, and the magnetization is described as having a real component and an imaginary component. Physically, the x' and y' components of Mxy are equally 'real' in the tangible sense.)
Thus, from the known symmetry properties for the Fourier transformation of a real valued function, if the transverse magnetization is entirely in the x'-component (i.e. the y'-component is zero), then an image can be formed from the data for only half of k-space (ignoring the effects of the imaging gradients, e.g. the readout- and phase encoding gradients).
The conditions under which Hermitian symmetry holds and the corrections that must be applied when the assumption is not strictly obeyed must be considered.
There are a variety of factors that can change the phase of the transverse magnetization:
Off resonance (e.g. chemical shift and magnetic field inhomogeneity cause local phase shifts in gradient echo pulse sequences. This is less of a problem in spin echo pulse sequences.
Flow and motion in the presence of gradients also cause phase shifts.
Effects of the radio frequency RF pulses can also cause phase shifts in the image, especially when different coils are used to transmit and receive.
Only, if one can assume that the phase shifts are slowly varying across the object (i.e. not completely independent in each pixel) significant benefits can still be obtained. To avoid problems due to slowly varying phase shifts in the object, more than one half of k-space must be covered. Thus, both sides of k-space are measured in a low spatial frequency range while at higher frequencies they are measured only on one side. The fully sampled low frequency portion is used to characterize (and correct for) the slowly varying phase shifts.
Several reconstruction algorithms are available to achieve this. The size of the fully sampled region is dependent on the spatial frequency content of the phase shifts. The partial Fourier method can be employed to reduce the number of phase encoding values used and therefore to reduce the scan time. This method is sometimes called half-NEX, 3/4-NEX imaging, etc. (NEX/NSA). The scan time reduction comes at the expense of signal to noise ratio (SNR).
Partial k-space coverage is also useable in the readout direction. To accomplish this, the dephasing gradient in the readout direction is reduced, and the duration of the readout gradient and the data acquisition window are shortened.
This is often used in gradient echo imaging to reduce the echo time (TE). The benefit is at the expense in SNR, although this may be partly offset by the reduced echo time. Partial Fourier imaging should not be used when phase information is eligible, as in phase contrast angiography.

See also acronyms for 'partial Fourier techniques' from different manufacturers.

(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.

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.

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.