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The respiratory phase can be used to control imaging either by only acquiring the image data during a particular portion of the respiratory cycle (which increases image acquisition time) or by adjusting the sequence of image data collection according to the phase of the respiratory cycle in such a way as to minimize motion-induced artifacts in the reconstructed image.

See also Respiratory Ordered Phase Encoding.

Quick Overview
Please note that there are different common names for this artifact.

A data truncation artifact may occur when the interface between high and low signal intensities is encountered in one imaging plane. The 2D-FT techniques transform the MR signal to spatial intensity image data with frequency and phase information encoding each axis in the plane of the scan. This artifact is found in both frequency and phase axes. Artifactual ripples adjacent to edges in an image or sharp features in a spectrum, caused by omission of higher frequency terms in Fourier transformation, particularly with the use of zero filling to replace unsampled higher frequencies.
Complex shapes are specified by series of sine and cosine waves of various frequencies, phase and amplitude. Some shapes are more difficult to encode than others. The most difficult shapes to represent with Fourier series of terms are waveforms with instantaneous transitions, tissue discontinuities or edges. The low-frequency components of the series describe the overall shape of the step function. Higher frequency components are needed to describe the corners if the step function more accurately. If not enough samples are taken, these areas cannot be accurately represented. The truncation of the infinite data series results in a ringing artifact because of the inability to accurately approximate this tissue discontinuity with a shorter truncated data set. Therefore, the ringing that occurs at all tissue boundaries on MR is called truncation artifact.

This problem can be easily resolved by taking more samples - a higher acquisition matrix and/or a smaller FOV. See Gibbs Artifact and Gibbs Phenomenon.

(2D FT) A form of sequential plane imaging using Fourier transformation imaging. In 2D FT, a line of data corresponds to the digitized NMR signal at a particular phase encoding level. The Fourier transformation process reconstructs the detected frequency and phase encoded image information (which are rotated 90° from each other) into a usable image.

(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.