Richard Mallozzi, Ph.D.
The Phantom Laboratory, Inc.
Image Owl, Inc.
Copyright © August, 2015. The Phantom Laboratory, Inc.
A number of MRI applications, such as MRI-guided stereotactic radiation therapy planning, are much more sensitive to geometric distortion than most diagnostic radiology applications. It is widely advised that to reduce geometric distortion, 3D sequences rather than 2D multislice sequences should be used whenever possible. In both cases we are referring to full 3D volume acquisitions, but distinguishing between MRI sequences of the type ‘3D, ‘ which use a phase-encoding gradient along slice direction, and those referred to as ‘2D,’ which use a slice-selective gradient and RF combination 
It is frequently not practical to use a 3D pulse sequence, however, and so it is worthwhile to understand the limitations of 2D pulse sequences and how they differ from 3D sequences. Understanding the difference sheds light on why 2D sequences should receive particularly high scrutiny in a quality control program aimed at controlling geometric distortion, as well as issues associated with correcting distorted images.
As has been described in earlier white papers [2,3], 3D and 2D sequences have an important difference in how distortion correction is applied. For both 3D and 2D sequences, in-plane correction is always applied by default. In the slice direction, however, the correction is generally performed by default only for 3D sequences, and not for 2D sequences. To understand more deeply why this is the case, we delve into how the data from 2D and 3D sequence is different, and why that affects geometric distortion in the slice direction.
3D and 2D MRI pulse sequences
The distinction between three-dimensional and two-dimensional pulse sequences lies in how the information in the slice direction is encoded. In two-dimensional sequences, each slice is excited in isolation by a combined gradient and RF pulse. The data from that slice is acquired, and then a different slice is excited. During the time that one slice is being excited and acquired, the other slices are undergoing the T1 relaxation that re-establishes the longitudinal spin equilibrium.
In three-dimensional sequences, the entire imaging volume is excited with every data acquisition. The spins along the slice direction are spatially encoded with a phase-encoding gradient pulse, just as they are for one of the in-plane directions. Phase-encoding gradients apply a particular spatial frequency modulation to the spin population.
The major benefit to the 3D approach is increased signal-to-noise, as all the spins contribute to the signal during every acquisition. The tradeoff is that one must wait for a long time (characterized by the T1 of the tissue) for the spin population to relax, or else use small flip angles, both of which reduce the signal-to-noise. The quantitative details of the trade-off depend therefore upon the T1 of the tissue and the desired repetition time (TR).
Three-dimensional sequences are more often used when T1-weighting is desired, as the time between excitations (TR) is much shorter anyway. If one attempted to use a 3D sequence when T2 weighting was sought, the excitation flip angle would have to be very small, or the wait between excitations would have to be very large, that the scan would be extremely long and have very low signal-to-noise.
Geometric Distortion in 3D vs 2D sequences
In both 2D and 3D sequences, the shape of the slice before any correction is applied is a warped plane as in the figure below. The main source of the distortion are nonlinearities of the gradient field along the slice direction. Although both types of sequences would exhibit similar distortion without any correction, there is an important difference that renders 3D sequences easier to correct than 2D sequences.
In 3D sequences, the entire volume imaging volume is excited with a single RF and gradient pulse. The spatial information along the slice direction is determined by using a phase-encoding gradient, which is an inherently bandwidth-limited method. The only spatial frequencies that are acquired are those that were deliberately generated by a phase-encoding gradient pulse. The data, therefore, has the proper bandwidth limit needed so that a discrete sampling at the slice spacing interval can completely characterize the underlying continuous function. A simpler way to understand this is to say that because of the limited bandwidth of the acquired data, enough information exists to correctly interpolate between slices and describe what the data would have looked like if the slices had been slightly shifted by an amount less than the slice thickness. It is important to note that this does not mean a higher resolution can be attained, only that one can interpolate exactly to view what would happen if the slices had been placed at different locations.
This differs from the 2D situation, in which each slice is acquired separately. Inherent in the signal acquisition is an averaging along the slice direction of the signal from excited spins. The nature of this averaging is such that the acquired signal does not have the same clean bandwidth-limited property as in the 3D case. The result is that interpolation is not exact -- if one attempted to reconstruct what a slice would have looked like had it been acquired at a shifted location relative to the original set, that calculation cannot be performed with complete accuracy as it can in the case of a 3D acquisition. The complete information to do an exact interpolation is not contained in the original set of slice data as it is in the case of a 3D pulse sequence.
Implications for Distortion Correction
Because 3D sequences can be exactly interpolated in the slice directions and 2D sequences cannot, MRI equipment manufacturers first implemented the full 3D correction on 3D sequences, even though many 2D sequences are acquired over a full volume with contiguous slices. More recently, full 3D correction of volume acquisitions using 2D sequences has also been made available on many MRI scanners. However, because the interpolation in the slice direction is not exact, there is greater reluctance to have such a correction performed by default. Because the vast majority of diagnostic radiology applications are not sensitive to MRI distortions up to a few mm, the rational choice for MRI manufacturers may be to leave the through-slice direction uncorrected in volume acquisitions performed with 2D sequences by default, and provide a setting for users to enable the correction if desired. Therefore those who are performing MRI studies sensitive to distortion, such as radiation therapy planning, need to be aware of the capabilities and the settings of their scanner regarding distortion correction for 2D pulse sequences.
There is a strong need for this through-plane distortion to be monitored as part of a quality control program for distortion-sensitive applications. Such a program should be designed both to assess the performance of the 3D correction for all sequences and to detect cases where the slice-direction correction may not be turned on for a 2D pulse sequence. This information is available from phantom data accompanied by the appropriate analysis.