Rigid-body motion correction with self-navigation MRI

Abstract

The use of phase correlation to detect rigid-body translational motion is reviewed and applied to individual echotrains in turbo-spin-echo data acquisition. It is shown that when the same echotrain is acquired twice, the subsampled correlation provides an array of delta-functions, from which the motion that occurred between the acquisitions of the two echotrains can be measured. It is shown further that a similar correlation can be found between two sets of equally spaced measurements that are adjacent in k-space. By measuring the motion between all adjacent pairs of k-space subgroups, the complete motion history of a subject can be determined and the motion artifacts in the image can be corrected. Some of the limiting factors in using this technique are investigated with turbo-spin-echo head and hand images.

FIG. 1

Shown in (a) are repeated, subsampled acquisition of k-space (such as acquiring the same echotrain twice) and the corresponding aliased images. The phase correlation, c_w(x,y) shown in (b) is obtained from the cross correlation of the aliased images. The crosscorrelation shows the replicated delta functions offset from the zero-offset position.

FIG. 2

2D TSE hand images reconstructed from a single echotrain (N_e = 17 and N_et = 31). The images correspond to three adjacent sets of equally spaced k-space lines from the (a) 15th, (b) 16th, and (c) 17th echotrains. The left side is the magnitude image and the right side is the real image. The real image shows the slow variation in phase caused by the shift in the k-space sampling pattern.

FIG. 3

Simulated motion tracking on TSE head images with an FOV double the object size, five interleaved slices with a 0.5 mm × 0.5 mm 2 mm resolution, ETL = 11, TR = 3 s, and TE = 13 ms. The top graphs show motion detection in the (a) readout or x direction, and (b) phase encode or y direction. The gray dots represent the motion calculated using self-navigation, and the solid line is the actual motion. The Fourier transform of the calculated data is multiplied by a low-pass filter to produce a smoothed line for the objects motion. A smoothed line is then fit to the calculated data and compared to the actual motion in (c). The solid line is the error in the x (readout) direction, whereas the dashed line is error in the y (phase encode) direction.

FIG. 4

TSE head images acquired with the parameters in Table 1 and the motion correction shown in Figure 3. Each vertical column represents a different slice location. The images without motion artifacts are shown in (a), the motion corrupted images in (b), images corrected individually in (c), and with constrained motion using all five slices in (d).

FIG. 5

TSE motion corrected head images with varying FOV. The top row contains images corrected using the proposed self-navigating technique and the bottom row shows the difference images (compared to the original motion free image). Each column represents a different FOV with (a) 105%, (b) 116%, (c) 126%, (d) 138%, (e) 149%, (f) 160%, and (g) 171% of the objects region of support.

FIG. 6

Coefficient of variation with the original motion free images for varying FOV. The dot-dashed line compares the uncorrected images, the solid line represents corrected images with a 2° degree rotation between echotrains, the dashed line is corrected images with a 1° rotation between echotrains, and the dotted line is corrected images with no object rotation during acquisition.

FIG. 7

Error in motion correction using the proposed self-navigation technique in the presence of small object rotations. The top row shows the (a) X motion error and (b) Y motion error when the FOV is 126% the object size. The bottom row shows the (c) X motion error and (d) Y motion error when the FOV is 171% the object size. The solid lines represent no object rotation, the dashed line is a 1° rotation between any two adjacent data sets and the dotted line is a 2° rotation between any two adjacent data sets.

FIG. 8

a: A single axial slice from a 22-slice T2w TSE images of the hand. Motion that occurred during acquisition caused severe blurring and some ghosting. b: An image obtained from the same measurement data of the same slice using the correction method described in this work.

FIG. 9

A plot of the x and y offsets in chronological order for 9 of the 11 interleaved slices where the SNR was strong enough for the correlation technique to be applied.