Methodology for Robust Motion Correction of Complex-valued MRI Time Series

Introduction: In functional MRI (fMRI), the presence of subject motion during the acquisition of an image series can confound results. In general practice, only the magnitude portion of the images is used in the functional analysis [1], and thus correction for subject motion is required in only the magnitude images. However, statistical models for performing complex-valued fMRI analysis are available [2] which can provide some benefits beyond the standard magnitude-only technique, and the investigation of a signal resulting from direct neuronal current involves complex-valued analysis [3]. Furthermore, it has been demonstrated that signal of potential functional interest can be found in the phase portion of the signal [4]. In order to maximize the utility of these investigative techniques, motion correction of the phase as well as the magnitude is required. Unfortunately, this correction is not as straightforward as magnitude correction alone. The image phase can be considered to consist of three separate parts: 1) that resulting from local tissue susceptibility differences, 2) that resulting from more spatially global bulk magnetic field inhomogeneity, and 3) that resulting from inhomogeneity of the RF pulse phase. It is desirable to only perform motion correction on the first part of this phase, because the second portion, while variable through time, does not behave like bulk motion. In other words, the bulk field inhomogeneity changes as the head moves, but these changes are unpredictable and cannot be accounted for using bulk motion correction techniques [5]. The phase from the RF pulse is considered to be constant through time for the amount of motion generally present during acquisition. Therefore, correction of this phase would also be invalid. The goal of this work is to demonstrate the ability to isolate the phase due to local tissue susceptibility and how doing so improves the performance of motion correction of the phase signal. Methods: An MRI time series was acquired for a single subject on a 3T MRI scanner (General Electric, Milwaukee, WI) using an echo planar imaging (EPI) pulse sequence (TE=42.7 ms, BW=125 Hz, matrix = 96×96, FOV=24 cm, slice thickness=2.5 mm, #slices=9, TR=1 s, repetitions=296). During the first 20 repetitions, even repetitions had their echo time increased to 47.7 ms to facilitate magnetic field off-resonance estimation. Dynamic magnetic field offset correction was applied using the Temporal Off-resonance Alignment of Single-echo Timeseries (TOAST) method as described by Hahn et al. [6]. After this correction, the mean of all the complex-valued images was computed and smoothed with a 12.5 mm FWHM Gaussian kernel. The phase of this smoothed image, representing the phase of the RF pulse, was then subtracted out of every image in the series. Finally, 2-dimensional motion parameters were computed from the magnitude portion of the TOAST corrected images and applied to the real and imaginary portions of the same images using the AFNI plugin 2dImReg [7]. Results: The spatially global phase variations remaining after removing the effects of bulk magnetic field inhomogeneities using TOAST can be seen in Figure 1a, and can be attributed to the RF pulse phase. After removing this low spatial frequency phase as described above, the remaining phase depicted in Figure 1b appears to have mainly anatomically related structure, which is the desired result. To investigate the benefit of the motion correction, the phase variance without correction was divided by the phase variance with correction. Images of the results of this analysis are shown for the case where the RF phase is not removed, and for the case where it is removed in Figures 2a and 2b, respectively. In these images, 1 has been subtracted from the ratio, so that larger (more positive) values indicate a greater reduction in variance, while negative values indicate that motion correction increased the phase variance. It should be noted that no data is presented without the TOAST correction, due to the fact that the phase variance due to motion is negligible compared to that resulting from temporal bulk field variation. The two images in Figure 2 are not extremely different, however there are a points of apparent difference. First, the area circled in red in Figure 2 indicated an area where removal of the RF phase significantly improves the performance of the motion correction. The areas circled in blue indicate areas where it appears the RF phase removal improves performance as well, although the differences are not as drastic as in the area indicated in red. Discussion: The results seem to show that areas are affected locally by the presence of the RF phase, while others are not, which is not unexpected. Areas where the RF phase appears detrimental seem to coincide with locations where the RF phase has more spatial variation (see Figure 1a), which is logical. If main magnetic field inhomogeneity is not corrected for using TOAST, similar results can be seen, and the phase induced by this inhomogeneity tends to have more rapid spatial variation (data not shown). Although the motion correction applied here was only in 2 dimensions, applying a 3 dimensional correction using this technique should be equally useful. It is not done here because of the limited data in 3 dimensions (only 9 slices) to determine appropriate motion parameters. Finally, it is worth noting that the motion correction is applied to the real and imaginary channels of the data rather than the phase channel directly in order to avoid the need to unwrap the image phase. If a 2 dimensional phase unwrap is applied to every image, the motion correction could be applied to the phase directly. References: 1. PA Bandettini et al., MRM 30:161-73, 1993. 2. DB Rowe, NIMG 25:1310-24, 2005b. 3. L Heller et al., HBM 30:1-12, 2007. 4. Z Feng et al., NIMG 47:540-8, 2009. 5. P Jezzard, S Clare, HMB 8:80-85, 1999. 6. AD Hahn et al., NIMG 44:742-52, 2009. 7. RW Cox, Computers and Biomedical Research 29:162-73, 1996. Acknowledgements: This work was supported in part by NIH EB00215 and EB007827. Figure 1 (above). Phase image of a single slice from the acquired image time series after TOAST correction only (a) and after TOAST correction and RF phase removal (b). The left image shows the low spatial frequency phase attributed to RF phase, while the right image shows phase which appears mainly anatomical in nature. Note the difference in scale. Images are masked above 10% of the maximum magnitude.