We have shown that statistical errors caused by bodily movements can be compensated by a combination of preprocessing techniques. We found that simulated arm movements (in the absence of yoked head movements) led to a reduction in the average t-statistics in a region of legitimate activation and an increase in temporal noise and false positive activations in regions where no legitimate activation was found. Both of these problems, corresponding to Type II and Type I statistical errors, respectively, were considerably reduced with data preprocessing. The full combination of NC+PR+SS improved data quality over all other combinations of preprocessing steps, including NC+SS, which is a more standard combination. Moreover, in some cases, interactions occurred. Specifically, the benefits of SS were amplified by the inclusion of either NC or PR while the combination of NC+PR led to smaller benefits than would be expected by the sum of the two components alone.
The inclusion of PR was beneficial not only for movement-contaminated runs, but also for control runs. Presumably this occurred because the PR algorithm reduced other artifacts that affect ΔB0, including respiration and small head movements. The PR algorithm is therefore not only useful for suppressing the contributions from large vessels, but it also improves the quality of data with or without movement artifacts. A modest improvement of only 10% between NC+SS and NC+PR+SS may be explained by a reduction in activation levels (and thus t-statistics) from the exclusion of large vessels. Similarly, the lack of a statistically significant difference in tavg between NC+PR and NC pipelines is likely to be due to the opposing effects of vessel suppression (which reduces tavg) and artifact suppression (which increases tavg). Indeed, NC+PR led to a significantly greater reduction in noise in the ventricles and outside the head compared to NC alone. In short, though the addition of PR to the processing pipeline (before spatial smoothing) may not increase the significance levels of legitimate activations, it excludes vessel contributions with no significant decrease in statistical power, thus making the spatial localization of activation more closely coupled to the neural events. The benefits of PR may be even greater in other areas of the brain. We chose to examine t-statistics in the visual cortex, a standard VOI for methodological studies; however, given that geometric distortions may be particularly problematic in anterior () and inferior regions closer to the bodily motion, greater improvements in statistics with PR may be expected.
Even with the combination of all three preprocessing steps, data from movement runs was still poorer than non-movement runs (lower t
-statistics and higher noise). This result is consistent with our previous findings from simulations exploring the effect of spatially and temporally varying field inhomogeneities due to respiratory-induced physiological noise on the time course of pixels in reconstructed images [29
]. Even though those simulations were conducted in the absence of additive thermal noise, the residual geometric distortions persisted in simulated images after navigator correction (global, 1D, or 2D), indicating that none of the navigator techniques considered were able to completely compensate for spatially varying magnetic field inhomogeneities – even under artificially ideal circumstances. Thus, residual distortions persist in real fMRI data after NC, and are more severe in movement data than control data. The efficacy of the subsequent PR and SS steps is unfortunately diminished by these distortions, which explains why NC+PR+SS is more effective in control runs than movement runs.
The most striking feature of is the positive impact that the chosen spatial smoothing kernel has on all of the pipelines. For example, data that have undergone only SS have tavg
that is not significantly different from NC. With the aim of choosing the best pipeline (for the three steps considered), the most significant benefits of spatial smoothing are realized when this step is applied to data that have already undergone NC+PR. Although there is no difference in tavg
between NC+PR and NC, there is a significant improvement in NC+PR+SS over NC+SS due to the fact that the sequential application of NC and PR suppresses geometric distortions better than either NC or PR alone, which preconditions the data to make them more amenable to the well-recognized benefits of spatial smoothing [39
The engineering of an algorithm to perform a specific task is typically done under ideal circumstances or in isolation from other algorithms. However, in reality, there are interactions between algorithms in the preprocessing pipeline because the output of one algorithm is also the input of the next algorithm. A limitation of k-space correction algorithms (such as the 2D navigator) stated in the literature is that they are only useful in low-frequency k-space where there is sufficient SNR; however, a significant advantage of k-space techniques is that they can apply different corrections to segments of k-space, which is important for multi-shot sequences. An advantage of PR is that it operates on individual pixels in image space and can correct temporal fluctuations that have high spatial frequencies. By combining NC and PR, data first undergo a correction for field inhomogeneities with low spatial frequencies, followed by a complementary correction for the highest spatial frequencies based on correlated phase and magnitude changes. Since PR by itself is barely an improvement over the pipeline with no preprocessing, another way of looking at this relationship is that uncorrected geometric distortions result in pixels with phase and magnitude changes that are influenced by the shifting of adjacent pixels in the phase-encode direction. In the presence of geometric distortions, phase and magnitude changes for each pixel become less correlated, and the PR algorithm is no longer able to accurately compensate for these unwanted fluctuations.
In addition to suppressing BOLD activation from larger vessels [33
] and increasing tavg
via interactions with NC and SS, the third benefit of the PR algorithm is decreasing spurious activations (Type I errors) by reducing extraneous noise fluctuations. Although false activations are more easily identified when they appear in white matter, cerebrospinal fluid, or at the edge of the brain, they may, without careful scrutiny, be mistaken as genuine activation in gray matter. Sources of extraneous fluctuations include physiological noise and field inhomogeneities caused by bodily movements. Although this paper considered a specific example of subject movement caused by movement of a subject’s forearm during reaching/grasping experiments, it must be emphasized that the benefits of PR are applicable to all fMRI experiments where unaliased complex data are retained.
The findings in this paper may also improve the reliability of motion correction algorithms. Despite the best efforts of the MR technician to immobilize a subject’s head in the RF coil and the good intentions of the subject to remain completely stationary, some degree of physical head movement is inevitable during scans. Head motion degrades the quality of fMRI data by obscuring regions of real activation and creating regions of false activation [40
]. Even small movements of less than 1 mm translation or 1° rotation can create false regions of activation if the movement is correlated with the paradigm [42
The use of an algorithm to estimate and correct for rigid-body head motion is generally believed to improve the quality of fMRI data [15
], although such algorithms can create spurious activations in the absence of subject motion [28
]. Motion correction can actually lead to erroneous corrections [16
] and create false regions of activation when the cost function used to estimate motion is sensitive to spatially varying changes in signal intensity due to BOLD activation and geometric distortions caused by ΔB0
. Future work can include rigid-body motion correction in the preprocessing pipeline to investigate the influence that steps to reduce geometric distortions (e.g., navigator correction and complex phase regression) have on the efficacy of the motion correction algorithm to compensate for genuine head motion without introducing additional artifacts.
In conclusion, an approach to compensate for spatiotemporally varying magnetic field inhomogeneities has been presented that combines complementary techniques of navigator correction and complex phase regression. The first step is applied to low-frequency k-space while the second step operates on individual pixels in complex image space, and their synergy in the preprocessing pipeline precondition the data to make them more amenable to the benefits of spatial smoothing. An fMRI study was performed that emulated magnetic field distortions expected from a reaching/grasping paradigm by moving a human arm phantom outside the imaging FOV. An analysis in the occipital lobe demonstrated a 10% increase in t
-statistics when phase regression is included between 2D navigator correction and spatial smoothing, leading to a decrease in Type II errors. Analyses in regions other than gray matter revealed a decrease in noise variance after phase regression, providing better control of Type I errors. As residual geometric distortions persisted in reconstructed images, future work can investigate the inclusion of additional steps in the preprocessing pipeline (for example, the Stockwell transform filter [43
]) to further compensate for non-trivial magnetic field inhomogeneities. Finally, since the scope of this study was limited to spatial smoothing for typical group analyses (a single kernel width used for all data sets), future work can also consider the role that phase regression may play in optimized spatial smoothing for both single-subject and group fMRI analyses.