A few years ago, Jo Etzel and I got into a brief but useful investigation of the effects of apparent head motion in fMRI data collected with SMS-EPI. The shorter TR (and smaller voxels) afforded by SMS-EPI generated a spiky appearance in the six motion parameters (three translations, three rotations) produced by a rigid body realignment algorithm for motion correction, such as MCFLIRT in FSL. The apparent head motion is caused by magnetic susceptibility variations of the subject's chest as he/she breathes, leading to a change in the magnetic field across the head which, in turn, adds a varying phase to the phase-encoded axis of the EPI. This varying phase then manifests as a translation in the phase-encoded axis. It's not a real motion, it's pseudo-motion, but unfortunately it is a real image translation that adds to any real head motion. I should emphasize here that this additive apparent head motion arises in conventional multi-slice EPI, too, but it's generally only when the TR gets short, as is often the case with SMS-EPI, that the apparent head motion can be visualized easily (as a spiky, relatively high frequency fluctuation in the six motion parameter traces). In EPI sampled at a conventional TR of 2-3 sec, there are only a small handful of data points (volumes) per breath for an average breathing rate of 12-16 breaths/minute and this leads to aliasing of most of the apparent head motion frequency. It may still be possible to see the spiky respiration frequency riding on the six motion parameters, but it's not always there as it is for TR much less than 2 seconds.
Once we'd satisfied ourselves we'd understood the problem fully, I confess I let the matter drop. After all, we have tools like MCFLIRT that try to apply a correction to all sources of head motion simultaneously, whether real or apparent. But now I'm wondering if we might be able to evaluate the real and apparent motion contributions separately, with a view to devising improved QC measures that can emphasize real head motion over the apparent head motion when it comes to making decisions on things like data scrubbing. Jo has been dealing with the appropriate framewise displacement (FD) threshold to use when including or excluding individual volumes. (See also this paper.)
Let's review one of the motion traces from my second 2016 blog post on this issue:
These traces come from axial SMS-EPI with SMS factor (aka MB factor ) of 6. The x axes are in seconds, corresponding to TR = 1 sec. (The phase-encoded axis is anterior-posterior, which is the magnet Y direction.) On the left is a subject restrained with only foam, on the right the same subject's head is restrained with a printed head case. During each run the subject was asked to take a deep breath and sigh on exhale every 30 seconds or so. We clearly see the deep breath-then-sigh episodes in both traces, regardless of the type of head restraint used. Yet it is also clear the apparent head motion, which is the high frequency ripple, dominates the Y, Z and roll traces on the left plot. On the right plot, the dominant effect of apparent head motion manifests in the Y trace, with a much reduced effect in the roll axis. Already we are seeing a slight distinction between the translations and rotations for apparent head motion. It looks like apparent head motion contributes more to translations than rotations, which makes sense given the physical origin of the problem. In which case, can we assume that by extension real head motion will dominate the rotations?
For now, let's assume that the deep breath-then-exhale episodes are producing considerable real head motion, in addition to the large apparent head motion spike from exaggerated chest movement. The left plot above shows that pitch, yaw and roll all characterize the six deep breaths readily. They are also visible in Z and X, but with considerably reduced magnitude. There's no clear effect in the Y trace which is dominated by the aforementioned apparent head motion. So far so good! When the head can actually move in the foam restraint, we have clear biases towards rotations for real head motion and translations for apparent head motion.
What about the right plots? Real head motion is far harder to achieve because of the printed head case restraint. But we assume the apparent head motion is basically the same magnitude because it's chest motion, not head motion. So we might think of this condition as being a low (or lowest) real motion condition. As with the foam restraint on the left, we again see Y translations dominated by apparent head motion. The roll axis also displays considerable apparent head motion. And as for the foam restraint, the roll and pitch axes display something that may be real or apparent head motion for each of the deep breath-then-exhale periods. We can't be sure if the head (or the entire head case, or even the entire RF coil!) was really moving during each breath, but let's assume it was. If so, then for good mechanical head restraint we have the same rough biases as for foam restraint in our motion traces: real motion dominates rotations, apparent motion manifests mostly as translations.
Jo sees a similar distinction between real and apparent head motion in the motion parameter plots of her 2023 blog post. In her top plot, which she suggests is a low real motion condition, the apparent motion dominates Y and Z translations and the roll traces, exactly as my example above. Her second plot exhibits considerable real head motion. The apparent head motion is still visible as ripples on the Y and Z translation traces, but now it's clear the biggest changes arise in the three rotations and these changes are probably real head motion. Again, we have real motion dominating rotations while apparent motion manifests more in the translations.
Finally, let's consider Frew et al., who looked at head motion in pediatrics. Here's Figure 3 from their paper:
Using framewise displacement (FD), they show a transition from FD dominated by translations to FD dominated by rotations when considering low, medium and high (real) head motion subjects. Rotations and translations are both affected significantly in the medium movement group. Still, the trend here suggests that we might consider rotations alone as an index of real head motion if, as suggested above, apparent head motion contributes mostly to translations.
So, what might we do to separately evaluate real and apparent head motion? This is where you come in. I only have one starting idea, and that's to shift to considering FD using only rotations, rather than rotations and translations, when setting thresholds for the purposes of QC and scrubbing. Based on what I've presented here, we might be able to set a threshold for FD(rotations only) that will capture most of the real head motion and have a much reduced dependency on apparent head motion. This measure could help avoid mischaracterizing large apparent head motions as events to reject when they are inherently fixable with MCFLIRT and similar. (Real head motion produces a big spin history effect and likely introduces non-linear distortions in the images.) Whether the reverse is true - that is, whether FD(translations only) captures most of the apparent head motion and a reduced contribution from real head motion - I leave as an exercise for another day, but my suspicion is that it is not. Put another way, I think the focus should be on using the rotations to capture and evaluate real head motion. Pooling translations and rotations in measures like FD may be complicating the picture for us.
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