Can we separate real and apparent motion in QC of fMRI data?

 

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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Using multiband-EPI for diffusion imaging on low-dimensional array coils

This is a continuation of the previous post looking at MB-EPI on a receive coil with limited spatial information provided by its geometry, such as the 12-channel TIM coil or the 4-channel neck coil on a Siemens Trio.

Simultaneous multi-slice (SMS), aka multi-band (MB), offers considerable time savings for diffusion-weighted imaging (DWI). Unlike in fMRI, where MB factors of 4 or more are quite common, in DWI few studies use MB factors greater than 3. While it may be feasible in principle to push the acquisition time even lower without generating artifacts using a large array coil like the Siemens 32-channel coil, we run into another consideration: heating. Heating isn't usually a concern for gradient echo MB-EPI used in conventional fMRI experiments. In fMRI, the excitation flip angles are generally 78° or less. But with DWI we have a double whammy. Not only do we want a large excitation flip angle to create plenty of signal, we also require a refocusing pulse that is, by convention, set at twice the flip angle of the excitation pulse. (The standard nomenclature is 90° for excitation and 180° for refocusing, but the actual angles may be lower than this in practice, for a variety of reasons I won't go into here.) Now the real kicker. The heat deposition, which we usually measure through the specific absorption rate (SAR), scales quadratically with flip angle. Thus, a single 180° refocusing pulse deposits as much heat as four 90° pulses! (See Note 1.) But wait! It gets worse! In using simultaneous multi-slice - the clue's in the name - we're not doing the equivalent of one excitation or refocusing at a time, but a factor MB of them. Some quick arithmetic to give you a feel for the issue. A diffusion scan run with 90° and 180° pulses, each using MB=3, will deposit fifteen times as much heat as a conventional EPI scan run at the same TR but with a single 90° pulse. On a 3 T scanner, it means we are quickly flirting with SAR limits when the MB factor goes beyond three. The only remedy is to extend TR, thereby undermining the entire basis for deploying SMS in the first place.

But let's not get ahead of ourselves. With a low-dimensional array such as the Siemens 12-channel TIM coil we would be delighted to get MB to work at all for diffusion imaging. The chances of flirting with the SAR limits are a distant dream.


Phantom tests for diffusion imaging

The initial tests were on the FBIRN gel phantom. I compared MB=3 and MB=2 for the 32-channel, 12-channel and neck coils using approximately the same slice coverage throughout. The TR was allowed to increase as needed in going from MB=3 to MB=2. Following CMRR's recommendations, I used the SENSE1 coil combine option throughout. I also used the Grad. rev. fat suppr. option to maximize scalp fat suppression, something that we have found is important for reducing ghosts in larger subjects (especially on the 32-channel coil, which has a pronounced receive bias around the periphery). For the diffusion weighting itself, I opted to use the scheme developed for the UK Biobank project, producing two shells at b=1000 s/mm² and b=2000 s/mm², fifty directions apiece. Four b=0 images are also included, one per twenty diffusion images. (For routine use we now actually use ten b=0 images, one every ten DW images, for a total of 111 directions.) The nominal spatial resolution is (2 mm)³. The TE is 94.8 ms, which is the minimum value attainable at the highest b value used.

There are over a hundred images we could inspect, and you would want to check all of them before you committed to a specific protocol in a real experiment because there might be some strange interaction between the eddy currents from the diffusion-weighting gradients and the MB scheme. For brevity, however, I will restrict the comparisons here to examples of the b=0, 1000 and 2000 scans. I decided to make a 2x2 comparison of a single band reference image (SBRef), a b=0 image (the b=0 scan obtained after the first twenty DW scans), and the first b=1000 and b=2000 images in the series. While only a small fraction of the entire data set, these views are sufficient to identify the residual aliasing artifacts that tell us where the acceleration limit sits.

First up, the results from the 32-channel coil, which is our performance benchmark. No artifacts are visible by eye for any of the b=0, b=1000 or b=2000 scans at either MB=2 or MB=3:

32-channel coil, MB=3. TL: Single band reference image. TR: first b=0 image (21st acquisition in the series). BL: first b=1000 image. BR: First b=2000 image

Using multi-band (aka SMS) EPI on on low-dimensional array coils

The CMRR's release notes for their MB-EPI sequence recommend using the 32-channel head coil for multiband EPI, and they caution against using the 12-channel head coil:

"The 32-channel Head coil is highly recommended for 3T. The 12-channel Head Matrix is not recommended, but it can be used for acceptable image quality at low acceleration factors."

But what does "low acceleration" mean in practice? And what if your only choice is a 12-channel coil? Following a couple of inquiries from colleagues, I decided to find out where the limits might be.

Let's start by looking at the RF coil layout, and review why the 12-channel coil is considered an inferior choice. Is it simply fewer independent channels, or something else? The figure below shows the layout of the 12-ch and 32-ch coils offered by Siemens:

From Kaza, Klose & Lotze (2011).

In most cases, the EPI slice direction will be transverse or transverse oblique (e.g. along AC-PC), meaning that we are slicing along the long axis of the magnet (magnet Z axis) and along the front-to-back dimension of the head coil. Along the long axis of the 12-ch coil there is almost no variation in the X-Y plane. At the very back of the coil the loops start to curve towards a point of convergence, but still there is no distinction in any direction in the X-Y plane. Compare that situation to the 32-ch coil. It has five distinct planes of coils along the Z axis. With the 32-ch coil, then, we can expect the hardware - the layout of the loops - to provide a good basis for separating simultaneously acquired axial slices, whereas there is no such distinct spatial information available from the coil elements in the 12-channel coil. In the 12-channel coil, every loop detects a significant and nearly equal fraction of any given slice along Z.

Use of split slice GRAPPA (aka Leak Block) for SMS-EPI reconstruction

Accurate separation of the simultaneously acquired slices is one of the bigger limitations of the SMS-EPI method, compared to the processing used for conventional multislice EPI. The default SMS reconstruction, as used in my two introductory posts on the SMS sequences from CMRR (MB-EPI) and MGH (Blipped CAIPI), is a slice dimension adaptation of the GeneRalized Autocalibrating Partial PArallel (GRAPPA) method that was originally applied in-plane to acceleration of the phase encoding direction. It's not essential to understand the GRAPPA method applied in-plane for the purposes of understanding this post or for SMS reconstruction more generally. But if you're curious I wrote a brief introduction to in-plane GRAPPA in 2011. That post was specifically concerned with motion sensitivity of (in-plane) GRAPPA. I'll be looking in more detail at the motion sensitivity of SMS in a future post. In this post I want to compare the standard SMS reconstruction - what is generally termed Slice GRAPPA - with an alternative known as Split Slice GRAPPA. The latter option is termed "Leak Block" in the CMRR pulse sequence, MB-EPI.

What's the concern?

CMRR's parameter nomenclature offers a strong clue to the problem. In conventional EPI reconstruction we use a 2D Fourier transform (FT) which produces some amount of ringing. We also use slices that have some degree of cross-talk to neighboring slices, arising out of the limitations of frequency selectivity. So, while we think of voxels as perfect little rectangles or cubes, in reality they are blurry beasts that spread their signal into adjoining voxels because of a non-rectangular point-spread function (PSF). The dimensions we assign a voxel are entirely nominal.

With SMS we have a broader spatial problem than just non-cubic PSF. Separation of the simultaneous slices can leave signal in an incorrect position that is quite some distance from where it is supposed to be. It's a longer length scale error than the simple PSF of a voxel. Let's suppose we acquire four 2 mm slices simultaneously, 84 total slices. In one SMS acquisition we will have four slices separated by one quarter of the total slice dimension extent of 168 mm, or about 42 mm (assuming no additional inter-slice gap). Do a quick thought experiment. Imagine that in the first slice there is a very strong activation and nothing in the other three. If there is a large residual spatial error arising from poor SMS separation then we might start seeing this activation projected 4.2, 8.4 or even 12.6 cm from where it should be! And how would we know that the distant activation sites were erroneous?

This slice leakage, as it's usually called in the literature, may be strongest for simultaneously acquired neighbors but may extend throughout the slice dimension, between simultaneously acquired slices that might be quite far apart in anatomical space. And, as the thought experiment illustrates, one might assume that distant leakage would be harder to spot than the conventional cross-talk between successively acquired slices in conventional multislice EPI, or errors arising from the PSF more generally. The PSF can usually be interpreted as a local phenomenon, with errors decreasing monotonically from a voxel. Not so with SMS slice separation, meaning there is more risk of interpreting a false positive remote from the true activation site.

At this point we can recognize that reducing leakage is a noble, perhaps essential, goal. As usual with MRI, however, there's a catch. Reducing leakage using the Split Slice GRAPPA reconstruction may come at the cost of increasing in-plane artifacts. The overall (total) artifact level might be higher, too. I'll go into these issues in some detail below. The goal of this post is to perform a rudimentary assessment of the artifacts and determine the circumstances when Split Slice GRAPPA might be preferred over the conventional Slice GRAPPA reconstruction. For the CMRR sequence this amounts to whether or not to enable the Leak Block option.