Using GRAPPA for fMRI in the presence of subject motion

I've received a few queries about my opinions on the use of GRAPPA for EPI time series, opinions which have been mentioned in passing in earlier posts. In my user training guide/FAQ are some sections that deal with GRAPPA features and performance, but I didn't include an in-depth illustration of the artifacts or the motion sensitivity. So, to help you make a decision on whether GRAPPA is something you should be using in your fMRI experiments, I'm going to post here a few more images and some movies to highlight the problems that can arise in the presence of significant head motion. I'll focus on R=2 accelerated EPI, but the principles hold for higher acceleration factors as well.

Whether or not you ultimately select GRAPPA for your experiment, it is important to make your determination objectively, taking into account your experimental needs, the benefits of the method, its failure modes and prior studies you can rely on for validation. (See "Beware of physicists bearing gifts!")

** Please note that the following information pertains to the GRAPPA implementation available as product on the Siemens Trio/TIM platform with VB15 software. If you have a different Siemens platform or a different vendor's scanner there may be significant differences in the implementation. **

A brief review of the GRAPPA method

If you don't have even a rudimentary understanding of parallel imaging (PI) generally or the GRAPPA method specifically, I would encourage you to stop reading this post now and go read at least one of these articles: Larkman & Nunes (2007) or Blaimer et al. (2004). Then come back when you're ready to proceed with a speedy review.

The figure below, from the Blaimer review, illustrates the effects of under-sampling the k-space matrix. In the nomenclature of PI, the lower part of the figure shows R=2 acceleration while the top part of the figure shows unaccelerated, full k-space sampling (or R=1 if you want consistency).

From a review article by Blaimer et al., Top Magn Reson Imaging 15, 223-36 (2004)

Having under-sampled k-space by R=2, a method is required to compensate for the missing gradient-encoded spatial information. In GRAPPA, the missing k-space lines are computed via a time domain (i.e. k-space) algorithm using some additional spatial information acquired in a separate step called the auto-calibrating signal (ACS) scans. Don't worry about the specific mathematics involved, it's not essential to understand totally the reconstruction process to follow the rest of this post, or to understand where the motion sensitivities arise. The reconstruction process is illustrated in the figure below:

From the original GRAPPA article by Griswold et al., Magn Reson Med 47, 1202-10 (2002).

Once the missing k-space lines have been synthesized and merged with the acquired k-space lines, the final EPIs can be produced with a 2D Fourier transformation.

For time series EPI acquisitions, the ACS lines are usually acquired at the start of the time series, after the dummy scans and before the first (under-sampled) volume of EPI. For R=2 accelerated EPI an R-fold set of interleaved ACS lines is needed, where each ACS segment has the same delta-k spacing as the under-sampled EPIs in the time series, so that the distortion level is matched between the ACS scans and the under-sampled EPI volumes. (See Note 1.)

Time series acquisitions

For fMRI, then, the temporal acquisition proceeds as follows (for R=2):

DS1 -- DS2 -- ACS1 -- ACS2 -- Vol(1) -- Vol(2) -- Vol(3) -- Vol(4) ...... Vol(N-1) -- Vol(N)

where DSq stands for a dummy scan, used to establish a T1 steady state, ACSr are the R-fold interleaved ACS scans (which for R=2 would comprise the odd and then the even k-space lines from the full phase-encoded k-space dimension), and Vol(s) are the time series under-sampled EPI volumes that you consider to be "your data." (Vol(1) would be the first event to put out a TTL pulse.) The N under-sampled EPI volumes typically use either the odd or the even k-space lines consistently throughout the time series. (See Note 2.)

GRAPPA's motion sensitivities

In essence there are two components to GRAPPA's motion sensitivity. The first is the effect of motion during the ACS scans themselves. As we will see below, movement during the ACS is a particularly bad thing because it corrupts the spatial information that isn't being encoded directly in k-space, thereby causing spatial artifacts that will carry through the entire time series.

The second motion sensitivity arises because of movement subsequent to the ACS scans. For convenience we can consider the ACS scans as a form of "reference scan" and, as with any reference scan, whether it's a field map to correct distortion, a ghost correction scheme or, as here, a method to compute some spatial dependencies, the method is reliant on a good match between the reference condition and the situation being referred to. In other words, movement subsequent to the ACS scans will cause a mismatch between the reference data and the current (under-sampled) volume of k-space. This will also cause spatial artifacts, though the artifacts will arise only while the mismatch condition persists; if the subject returns to the original position that existed during the ACS, the artifacts will be removed.


The effects of motion on data from a real subject

The data I'm about to show were obtained on a normal volunteer as part of a routine study. (Siemens Trio/TIM using a 32-channel receive coil, EPI with GRAPPA R=2, in-plane res=2.1x2.1 mm, slice thickness=3 mm, TR/TE=2200/26 ms.)

Each of the three time series data sets you'll see were part of a single session. I picked out the cleanest run (lowest subject movement) as well as two other runs, one where it was clear the subject hadn't moved during the ACS scans but had moved noticeably thereafter, and another run where the subject had moved during the ACS and moved quite a bit later in the run, too. As always with these things, keep in mind this is a case study; I'm not about to draw detailed quantitative conclusions, I'm simply going to illustrate what can happen when a subject moves.

Contrasting images to reveal artifacts

Let's start by doing something that can be misleading from a data quality perspective: windowing the images so that they reveal good anatomical contrast. Here are three sample volumes from the three data sets I mentioned (click image to enlarge):

Hard to see much difference, isn't it? Windowing for anatomical contrast can make it hard or impossible to assess artifacts. Now look at the same three images with the background intensity increased:

There is clearly something going on in the "noise" when movement happens during the ACS scans. But these static views, even of the background windowed high, don't reveal the true nature of the artifacts. Let's view each of these three data sets as cine loops, first with the contrast set to reveal anatomy and then with the background intensity brought up:

 

No significant subject motion

Significant motion during and after the ACS scans

Significant motion after ACS scans

No significant subject motion - background contrasted

Significant motion during and after the ACS scans - background contrasted

Significant motion after ACS scans - background contrasted

When head movement happens during the interleaved ACS scans, the "reference" spatial information becomes corrupted such that there are artifacts visible in the background during the entire time series. (Artifacts are also present during the entire time series in the brain signal, too, but it's harder to notice by eye.) Understanding why this should be the case is straightforward: the ACS set is being used to synthesize the omitted k-space lines from the under-sampled EPIs in the time series. If the two halves (for R=2) of interleaved ACS data are mismatched due to motion then the spatial solution will be corrupted; it will start out corrupted and remain corrupted for all time. [An aside: If R and/or TR is high, consider the effects of motion during the ACS especially carefully. Diffusion imaging with GRAPPA is often performed with high R and long TR. See Note 3.]

If the ACS are acquired relatively uncontaminated by motion then the situation improves considerably. (See Note 4.) The remaining concern is the mismatch between the (uncontaminated) ACS and the current under-sampled k-space volume in an ongoing time series acquisition. When this situation occurs the current EPI volume will exhibit artifacts, but these artifacts will disappear in subsequent EPI volumes once the head returns to its original position, matched with the location that arose during the ACS. Of course, there is one form of motion for which a mismatch would persist: if the subject's head moves to a new position and remains in that position, a mismatched condition would persist (and spatial artifacts would result) for as long as the new position is maintained. In a way, it's like saying that the time series is relatively robust to acute (or short-lived) head motion but is susceptible to chronic (or long-lived) head motion. That's not entirely accurate but it's a useful conceptual picture.

Unsurprisingly it is the frontal and temporal lobes as well as deep sub-cortical regions, where the magnetic field is most heterogeneous, that exhibit the largest spatial artifacts during GRAPPA-EPI time series. Relatively small amounts of motion can have disproportionately large corrupting effects on the ACS set as well as causing mismatches from the ACS to the under-sampled EPIs. Which is not to say that the occipital and parietal cortices are immune to these reconstruction errors, just that it will generally take less head movement to render useless an inferior axial slice than a coronal slice through the occipital pole!


The effects of motion on TSNR

Viewing time series data as movies highlights the degradation of image quality but it doesn't tell us much about the consequences for fMRI power. We can assess the effects of motion on each image series above using the TSNR. But before we proceed, we should remember that the actual movement contaminating each time series is different so we need to be careful about making too many specific deductions from this particular comparison; again, it's designed to be illustrative of the problem.

To facilitate comparisons I've put the TSNR from the series with the lowest head movement between the TSNR images for the two motion-contaminated series. The three TSNR images are shown with a constant gray scale setting:

TSNR map: subject movement during and after interleaved ACS scans.

TSNR map: low movement throughout the acquisition.

TSNR map: subject movement after ACS scans.

As we already saw in the movies, head motion during interleaved ACS scans is especially damaging to the inferior slices. Also now clearly visible are regional reductions of TSNR in higher slices, effects that weren't obvious in the movie data. Moreover, the effects are quite heterogeneous spatially; notice, for example, the left-right shadowing that is visible in the fourth row down of the top figure.

Motion following the ACS tends to reduce the TSNR globally. You should just be able to make out that the brightness is reduced overall for the bottom image compared to the central (low motion) image. Furthermore, motion following the ACS causes edges to become darker in the TSNR map; compare the bottom to the middle TSNR map and it's quite clear there is more gray/white anatomical contrast in the bottom image, indicating localized regions of TSNR attenuation.


Considerations and recommendations

At the risk of sounding like a broken record, it's important to remember that this is data from a single subject. It is, however, a real result that was obtained from a typical volunteer for a research study. Clearly, it calls into question the robustness of GRAPPA for fMRI.

Now, please also note that I'm not recommending that GRAPPA never be used for fMRI! I'm simply pointing out the motion sensitivity. There haven't yet been many studies that have investigated GRAPPA versus unaccelerated EPI for fMRI, and fewer still that have looked specifically at motion sensitivity. (To date I've found precisely none.) Lutke et al. (2006) showed that there was 15-20% reduced sensitivity at 2.9 T using GRAPPA-EPI for a visual fMRI experiment. But they attributed this reduction of sensitivity to the sqrt(R) reduction of SNR for individual EPIs, as well as the reduced range of echo times covered in the shortened echo train. There was no mention of head motion, leaving a couple of possibilities: either head motion actually played a role in the sensitivity attenuation (instead of or in addition to the sqrt(R) reduction of single image SNR and the duration of the echo train), or their interpretation was correct and motion could actually exacerbate the decreased sensitivity in subjects who move more than those in their study. Either way, there's a cost.

Many physics papers on parallel imaging focus on the artifacts in static (single) images, or on the relative magnitudes of thermal and physiologic noise for time series (fMRI) applications. For example, a recent paper by Triantafyllou et al. (2011) investigated the effects of thermal and physiologic noise regimes on fMRI data collected with 12-channel and 32-channel coils; GRAPPA was used in some measurements to provide higher spatial resolution. While consideration of these two regimes for coil and pulse sequence selection is of course very important, they are not the only considerations. In the realm of "everyday" fMRI, especially for whole brain applications where regions of interest fall within frontal and temporal cortices or sub-cortical structures, or for certain populations where movement is expected to be a challenge (e.g. pediatric fMRI), motion sensitivity is critically important, too. Stability and robustness are two watchwords for general-use, whole brain fMRI.

Processing implications

One tactic employed in fMRI processing is to eliminate volumes from the time series when motion (or artifacts) exceeds some threshold. That could be done in GRAPPA-EPI time series, too, with one important caveat: if, as a result of subject movement, the head ends up in a different position than during the ACS, a mismatch results and artifacts will likely increase for a long time. Removing the "bum" volumes might not be applicable.

Compare this situation with the use of conventional, unaccelerated EPI. With single-shot EPI, a new head position may result in slightly higher ghosting and dropout due to a degradation of the magnetic field (the shim) across the brain, but in general the data after the movement would be qualitatively similar to before the movement; the persistent effects of the new position might be sufficiently benign for a realignment algorithm to salvage the time series.

Deciding whether or not to use GRAPPA

You should first determine whether you need GRAPPA, e.g. to achieve a particular spatial or temporal resolution. Next, consider alternative schemes that might permit the same specifications without the motion sensitivity, e.g. partial Fourier. (See my user training guide/FAQ for a brief discussion on partial Fourier versus GRAPPA.) Finally, establish a pilot experiment wherein you compare the performance of your options, ideally using a simple (robust) functional experiment or, failing that possibility, using a TSNR comparison. In your pilot tests be sure to use subjects who represent all of the characteristics of your target experimental and control populations, especially their propensity to move during the scan session.

Anything less than this procedure could see you conducting a diagnostic post mortem (oxymoron?) on a pile of experimental data at some future point, with you stressing to explain many more false positives or false negatives than you were expecting to get. Much better to know what's likely to happen before you start data acquisition with a vengeance.

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Notes:

(1)  By default the Siemens EPI sequences, ep2d_bold and ep2d_pace, use a single ACS scan for R=2 GRAPPA. In this instance, the delta-k of the ACS scan is half that of the under-sampled EPI, causing a mismatch of distortions between the ACS and the subsequent EPI time series. In regions of high susceptibility this mismatch usually leads to image domain artifacts. However, Siemens uses interleaved R-fold ACS scans (with delta-k matched to the under-sampled delta-k of the EPI volumes) for R=3 and R=4, eliminating the distortion mismatch. BIC users, please note (as described in the user training guide/FAQ) that our local default sequence, ep2d_neuro, uses interleaved R=2 with matched delta-k.

(2)  It is possible to alternate odd and even k-space lines through the time series and use the preceding pair of odd/even k-space lines as the ACS and generate the missing k-space on-the-fly. This is the temporal GRAPPA (TGRAPPA) method. But since it isn't presently available on the Siemens Trio I'll say no more about it here.

(3)  If you are using GRAPPA for diffusion imaging, especially high R, then you probably have a very significant motion risk! If you use R=4 and a TR of 7500 ms then you have thirty seconds - half a minute! - of ACS acquisitions, during which it is imperative that the subject remains very still. I suggest that you ask the subject to swallow just before the EPI noise starts, then not swallow again until a minute into the acquisition (ask the subject to count silently in his head). Also remind the subject not to move his hands or feet during that vital first minute; any movement of the body whatsoever will translate into head motion via the spine.

(4)  The Siemens default of using a single ACS scan for R=2 acceleration, as mentioned in Note 1, circumvents the problem of a set of motion-contaminated ACS, but doesn't alleviate the mismatch problem between ACS and under-sampled EPIs. Furthermore, there are additional time-invariant artifacts arising from the different distortion properties of the single-shot ACS (delta-k phase encode increment) and under-sampled EPIs (2 x delta-k phase encode increment).


References:

M Blaimer, F Breuer, M Mueller, RM Heidemann, MA Griswold & PM Jacob. "SMASH, SENSE, PILS, GRAPPA: How to choose the optimal method." Top. Magn. Reson. Imaging 15, 223-36 (2004).

MA Griswold, PM Jakob, RM Heidemann, M Nittka, V Jellus, J Wang, B Kiefer & A Haase. "Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA)." Magn. Reson. Med. 47, 1202-10 (2002).

H Lutke, K-D Merboldt & J Frahm. "The cost of parallel imaging in functional MRI of the human brain." Magn. Reson. Imaging 24, 1-5 (2006).

DJ Larkman & RG Nunez. "Parallel magnetic resonance imaging." Phys. Med. Biol. 52, R15-55 (2007).

C Triantafyllou, JR Polimeni & LL Wald. "Physiological noise and signal-to-noise ratio in fMRI with multi-channel array coils." NeuroImage 55, 597-606 (2011).