Partial Fourier versus GRAPPA for increasing EPI slice coverage

This is the final post in a short series concerning partial Fourier EPI for fMRI. The previous post showed how partial Fourier phase encoding can accelerate the slice acquisition rate for EPI. It is possible, in principle, to omit as much as half the phase encode data, but for practical reasons the omission is generally limited to around 25% before image artifacts - mainly enhanced regional dropout - make the speed gain too costly for fMRI use. Omitting 25% of the phase encode sampling allows a slice rate acceleration of up to about 20%, depending on whether the early or the late echoes are omitted and whether other timing parameters, most notably the TE, are changed in concert.

But what other options do you have for gaining approximately 20% more slices in a fixed TR? A common tactic for reducing the amount of phase-encoded data is to use an in-plane parallel imaging method such as SENSE or GRAPPA. Now, I've written previously about the motion sensitivity of parallel imaging methods for EPI, in particular the motion sensitivity of GRAPPA-EPI, which is the preferred parallel imaging method on a Siemens scanner. (See posts here, here and here.) In short, the requirement to obtain a basis set of spatial information - that is, a map of the receive coil sensitivities for SENSE and a set of so-called auto-calibration scan (ACS) data for GRAPPA - means that any motion that occurs between the basis set and the current volume of (accelerated) EPI data is likely to cause some degree of mismatch that will result in artifacts. Precisely how and where the artifacts will appear, their intensity, etc. will depend on the type of motion that occurs, whether the subject's head returns to the initial location, and so on. Still, it behooves us to check whether parallel imaging might be a better option for accelerating slice coverage than partial Fourier.


Deciding what to compare

Disclaimer: As always with these throwaway comparisons, use what you see here as a starting point for thinking about your options and perhaps determining your own set of pilot experiments. It is not the final word on either partial Fourier or GRAPPA! It is just one worked example.

Okay, so what should we look at? In selecting 6/8ths partial Fourier it appears that we can get about 15-20% more slices for a fixed TR. It turns out that this gain is comparable to using GRAPPA with R=2 acceleration with the same TE. To keep things manageable - a five-way comparison is a sod to illustrate - I am going to drop the low-resolution 64x48 full Fourier EPI that featured in the last post in favor of the R=2 GRAPPA-EPI that we're now interested in. For the sake of this comparison I'm assuming that we have decided to go with either pF-EPI or GRAPPA, but you should note that the 64x48 full Fourier EPI remains an option for you in practice. (Download all the data here to perform for your own comparisons!)

I will retain the original 64x64 full Fourier EPI as our "gold standard" for image quality as well as the two pF-EPI variants, yielding a new four-way comparison: 64x64 full Fourier EPI, 6/8pF(early), 6/8pF(late), and GRAPPA with R=2. Partial Fourier nomenclature is as used previously. All parameters except the specific phase encode sampling schemes were held constant. Data was collected on a Siemens TIM/Trio with 12-channel head coil, TR = 2000 ms, TE = 22 ms, FOV = 224 mm x 224 mm, slice thickness = 3 mm, inter-slice gap = 0.3 mm, echo spacing = 0.5 ms, bandwidth = 2232 Hz/pixel, flip angle = 70 deg. Each EPI was reconstructed as a 64x64 matrix however much actual k-space was acquired. Partial Fourier schemes used zero filling prior to 2D FT. GRAPPA reconstruction was performed on the scanner with the default vendor reconstruction program. (Siemens users, see Note 1.)


Image quality assessment

In this comparison the phase encoding direction is anterior-posterior (A-P), the Siemens default. (See Appendix 1, below, for a similar four-way comparison using P-A phase encoding.) There are 37 slices in TR=2000 ms, which is the maximum number of slices permitted by the full Fourier 64x64 matrix EPI. Here are the images after zooming to crop the uppermost two slices from each data set:

EPI with phase encoding set A-P and all parameters held constant except for the phase encode sampling scheme. Top left: 64x64 full Fourier. Top right: GRAPPA-EPI with R=2 acceleration. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

And here are the same images but zoomed so that we can get a better look at likely problem areas:

EPI with phase encoding set A-P and all parameters held constant except for the phase encode sampling scheme. Top left: 64x64 full Fourier. Top right: GRAPPA-EPI with R=2 acceleration. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

Comparing the pF schemes to the full Fourier EPI first, we see the now familiar regions of enhanced dropout - primarily temporal lobes (and eyes!) for 6/8pF(early), midbrain for 6/8pF(late) - and also the smoother images arising from zero filling the partial Fourier EPIs.

The most immediate difference between the GRAPPA-EPI and the other three data sets is the reduced distortion in the A-P direction. Partial Fourier doesn't alter the amount of distortion whereas GRAPPA reduces distortion by the acceleration factor, R=2 in this case. The distortion is worst where the magnetic susceptibility gradients are worst, so the reduced distortion is most evident in the temporal lobes. Distortion of the frontal lobe signal is also halved but the benefit is less obvious because it appears that there might be additional dropout with the GRAPPA acquisition. Why the dropout should get worse isn't immediately obvious, but we can speculate that it's a reconstruction error arising from a mismatch between the ACS and this undersampled volume. Not a good sign.

It's time to look at the performance of GRAPPA in a time series. Here are the standard deviation images for 50-volume time series:

Standard deviation images for fifty EPI time series acquisitions, with phase encoding set A-P and all parameters held constant except for the phase encode sampling scheme. Top left: 64x64 full Fourier. Top right: GRAPPA-EPI with R=2 acceleration. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

Uh-oh. Clearly, the temporal stability of the GRAPPA data is worse than all the other three schemes. The experienced subject was careful not to move during the ACS - for instance, he swallowed immediately before the start of the scan - and did his best not to move during the time series, too. Yet the frontal lobes in particular exhibit large standard deviations, and there is a pronounced ring around the circumference of the head for all slices. What does this do to the temporal SNR? Let's look:

Temporal SNR images for fifty EPI time series acquisitions, with phase encoding set A-P and all parameters held constant except for the phase encode sampling scheme. Top left: 64x64 full Fourier. Top right: GRAPPA-EPI with R=2 acceleration. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

As we might expect when the standard deviation is high, the tSNR for the GRAPPA scheme is reduced below that for the two partial Fourier schemes as well as the reference 64x64 full Fourier EPI. The price for the speed gain seems to be about half of the tSNR, according to the region-of-interest selected in this throwaway comparison.

It is important to note that the performance of GRAPPA is quite variable. In Appendix 1, below, you will find the same four-way comparison but with the phase encoding direction reversed, to P-A. In those images you'll see that the GRAPPA stability is still the worst of the four, but it isn't quite as bad as in the A-P data above. This is the problem when using GRAPPA: just one head movement - a swallow, say - can have very severe consequences for the overall time series. More on the costs and benefits below.


Going at maximum speed

For the purposes of this post, the motivation for adopting partial Fourier or GRAPPA is to attain more slices in the TR. So let's look at the time series statistics when the TE is reduced as far as possible in order to permit the maximum number of slices in TR = 2000 ms. (Reducing TE to the minimum attainable isn't always what you would want to do for BOLD contrast, but I'm doing it here to get the maximum number of slices.) Except for the TE and the number of slices, all other parameters were left set at the values given previously.

The good news is that GRAPPA with R=2 acceleration and a minimum TE of 14 ms allows a whopping 52 slices in TR = 2000 ms! Mission accomplished, right? Perhaps. If you don't mind giving up that temporal stability. Here is the four-way comparison of standard deviations for fifty-volume time series acquisitions:

Standard deviation images for "maximum performance" acquisitions with phase encoding set A-P. Top left: 64x64 full Fourier. Top right: GRAPPA-EPI with R=2 acceleration. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

It looks like we have a similar motion sensitivity as before. The shorter TE for GRAPPA will enhance the image SNR and this should translate into improved temporal SNR in the absence of motion. We end up seeing a net loss, however, because of the motion sensitivity:

Temporal SNR images for "maximum performance" acquisitions with phase encoding set A-P. Top left: 64x64 full Fourier. Top right: GRAPPA-EPI with R=2 acceleration. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

Note that the region-of-interest in the top-right matrix doesn't precisely match the other three because the high number of slices caused the image display to shift in Osirix. I did my best to get a similar region. Still, it is clear that there is a rather large global penalty in the GRAPPA data compared to the partial Fourier options.

Appendix 2 contains the same four-way comparison but with the phase encoding reversed, to P-A. GRAPPA again performs the worst of the bunch.


Lessons learned

It appears that using GRAPPA with R=2 is quite costly in terms of reduced temporal SNR. In the "maximum performance" test I reduced the TE to the minimum of 14 ms, a situation that probably isn't something that you would do for fMRI. You might reduce the TE to around 20 ms for BOLD.

At a TE of around 20 ms the major apparent benefit of GRAPPA - more slices per TR than for partial Fourier - becomes marginal, yet it comes at the cost of greatly enhanced motion sensitivity. To me, it doesn't seem worth the cost for such a relatively small gain in imaging speed. If the objective is to tease out an additional 20% more slices in TR then it appears that partial Fourier EPI is the better (safer) alternative.

So, what about going even faster? Why stop at R=2 for GRAPPA? It is certainly possible to use R=3 or 4 with large phased-array coils, but at the cost of further enhancement of motion sensitivity. What's more, using in-plane acceleration gets us percentages of speed increase but it doesn't get us factors. What if you wanted to get twice as many slices in a fixed TR, or three times as many? In that case you should probably focus on the slice dimension itself and accelerate it directly, using simultaneous multi-slice (aka multi-band) EPI. That will be the subject of the next post.

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Notes:

1.  On VB17A software, and previously on VB15, the product EPI sequence uses a single ACS for R=2 accelerated GRAPPA EPI. This means that there is a mismatch between the k-space step size for the ACS and the step size - twice as big - for the undersampled EPI of the time series. Such a mismatch leads to reconstruction errors whenever there are appreciable magnetic susceptibility gradients acting to distort the phase encoding. On my scanner we therefore use a tweaked version of ep2d_bold for which the correct R-shot ACS is acquired for R=2. Note, however, that Siemens does correctly acquire 3-shot and 4-shot ACS for R=3 and 4. It's just R=2 that has the potential mismatch. See the introduction section of this arXiv paper for more details.



Appendix 1:

All parameters except the phase encoding fraction are constant: Siemens TIM/Trio, 12-channel head coil, TR = 2000 ms, TE = 22 ms, FOV = 224 mm x 224 mm, slice thickness = 3 mm, inter-slice gap = 0.3 mm, echo spacing = 0.5 ms, bandwidth = 2232 Hz/pixel, flip angle = 70 deg, phase encoding direction = P-A. Each EPI was reconstructed as a 64x64 matrix however much actual k-space was acquired:

EPI with phase encoding set P-A and all parameters held constant except for the phase encode sampling scheme. Top left: 64x64 full Fourier. Top right: GRAPPA-EPI with R=2 acceleration. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

Zoomed to show likely problem regions:

EPI with phase encoding set P-A and all parameters held constant except for the phase encode sampling scheme. Top left: 64x64 full Fourier. Top right: GRAPPA-EPI with R=2 acceleration. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

Standard deviation images for fifty-volume time series acquisitions with P-A phase encoding:

Standard deviation images for fifty EPI time series acquisitions, with phase encoding set P-A and all parameters held constant except for the phase encode sampling scheme. Top left: 64x64 full Fourier. Top right: GRAPPA-EPI with R=2 acceleration. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

Temporal SNR images for fifty-volume time series acquisitions with P-A phase encoding:

Temporal SNR images for fifty EPI time series acquisitions, with phase encoding set P-A and all parameters held constant except for the phase encode sampling scheme. Top left: 64x64 full Fourier. Top right: GRAPPA-EPI with R=2 acceleration. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

Appendix 2:

Standard deviation images for fifty-volume time series acquisitions with P-A phase encoding and "maximum performance" parameters:

Standard deviation images for "maximum performance" acquisitions with phase encoding set P-A. Top left: 64x64 full Fourier. Top right: GRAPPA-EPI with R=2 acceleration. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

Temporal SNR images for fifty-volume time series acquisitions with P-A phase encoding and "maximum performance" parameters:

Temporal SNR images for "maximum performance" acquisitions with phase encoding set P-A. Top left: 64x64 full Fourier. Top right: GRAPPA-EPI with R=2 acceleration. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)