Using partial Fourier EPI for fMRI

Back in August I did a post on the experimental consequences of using partial Fourier for EPI. (An earlier post, PFUFA Part Fourteen introduces partial Fourier EPI.) The main point of that post was to demonstrate how, with all other parameters fixed, there are two principal effects on an EPI obtained with partial Fourier (pF) compared to using full phase encoding: global image smoothing, and regionally enhanced signal dropout. (See Note 1.)

In this post I want to look a little more closely at how pF-EPI works in practice, on a brain, with fMRI as the intended application, and to consider what other parameter options we have once we select pF over full k-space. I'll do two sets of comparisons. In the first comparison all parameters except the phase encoding k-space fraction will be fixed so that we can again consider the first stage consequences of using pF. In the second comparison each pF-EPI scheme will be optimized in a "maximum performance" test. The former is an apples to apples comparison, with essentially one variable changing at a time, whereas the latter is how you would ordinarily want to consider the pF options available to you.


Why might we want to consider partial Fourier EPI for fMRI anyway?

If we assume a typical in-plane matrix of 64 x 64 pixels, an echo spacing (the time for each phase-encoded gradient echo in the train, as explained in PFUFA Part Twelve) of 0.5 ms and a TE of 30 ms for BOLD contrast then it takes approximately 61 ms to acquire each EPI slice. (See Note 2 for the details.) The immediate consequence should be obvious: at 61 ms per slice we will be limited to 32 slices in a TR of 2000 ms. If the slice thickness is 3 mm then the total brain coverage in the slice dimension will be ~106 mm, assuming a 10% nominal inter-slice gap (i.e. 32 x 3.3 mm slices). With axial slices we aren't going to be able to cover the entire adult brain. We will have to omit either the top of parietal lobes or the bottom of the temporal lobes, midbrain, OFC and cerebellum. Judicious tilting might be able to capture all of the regions of primary interest to you, but we either need to reduce the time taken per slice or increase the TR to cover the entire brain.

Partial Fourier is one way to reduce the time spent acquiring each EPI slice. There are two basic ways to approach it: eliminate either the early echoes or the late echoes in the echo train, as described at the end of PFUFA: Part Fourteen. Eliminating the early echoes doesn't, by itself, save any time at all. Only if the TE is reduced in concert is there any time saving. But omitting the late echoes will mean that we complete the data acquisition for the current slice earlier than we would for full Fourier sampling, hence there is some intrinsic speed benefit. I'll come back to the time savings and their consequences later on. Let's first look at what happens when we enable partial Fourier without changing anything else.


Image quality assessment for pF-EPI

Our gold standard will be full k-space EPI with a 64 x 64 matrix. For this post I am only going to use the 6/8ths partial Fourier option, meaning that one quarter (2/8ths) of the phase encoding k-space will be omitted from the acquisition. Thus, we will have acquired 48 of 64 phase encode lines and will simply zero fill the missing lines prior to 2D FT of a (synthetic) 64 x 64 matrix. Again, see PFUFA: Part Fourteen for an introduction to partial Fourier EPI if this vernacular leaves you cold.

As we saw previously, one effect of acquiring a partial k-space is image smoothing. Which immediately begs the question: why bother using pF at all, and why not just reduce the matrix size (symmetrically) instead? So, one comparison we want to make, specifically to evaluate image smoothing, is the acquisition of a full Fourier 64 x 48 matrix lower resolution EPI. In this case we acquire k-space symmetrically in the phase encoding dimension; we're leaving off 1/8th of the early and 1/8th of the late echoes compared to the full 64 x 64 matrix acquisition.

As we've seen previously, there are two options for 6/8ths pF-EPI. We can omit the early or the late phase encoded echoes, as illustrated in this figure (see Note 3):

I shall try always to refer consistently to the former as pF(early) and the latter as pF(late), but in some of the images you may notice that in practice I tend to refer to the former as simply pF while the latter is pFrev, for "reversed" pF. So if you see "rev" or "reversed" in any data just think "late" instead.

I also want to emphasize here that early and late (or reversed) are designations made relative to the phase encoding direction that's being used. For axial slices the Siemens default is to use anterior-posterior (A-P) phase encoding. (I've noted previously that GE uses P-A by default.) If the imaging gradients were perfect and there were no magnetic susceptibility gradients across the head then omitting the late echoes for A-P phase encoding would be tantamount to omitting the early echoes for P-A phase encoding. But we don't have a perfect system and we shall therefore want to do a separate set of comparisons for P-A phase encoding, distinct from those for A-P. The imperfections? Mostly, it's those pesky magnetic susceptibility gradients that cause distortion and dropout. The phase encoding dimension dictates the direction of distortion and you will almost certainly have a preference. Also, the local regions that exhibit enhanced signal dropout will differ with phase encoding direction.

Disclaimer:  Do not, under any circumstances, treat these results as a validation of either of the pF variants!!! All I offer is a starting point for you to ponder your alternatives. Unless and until someone provides a validation of pF you should remain skeptical. At a minimum, you would want to conduct a thorough pilot experiment before selecting a pF variant for a full-blown fMRI experiment.


Disclaimer over, here is our first set of comparisons, in this case using A-P phase encoding:

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: 64x48 full Fourier. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

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. Each EPI was reconstructed as a 64x64 matrix however much actual k-space was acquired, and any omitted portions were zero-filled prior to 2D FT.

Let's zoom in a bit to get a better look at those slices that typically exhibit regions of dropout:

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: 64x48 full Fourier. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

Additional dropout is evident for both of the pF options as well as for the low resolution full k-space EPI, compared to the 64 x 64 reference images. Temporal lobes and midbrain are affected most, consistent with the brain data shown in the last post on pF-EPI. (See Note 4 for more information on the effects of resolution on dropout.)

What about image smoothing? It's hard to see on brains, but there are a couple of slices on which you can, if you have a good eye, just about discern the different edge detail:

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: 64x48 full Fourier. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

We aren't exclusively interested in the appearance of EPI or the brightness of a particular region when doing fMRI, however. We are using time series acquisitions so we need to consider motion sensitivity and the signal stability over time. So let's shift to assessing temporal images.

We can make a reasonable assessment of any differential motion sensitivity by looking at standard deviation images. Here are the results for the A-P phase encoding data from above, for fifty-volume time series acquisitions (100 secs of data) in each case:

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: 64x48 full Fourier. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

As we would expect for single shot EPI acquisitions, the motion sensitivity is fairly consistent. Using partial Fourier doesn't change the fact that the acquisition is still a single echo train acquired after a single slice-selective RF pulse. Thus, no one scheme exhibits vastly different variance than the others. There will probably be localized differences, however. In the case of partial Fourier, signals might be on the very edge of the k-space "cliff" and they might be one or other side of that drop with quite small subject movement. But determining relative performance requires regions-of-interest - something that will vary depending on your application - or some way to collapse the signal stability for the whole brain down to a single value, a process that might easily obscure subtle effects that are actually important. So, let's just accept that the motion sensitivity is operationally similar, and move on.

Of even more relevance to fMRI is the temporal SNR (tSNR), a handy proxy for signal level as well as stability. Here are voxelwise tSNR maps of the same fifty-volume time series as used in the standard deviation images above:

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: 64x48 full Fourier. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

Now we can see the full effects of image smoothing. The tSNR is higher for 64x48 full Fourier and both partial Fourier options compared to the 64x64 full Fourier baseline image. But we have netted "extra" SNR purely by smoothing the image, an effect we could get in post processing with a smoothing function applied to the 64x64 full Fourier image! Is there a difference between the 64x48 full Fourier and either of the pF options? In regions with good signal, not really. But where the sampling scheme enhances signal dropout compared to 64x64 full Fourier then we see the same holes in the tSNR images as we saw in the raw EPI above. What's gone is gone.

That about wraps up the quick and dirty visual assessment of the pF-EPI options using A-P phase encoding. There is another entire four-way comparison on offer, however: the same four sampling schemes but applied with P-A phase encoding! I've put all the data for P-A phase encoding into Appendix 1. Here, let's stick with A-P phase encoding but turn our attention to some comparisons when the timing parameters aren't held constant, which is far more realistic.


How fast can we make pF-EPI go?

Let's assume we have valid reasons for not wanting to increase TR beyond 2000 ms, and let's further assume that the gradients are being driven as fast as they can go. (In all of the data shown in this post the echo spacing is fixed at 0.5 ms.) We need a way to save some time if we are to acquire more slices in the specified TR. Partial Fourier is one option for saving time per slice.

By setting the parameters for "maximum performance" - meaning the use of minimum TE and as many slices as we can fit in TR=2000 ms - it turns out that we get 43 slices for the two pF options as well as for the 64x48 low-res option, compared to 37 slices for the 64x64 full k-space standard. But in achieving the 43 slices, only 6/8pF(late) uses the same TE=22 ms as the 64x64 standard. For pF(early) the TE is reduced to the minimum value of 14 ms while for 64x48 low-res the TE is reduced to 18 ms. Using longer than the minimum TE in either case results in fewer than 43 slices in TR=2000 ms.

For space considerations, and to allow you to make better comparisons on your own screens, I've put large matrix figures for each of the four options (all using A-P phase encoding) in Appendix 2. I'll note in passing that these images show the same effects of smoothing and regional dropout as the constant parameter comparisons above, and move on.

With the "maximum performance" parameter settings the motion sensitivity remains quite similar to the prior comparisons. This is as we should expect for single shot EPI; minor differences in TE won't have a large effect. Thus, the standard deviation images have comparable artifact levels for edges (due to motion), physiologic fluctuations and for N/2 ghosts:

Standard deviation images for "maximum performance" acquisitions with phase encoding set A-P.  Top left: 64x64 full Fourier. Top right: 64x48 full Fourier. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

What about tSNR over a fifty volume time series?

Temporal SNR images for "maximum performance" acquisitions with phase encoding set A-P.  Top left: 64x64 full Fourier. Top right: 64x48 full Fourier. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

As with the fixed parameter comparison, the effects of smoothing - enhanced tSNR - on the 64x48 images is especially noticeable compared to the 64x64 case. The tSNR is higher still for the 6/8pF(early) case, a combination of image smoothing plus the use of a shorter TE of 14 ms. The tSNR for 6/8pF(late) is comparable to that for 64x64 full Fourier, however. But this is only part of the story, which is why I'm avoiding quantitative comparisons for any one region. Let's consider dropout. We can see that dropout of midbrain signal is higher for 6/8pF(late) than it is for any of the other three options. Yet signal in temporal lobes is well preserved for 6/8pF(late), comparable to that in the full Fourier 64x64 images. Signal for temporal lobes in both the 64x48 full and 6/8pF(early) images show more dropout. Thus, if you were interested in auditory fMRI you might want to consider 64x64 full or 6/8pF(late), but if you're doing, say, hypothalamus then either 64x48 full or 6/8pF(early) look to be better candidates.

A comparison for "maximum performance" parameters but with P-A phase encoding is given in the appendices. The individual image mosaics are in Appendix 3 while the standard deviation and tSNR images for fifty-volume time series are in Appendix 4.


Summary

In the previous post on partial Fourier EPI you saw how partial Fourier affects a single image. In this post, the analysis was expanded to consider the effects on a time series and also different parameter combinations for time series acquisitions. What are the broader lessons to take away so far?

• Partial Fourier leads to image smoothing. It's important to note that any apparent gain in SNR (for otherwise fixed parameters) is due to the smoothing.
• Partial Fourier usually contributes to enhanced signal dropout, especially in the "problem" brain regions of midbrain, frontal lobes and temporal lobes where magnetic susceptibility gradients are worst. You may be able to select which regions exhibit worse dropout by judicious combination of phase encode direction and early or late echo omission.
• Omitting the early echoes from the gradient echo train can benefit EPI by permitting a shorter TE. If we use pF(early) and we don't shorten the TE then all we're really doing is giving up SNR, especially for the regions mentioned in the previous point. (Remember that there is still considerable BOLD (T2*) weighting during the EPI echo train. BOLD contrast isn't entirely dependent on the TE!)
• Omitting the late echoes from the gradient echo train doesn't change the minimum TE but it does permit faster acquisition of slices, i.e. more slices in TR.
• Partial Fourier doesn't make EPI more motion-sensitive. Strictly speaking, the image contrast does impact motion sensitivity and motion correction a little bit, but these factors are affected by many other parameters, too, such as the excitation flip angle.

To finish up, here is a little general guidance when considering partial Fourier EPI:

• Consider what you want to do with TE whenever you are assessing partial Fourier as an option.
• If you omit early echoes then you'll almost certainly want to reduce TE as well.
• If reduced dropout is your focus then you may want a reduced TE for its own sake, and perhaps thinner slices (see two points down).
• If you omit late echoes then the assumption is that you're aiming for more slices in TR.
• Even if you are happy with your slice coverage sans pF, using pF may permit a greater number of thinner slices for the same total coverage in the slice dimension. But you would have to determine whether there is net benefit from thinner slices versus the enhanced regional dropout mentioned already.
• Regarding regional dropout, you may have a degree of choice as to which signals are sacrificed in setting early or late echo omission by setting the phase encode gradient polarity, e.g. P-A instead of A-P. But there is a concomitant effect on distortion direction, too.

The next post in this series will consider partial Fourier EPI compared to alternative "go faster" options, in particular the use of GRAPPA. And then we'll shift focus to simultaneous multislice (SMS), aka multiband (MB) EPI.

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Notes:

1.  In textbooks you will usually encounter a description of partial Fourier phase encoding that involves the decrease of image SNR because of the reduced signal averaging compared to a fully sampled k-space plane. Strictly speaking, it will be accurate. In practice, however, a loss of SNR with pF doesn't manifest in EPI the way the textbooks describe it. Instead, we tend to fnd an apparent increase of image SNR across most of the EPI, arising from the smoothing imposed by the 'zero filling' filter effect. Thus, a higher apparent SNR resulting from pF isn't a "real" SNR gain but comes from smoothing. You could get the same - or better - SNR from taking a fully sampled EPI and applying a smoothing function in post-processing. We do see decreased SNR but it tends to be regional. Signals from some brain areas 'fall off' the sampled k-space plane due to magnetic susceptibility gradients. Keep these points in mind when comparing the different SNR levels observed in the comparisons that follow.

2.  A real EPI pulse sequence was considered in PFUFA: Part Thirteen. In addition to sampling of the k-space plane with the repeated gradient echoes, there are also temporal overheads for each slice: fat suppression, slice selection, and a short crusher gradient at the end of each slice that eliminates any residual signal prior to the next slice (hopefully). For simplicity, let's assume that it takes a total of 15 ms to do a fat suppression pulse, the first half of a slice selection (the second half being accounted for within TE), and a short crusher gradient after each slice is acquired. This is the temporal overhead per slice. Next we need to determine the time taken to sample the 2D k-space plane.
         For a 64 x 64 matrix EPI with 0.5 ms echo spacing it takes 32 x 0.5 ms = 16 ms to reach the center of k-space, then a further 16 ms to reach the end of the in-plane information. The TE defines the center of k-space, however, so the mid-point of the 64 echoes has to be "parked" at TE. Thus, the first 32 echoes, taking 16 ms, can be acquired within the 30 ms allowed for TE. The latter 32 echoes take a further 16 ms after TE to acquire. Thus, the total time per slice is  TE + 16 ms + 15 ms (overhead) = 61 ms to acquire a single 2D plane. There may be small variations but this is a pretty good estimate.

3.  Siemens users, I'm afraid that you can only neglect the early echoes in the product EPI sequences such as ep2d_bold and ep2d_pace. I'm working on getting an early/late option into a subsequent product sequence, and/or making available a research version of ep2d_bold. Big, bureaucratic subject for another day. Right now the question is whether there's any benefit to having the early/late option at all!

4.  There is a general principle at work here: higher resolution for EPI - whether in-plane or thinner slices or both - will tend to reduce the extent of magnetic susceptibility gradients across a voxel and thus tend to reduce the dephasing causing signal loss. It's the same principle that was demonstrated for the slice thickness in the "Signal dropout" section of PFUFA: Part Twelve, but we can extend it to 3D. Now, there's no free lunch. In exchange for reducing the dephasing across a (smaller) voxel we lose the SNR on a volumetric basis; voxels with 2 mm sides produce base SNR that is less than one third that of voxels with 3 mm sides. And because we have smaller voxels we now have a potential brain coverage issue, especially in the slice dimension. Still, aiming for smaller voxels is one of the tactics for reducing dropout in EPI.


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: 64x48 full Fourier. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

Again, we can zoom in to assess 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: 64x48 full Fourier. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

And check on smoothing:

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: 64x48 full Fourier. 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: 64x48 full Fourier. 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: 64x48 full Fourier. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)

Appendix 2:

High resolution versions of the four "maximum performance" acquisitions with A-P phase encoding:

64x64 full Fourier, A-P phase encoding, 37 slices in TR=2000 ms, TE = 22 ms.

64x48 full Fourier, A-P phase encoding, 43 slices in TR=2000 ms, TE = 18 ms.

6/8pF(early), A-P phase encoding, 43 slices in TR=2000 ms, TE = 14 ms.

6/8pF(late), A-P phase encoding, 43 slices in TR=2000 ms, TE = 22 ms.

Appendix 3:

High resolution versions of the four "maximum performance" acquisitions with P-A phase encoding:

64x64 full Fourier, P-A phase encoding, 37 slices in TR=2000 ms, TE = 22 ms.

64x48 full Fourier, P-A phase encoding, 43 slices in TR=2000 ms, TE = 18 ms.

6/8pF(early), P-A phase encoding, 43 slices in TR=2000 ms, TE = 14 ms.

6/8pF(late), P-A phase encoding, 43 slices in TR=2000 ms, TE = 22 ms.

Appendix 4:

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: 64x48 full Fourier. 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: 64x48 full Fourier. Bottom left: 6/8pF(early). Bottom right: 6/8pF(late). (Click image to enlarge.)