PFUFA Part Fourteen introduced the idea of acquiring partial k-space and explained how the method, hereafter referred to as partial Fourier (pF), is typically used for EPI acquisitions. At this point it is useful to look at some example data and to begin to assess the options for using pF-EPI for experiments.
The first consequence of using pF is image smoothing. It arises because we've acquired all of the low spatial frequency information twice - on both halves of k-space - but only half of some of the high spatial frequency information. We've then zero-filled that part of k-space that was omitted. This has the immediate effect of degrading the signal-to-noise ratio (SNR) for the high spatial frequencies that reside in the omitted portion of k-space. (PFUFA Part Eleven dealt with where different spatial frequencies are to be found in k-space.) Thus, the final image has less detail and is smoother than it would have been had we acquired the full k-space matrix, and because of the smoothing the final image SNR tends to be higher for pF-EPI than for the full k-space variant.
It was surprising to me that pF-EPI has higher SNR - due to smoothing - than full Fourier EPI in spite of the reduced data sampling in the acquisition. Conventional wisdom, which is technically correct, states that acquiring less data will degrade SNR. To understand this conundrum, we can think of pF as being like a square filter applied asymmetrically to the phase encoding dimension of an EPI obtained from a complete k-space acquisition. Indeed, as we start to evaluate the costs and benefits of pF for EPI we should probably be thinking about a minimum of a three-way comparison. Firstly, we obviously want to compare our pF-EPI to the full k-space alternative having the same nominal resolution. But we should also consider whether there is any advantage over a lower resolution EPI with full k-space coverage, too. Why? Because this lower resolution version is, in effect, what you get when partial Fourier is applied symmetrically, i.e. when the high spatial frequencies are omitted from both halves of the phase encoding dimension!
Let's do our first assessment of pF on a phantom. There are four images of interest: the full k-space image, two versions of pF - omitting the early or the late echoes from the echo train - and, for the sake of quantifying the amount of smoothing, a lower resolution full k-space image which is tantamount to omitting both the early and late echoes. (See Note 1.) From this point on I'm going to refer to omission of the early and late echo variants as pF(early)-EPI and pF(late)-EPI, respectively.
I'm afraid it's not immediately clear, but if you look carefully you should be able to see that there are small features - a group of little dots in the middle of the central circle, for example - that are better resolved in the 64x64 full Fourier image than in either of the partial Fourier variants. The 64x48 matrix image is smoothest of all, as we would expect. It's also interesting to note that (Gibbs) ringing is prominent in the 64x64 matrix but much less so in the other three images. This prominence is another consequence of improved spatial resolution: ringing is always present to some extent because our pixels are, strictly speaking, sinc-shaped rather than square. Hard edges, as in this phantom, tend to exhibit the strongest ringing, and the higher the resolution the better the ringing is defined. (There's a review of ringing in this post.)
In fMRI we are interested in temporal stability, of course, so let's take a look at how partial Fourier affects temporal SNR (TSNR) when all other parameters (including TE) are held constant:
The TSNR for the regions of interest in the above figure are as follows:
Top left Full 64x64 TSNR = 343
Top right Full 64x48 TSNR = 437
Bottom left 6/8ths pF(early) TSNR = 435
Bottom right 6/8ths pF(late) TSNR = 425
(Note: this is a throwaway comparison, for the purposes of illustration only! Please don't take the numbers you see here as absolutes, I am simply showing the effects of smoothing via SNR and TSNR because it may be difficult to see the smoothing on the limited details in these phantom images.)
The low resolution image (64x48) has higher TSNR than the higher resolution image (64x64 full k-space). We should expect a boost in SNR (and hence TSNR in a stationary object) from 343 to (64/48 x 343) = 457 because of the difference in voxel size. The observed TSNR of 437 isn't too far off.
Where things get slightly more interesting is for the pF-EPI variants. Conventional wisdom states that using partial Fourier will degrade the SNR in an image because less data is being recorded for an image that has the same nominal spatial resolution. For pF-EPI, however, the effect of smoothing (that is, the broadened point-spread function for the pixels) outweighs the signal-reducing effect of acquiring less data. Indeed, the observed TSNR is very close to that for the 64x48 full Fourier acquisition, indicating that the smoothing function is pronounced.
What about differences between the early and late echo variants of pF-EPI? Omitting the early echoes seems to boost TSNR very slightly more than omitting the late echoes, which is counter-intuitive because the early echoes will almost certainly have higher signal than the late echoes. Whether the difference in TSNR significant I won't get into because the difference is quite small and in other ROIs (not shown) the TSNR is almost identical. Besides, as you'll see below, there are other differences that might subjugate any smoothing differences. So, what's important at this juncture is that we recognize that the use of partial Fourier - omitting either the early or the late echoes - generates considerable image smoothing for EPI reconstructed with zero filling of the missing k-space.
Before we leave the smoothing issue, let's take a quick look at the effects on brain data since that's probably your interest. (My apologies, I didn't acquire the 64x48 full Fourier option from the brain. I'll do so for the next post, when I consider different pF-EPI schemes for fMRI.) Here's how 64x64 matrix full Fourier EPI compares to early and late 6/8ths pF-EPI variants:
|Left: Full Fourier EPI acquired and processed as a 64x64 matrix. Center: 6/8ths pF(early)-EPI reconstructed to a 64x64 matrix with zero filling. Right: 6/8ths pF(late)-EPI reconstructed to a 64x64 matrix with zero filling. (Click picture to enlarge.)|
If you have a good eye you may be able to see that the full Fourier acquisition, on the left, has finer detail than either of the pF-EPI options. I haven't quantified the SNR because it is highly region-dependent. (I cover the TSNR for these three acquisitions below.) On the basis of the phantom data above, however, we should expect the SNR to be increased for the pF variants entirely due to the smoothing effect. Whether this smoothing is acceptable or not for fMRI will be covered in the next post. Before we can make that determination we need to consider something else.
Not all brain regions will see increased SNR because of smoothing. Some regions will see a degradation of SNR as a result of enhanced dropout. The origin of this effect was explained in PFUFA Part Fourteen. It is a consequence of the signals "falling off the edge" of the (curtailed) k-space plane because of magnetic susceptibility gradients.
Here are some brain images using 64x64 full Fourier EPI compared to 6/8ths pF(early)-EPI and 6/8ths pF(late)-EPI:
|Left: 64x64 full Fourier EPI. Center: 6/8ths pF(early)-EPI. Right: 6/8ths pF(late)-EPI. (Click image to enlarge.)|
Omitting the early echoes tends to enhance signal dropout in the temporal and frontal lobes (red and yellow arrows) while omitting the late echoes preserves temporal and frontal lobes but causes enhanced dropout in deep brain regions (blue arrows). This is interesting because it suggest that we have a degree of flexibility over where we pay the penalty for using partial Fourier EPI. I'll return to this issue later on, and in a subsequent post, because when we start to consider all the costs and benefits of pF-EPI we need to consider other parameters that might be changed in concert, such as the phase encoding direction, TE and the slice thickness.
Let's finish up this first look at pF-EPI in brain by assessing the TSNR. These images were obtained from 100 volumes with TE=22 ms and TR=2000 ms. All parameters were constant except the degree of partial Fourier sampling in the phase encoding dimension:
|TSNR for different EPI sampling schemes. Left: 64x64 full Fourier EPI. Center: 6/8ths pF(early)-EPI. Right: 6/8ths pF(late)-EPI. (Click image to enlarge.)|
Left Full 64x64 TSNR =100
Center 6/8ths pF(early) TSNR =115
Right 6/8ths pF(late) TSNR = 123
All we can state with confidence is that the full Fourier images show a TSNR that is lower than either pF-EPI variants because of the smoothing, and that there are regions that have far lower - approaching zero - TSNR for the pF-EPI, due to the enhanced dropout that we saw above. Nothing new here, except one thing to note in passing: there doesn't appear to be a substantial difference in motion sensitivity when using pF-EPI. The smoothing-induced boost in TSNR is preserved in the brain images as it was in the stationary phantom images. This is as we expect because all we're doing is shortening a single-shot acquisition. (See Note 2.)
Options with partial Fourier
In the comparisons presented here I intentionally fixed all parameters except the partial Fourier scheme. That way you were able to get a sense of the direct costs or benefits of a partial Fourier scheme. But there are at least three other parameters that should be considered when setting up a partial Fourier scheme: (i) omitting the early echoes will permit a shorter minimum TE, (ii) omitting the late echoes will permit faster acquisition (i.e. more slices per TR) even when TE is unchanged, and (iii) the phase encoding direction makes "early" and "late" a relative property of the echo train. I'm going to leave consideration of these issues for the next post, when I will look at setting up pF-EPI for an fMRI experiment. None of these options is trivial. The TE affects BOLD sensitivity, the TR affects statistical power and brain coverage, while the phase encoding direction establishes whether distortions will be a stretch or a compression in a particular brain region. All of these issues interact depending on what parameters we change having selected a particular pF-EPI option, and the optimal combination of parameters will depend on the brain region(s) of interest in your experiment.
1. Please note that Siemens' product EPI sequences don't have a way to select the late echoes for their partial Fourier options. The early echoes are always omitted with these sequences. However, in the coming months/years I hope to offer to research users a modified sequence that has early/late echo omission as an option, along with a host of other small tweaks that can be useful for fMRI. As soon as this sequence is available for distribution I'll be sure to blog about it.
2. Pedants will note that the actual motion sensitivity is a function of the underlying image contrast so that, in strict terms, the pF-EPI and full Fourier EPI scans do have different motion sensitivities. But this difference also exists for different brain shapes, different head orientations, different RF flip angles (because flip angle and TR establish the T1-based image contrast), etc. Might the motion sensitivity actually be reduced with pF-EPI,? It seems unlikely. Although the per slice time is decreased with pF-EPI, we also have to recognize that the effects of magnetic susceptibility are changed, too. So, what we gain with speed on the one hand we might give up with susceptibility contrast effects - signal dropout in other words - on the other. I really couldn't say whether these effects will be offsetting or not, and as far as I know nobody has ever assessed it. My bet would be that proving a systematic difference would be difficult because I suspect the motion sensitivity differences would be tiny.