Education, tips and tricks to help you conduct better fMRI experiments.
Sure, you can try to fix it during data processing, but you're usually better off fixing the acquisition!

Tuesday, July 3, 2012

Physics for understanding fMRI artifacts: Part Thirteen

A tour through a real EPI pulse sequence

In some posts I've got planned it will be important for you to know something about all of the different functional modules that are included in a real EPI pulse sequence. So far in this PFUFA series I've used schematics of the particular segment of the sequence that I was writing about, e.g. the echo train that covers 2D k-space for single-shot EPI. Except that there comes a time when you need to know about the sequence in its entirety, as it is implemented on a scanner. Why? Because there are various events that I've given short shrift - fat saturation and N/2 ghost correction, for instance - that have significant temporal overheads in the sequence, and these additional delays obviously affect how quickly one can scan a brain.

So, without further ado, here is a pulse sequence for fat-suppressed, single-shot gradient echo EPI, as used for fMRI:

(Click to enlarge.)

Okay, so it's not the entire pulse sequence. The readout gradient echo train in this diagram has been curtailed after just nine of 64 total gradient echoes that will be acquired, for EPI with a matrix of 64x64 pixels. The omitted 55 echoes are simply clones of the nine echoes that you can see. (Note that there are no additional gradient episodes at the end of this particular EPI sequence; all the crusher gradients occur at the start of the sequence and these are visible in the above figure. More on crusher gradients below.) I should also point out that this is the timing diagram for acquisition of a single 64x64 matrix EPI slice. The pulse sequence as shown would be repeated n times for n slices within each TR. (See Note 1.)

Interpreting what you see

Let's first determine what information is being displayed on the figure above. There are five axes, all handily labeled on the far right-hand side of the figure. The top axis is the RF transmit channel; we've got two RF pulses in this sequence. The second axis down is the receiver, or analog-to-digital converter (ADC) channel. The scanner is receiving signals only when there's a rectangle specified on the second axis. Finally, the bottom three axes represent the pulsed field gradients, in the order X, Y, Z.

Just for fun, let's quickly determine what the scanner is doing in the logical frame of reference, before we delve into the nitty-gritty. The slice selection gradient will occur in concert with an RF excitation pulse, and we have two RF pulses to choose from. Slice selection can't be the first RF pulse because that pulse occurs without any concomitant gradients. Thus, the slice excitation pulse must be the second one and we can deduce that slice selection is along the Z axis, which is the magnet bore axis. We're doing axial slices.

The read gradient axis is the one that does most of the work during spatial encoding; it's recognizable as a gradient echo train that is coincident with the data sampling (ADC) periods. (The first two diagrams in PFUFA Part Twelve should provide a useful reminder. The read gradients were colored green in that post.) There are a lot of gradient echoes on the X channel, so it's safe to assume that X is the read dimension, making the Y axis the phase encoding dimension by deduction. So, we're doing axial slices, with the read gradient aligned left-right (magnet X axis) and phase encoding aligned anterior-posterior (magnet Y axis) relative to the subject's brain.

Pulse sequences are generally schematic, but it is standard procedure to try to show the gradient amplitudes with correct intensities as far as possible. Thus, if we look at the X axis for a moment, you can see that the dark and light blue gradient episodes are equal magnitude and area but opposite sign; they are a balanced pair. Furthermore, the blue gradient episodes are larger (magnitude and area) than the green readout gradients. Think of the diagrams as being pseudo-quantitative. In this particular case the diagram displays accurate timing as well as accurate gradient intensities, but that isn't always the case with pulse sequences.

To interpret the sequence I'm going to break it down into functional blocks (which is, interestingly enough, often how the pulse sequence is actually programmed).

Fat saturation

Ignore for a moment the three dark blue gradients that occur first in the pulse sequence diagram. Instead, consider the action of the Gaussian-shaped RF pulse labeled FatSat in the diagram. This RF pulse occurs in the absence of pulsed gradients, making it chemical shift-selective rather than slice selective.

Fat is a particular problem for EPI because it resonates several hundred Hz away from water, leading to a strong N/2 ghost for subcutaneous (scalp) fat unless the fat resonances are either avoided or, as here, presaturated so that there is minimal fat signal during the subsequent slice excitation and signal readout. (An example of the intense ghosting that occurs in the absence of fat suppression (or some other scheme to avoid fat signals) was shown in the post, Common persistent EPI artifacts: Abnormally high N/2 ghosts (2/2), in the section entitled "No fat suppression.") (See Note 2.)

How does the fat saturation work? In brief, the Gaussian-shaped RF pulse excites another Gaussian shaped "notch" of frequencies symmetrically about the transmitter offset frequency, where the transmitter frequency is set at the fat resonances. (See Note 3.) The duration of the Gaussian RF pulse (in the time domain) is sufficiently long that the width of frequencies excited is broad enough to affect the fat resonances but not so broad as to impact the water resonance a few hundred Hz away. (Recall that there is a reciprocal relationship between the time and frequency domains, so a broad RF pulse will excite a narrow band of frequencies.)

The width of the RF pulse is carefully set to affect fat resonances without any significant effect on water resonances (see Note 4), and the amplitude is set to achieve a 90 degree (i.e. maximum) excitation of fat. In this way the fat resonances in the scalp are maximally excited and would, in the absence of any other gradients or RF pulses, generate a strange image that would be just a ring of scalp signal. But of course that's exactly the reverse of the intent of the fat saturation scheme, so we need to consider how this RF pulse works in conjunction with the gradients.

Crusher gradients for fat suppression

Now let's take a step back and consider those dark blue crusher gradients that occur prior to the fat suppression RF pulse. We'll consider the light blue gradients following that RF pulse at the same time. Notice that the dark and light blue gradients are balanced - equal areas with opposite signs - for each gradient axis. Any signal that exists prior to the fat saturation pulse experiences the dark and light blue gradients as a gradient echo; no net phase is imparted to the magnetization. However, any magnetization created by the fat saturation pulse experiences just the light blue gradients following the pulse, and this causes a net phase shift that is designed to render zero signal at the end of the light blue gradients. (There will be no net signal once the phase variation across a length scale equal to a pixel's dimensions becomes 360 degrees or greater. This is analogous to a T2* relaxation process. See PFUFA Part Seven for a reminder of how gradients impart phase across a sample, and lead to loss of signal intensity.)

To recap, then, the fat saturation pulse is designed to excite maximally the lipid resonances in the subcutaneous (scalp) fat, and this excitation is followed by a spoiling, or crushing, of the lipid signals by a set of gradients. The net result is (ideally) zero signal from subcutaneous fat, such that there is no fat magnetization available for excitation by the slice selection process that occurs later in the sequence. Provided the time between the fat suppression and slice selection pulses is short relative to the T1 of fat then there will be minimal recovery of fat spins. This assumption is usually well satisfied; the time between the two RF pulses is typically less than 10 ms whereas the T1 for fat is several hundred milliseconds at 3 T.

Crusher gradients to eliminate signal from prior slice excitations

There is another set of crusher gradients in the pulse sequence, following the light blue fat signal crushers, and these are colored purple in the diagram. Now, although these gradients would also lead to dephasing of signal generated by the preceding fat suppression RF pulse, the primary intent is to dephase any signal that remains from the previous slice excitation. That's because signal surviving from a prior slice would experience the dark and light blue crusher gradients as a balanced set - no net dephasing. (Water signal surviving from a prior slice would also be unaffected by the fat suppression pulse of the current slice because the fat suppression pulse is restricted to a narrow band of fat resonance frequencies.) Thus, there is a need to specifically target prior slice water signal(s).

Now, there are many ways that signals can survive from earlier slices. The simplest residual signal to understand is that left over from the very last slice just acquired, i.e. signal that survived because its T2* is long relative to the readout time. (There will be essentially no signal remaining once the time following slice excitation reaches three times T2* for each signal in the sample.) CSF in ventricles and some parts of brain tissue can easily pass this threshold, and thus provide spurious signal for the subsequent slice acquisition.

But there are other ways that signals can survive: from multiple prior RF excitations, as spin or stimulated echoes. The precise "coherence pathways," as they're called, aren't especially important for today's post (but are critical when setting up crusher gradients in a real sequence). We have to assume that the person who wrote and tested the sequence took into account these various contaminating signal pathways, and set up the crusher gradients appropriately. (See Note 5.)

Why are the purple crusher gradients operating on only two of the three axes, and why with negative sign? The short answer is efficacy. Using a gradient on the read channel (X in our example) might prove to be less effective than a gradient on Y or Z, because there are already multiple gradient echoes being (intentionally) played out along X, as we shall see in a moment. Adding a crusher gradient along X introduces the chance of eliminating some spurious signals while enhancing others, unless the crusher gradient area is made large relative to the readout gradient episodes. That adds time and can increase N/2 ghosts arising from gradient eddy currents. (See Note 6.)

The signs of the crusher gradients along Y and Z, as well as the relative intensities/areas of those gradients, are set to minimize spurious signals while simultaneously minimizing any eddy current effects. Other crusher gradient schemes are possible, even advisable, if it is determined that prior slice signal(s) are surviving the crushers as shown here, but the principles of operation are the same. (There are multiple "coherence pathways" that may be established when so many slice excitation RF pulses are applied so quickly, relative to T1 and T2 values for the signals in the head. A slice excitation pulse occurs every 40-60 ms, which is comparable to brain T2 values and far shorter than T1 values. This almost guarantees that spin and stimulated echoes will form in the steady state, unless crusher gradients are used to disrupt them.)

Slice selection

The gradients for slice selection and refocusing are colored orange in the figure. In concert with the slice selection gradient is a slice-selective RF pulse; a filtered sinc shape, which excites an approximate square in the frequency domain. (Slice selection was introduced in PFUFA Part Eight.) The magnetization excited by the RF pulse is created in the presence of a magnetic field gradient, and this causes an undesirable phase gradient in addition to the (desired) frequency-selective excitation. Thus, we need to rephase (eliminate) this phase gradient by applying a correction gradient episode, which is the positive gradient in orange following the slice selection itself. As described in PFUFA Part Eight, this is a simple example of a gradient echo. At the end of the rephasing gradient we have what we want: a slice of coherent magnetization with no phase gradient across it.

The sign of the slice select gradient doesn't matter; the slice selection gradient just happens to be negative here. Provided the refocusing gradient following the excitation pulse has the opposite sign a gradient echo is created. (See Note 1 for more information on how the different slices within TR differ only in one aspect. There may be practical benefits for using a negative rather than a positive slice selection gradient, but it isn't usually something a routine user has control over. Compared to other parameters that can be controlled, the benefits or otherwise aren't huge and it's not worth worrying whether your EPI sequence has negative or positive slice selection gradients. If that situation ever changes then rest assured I'll write a blog post on it!)

N/2 ghost correction echoes

The next event in the sequence is the acquisition of three gradient echoes for the purposes of N/2 ghost correction. (See the section entitled "Ghosting" in PFUFA Part Twelve.) The gradient episodes are shown in bright yellow while the concomitant acquisition periods are shown in pale yellow. Note that these three echoes are acquired in the absence of any phase encoding gradients; the k-space trajectory is restricted to the k-read axis, as we saw in the one-dimensional k-space representation of a gradient echo in PFUFA Part Nine.

So what's the point of these three echoes, and why are they restricted to one-dimensional projections of the read axis? If you go back to the explanation of how EPI ghosting arises in PFUFA Part Twelve you will see how the offsets alternate in a zigzag pattern across the phase encoding dimension. Thus, in principle, all we need to do is get a measurement of the amount of zig and the amount of zag and we can correct the odd and even lines of 2D k-space, leaving no zigzag offsets whatsoever. The three echoes give us an estimate of the zigzag by forming two comparisons: the second echo compared to the first echo estimates the zig, the third echo compared to the second echo estimates the zag. The zigzag estimates are then essentially subtracted out of the phase-encoded gradient echoes that will be acquired during the 64-echo readout train to come. (See Note 7.)

Phase encode dephasing gradient

Now we come to the 2D k-space readout. (The 2D k-space trajectory for EPI was explained in PFUFA Part Twelve.) The three phase correction echoes have left the magnetization at the positive k-read position; it wasn't necessary to refocus the latter half of the final phase correction echo period because we need to start the 2D k-space readout on one side of the readout k-space dimension. But we do need to shift our 2D readout starting point in the phase encoding dimension, so that we are in one corner of 2D k-space before we zip back and forth across the 2D k-space plane. Accordingly, a large red triangle of phase encoding gradient - often referred to as the dephasing gradient - moves us in the positive k-phase direction, placing us in the (+k-read, +k-phase) corner of the 2D k-space plane, all ready for the 2D readout echo train.

Readout gradient echoes

We've come to the final act of the EPI pulse sequence: acquisition of the rapid back and forth journey across a 2D k-space plane. It's difficult to see in the figure, but each alternating positive and negative readout gradient, colored dark green (with concomitant data acquisition periods colored pale green), has a small negative red triangular blip of phase encoding between them. I've added red dotted lines to help you line up the events. Note that the red gradient triangles occur in between the data readout periods - the phase encoding triangles are ramped at the same time as the readout gradients are switched quickly from positive to negative or from negative to positive. (See Note 8.)

If the final image matrix is 64x64 pixels then the area of thirty-two small red triangles is equivalent to the single large (positive) dephasing gradient in the phase encode direction, causing the center of k-space to occur after 32 readout echoes in the train. (Again, only the first nine echoes are shown in the figure.)

Relative duration of functional modules in the EPI sequence

Now that you've got an appreciation of the different functional events in a real EPI sequence you can start to assess which events take the majority of the time for each 2D image. (The figure is displayed to scale.) You should be able to recognize that the fat saturation pulse and its associated crusher gradients takes some 3-4 times longer to achieve than does the slice selection. The three ghost correction echoes add only a small temporal overhead, about the same duration as the slice selection. But the bulk of the time to prepare and acquire a single EPI slice is spent reading out the spatial information during the multi-echo readout echo train. The nine echoes in the readout train already take as long as the fat saturation scheme and we have 55 more echoes to go, making the total readout (of 64 echoes) at least six times longer than the next longest functional module of the sequence. If we're looking to save time, then, the first place to look is in the multi-echo readout train!

In the next few posts of this series (and some tangential posts to them) I want to start to consider "go faster" methods that you might want to consider for fMRI. As we consider each option we will need to refer back to this real EPI sequence, in order to comprehend the temporal savings on offer.



1.  I'm not going to get into the details here because it doesn't affect sequence timing, but for those of you wondering, each slice of the n slices in TR differs in only one aspect: the "carrier," or central frequency, of the RF excitation pulse is shifted for each slice by an amount sufficient to shift the excitation under the slice select gradient - on the Z axis here - to a new spatial position. Thus, the pulse sequence as displayed would be identical for any of the n slices in TR, because the RF excitation carrier frequency isn't displayed. Now, there are EPI pulse sequence variants that are exceptions to my prior statement - where there might be a slightly different gradient scheme for odd or even slices, say - but they're not common. For example, an option might be to use crusher gradients that alternate polarity with each successive slice; positive crushers for odd slices, negative crushers for even slices. But these aren't issues that we need to be concerned with today. I may discuss these issues in a future post, dedicated to crusher gradients.

2.  Chemical shift-selective RF saturation - or fatsat for short - is only one way to avoid the intense N/2 ghosts from fat. Another commonly used method, especially on GE scanners, is to use a spatial-spectral RF pulse for excitation. This pulse is designed to excite a 2D slab of water signal only, avoiding excitation of the fat signal in that slab. Yet another method, used in anatomical scanning but not so much for EPI because it is slow, is to use a T1 inversion null, i.e. an inversion recovery sequence where the post-inversion delay is set so that the fat signals are passing through the T1 null at the time of slice excitation. Yet another scheme is known as "the Dixon method," after it's inventor, and this uses a timed phase difference between the water and the fat spins based on their chemical shift differences. Choices, choices! I may do a separate post on some or all of the common fat avoidance schemes and include a comprehensive review of the pros and cons. But the bottom line for today is that fat suppression is generally regarded as the most robust and efficacious of the methods when applied to single-shot EPI for fMRI. A spatial-spectral pulse can work pretty well, too, but it tends to be limited to fairly thick slices compared to a standard (sinc-shaped) RF excitation applied following a fatsat pulse.

3.  The Fourier transform of a Gaussian is another Gaussian, as explained under the Properties section of this wiki page. The transmitter frequency of the time domain Gaussian-shaped RF pulse (where the Gaussian shape is achieved by amplitude modulation of RF intensity) is placed at or near the major fat resonance, at around 1.32 parts per million (ppm), where the ppm scale is referenced to the chemical shift of the proton resonance of tetramethylsilane (TMS) at 0.0 ppm. Relative to TMS, water protons resonate at approximately 4.7 ppm. Thus, the frequency difference between water protons and fat protons is approximately (4.7 - 1.32)ppm * 127 MHz = 429 Hz at 3 T.

4.  Some of you may be aware of something called "magnetization transfer" contrast (MTC), which is a mechanism whereby an off-resonance RF pulse (off-resonance relative to the usual water resonance at 4.7 ppm) is used to presaturate bound water spins. This pulse is followed by a delay that allows the bound water spins to exchange with free water spins, thereby decreasing slightly the total amount of free water signal available to be imaged. MTC can be a useful anatomical contrast mechanism, but it has little application for fMRI. Except that the fat saturation pulse will actually generate a teeny bit of MTC in addition to fat suppression because it is an off-resonance pulse with respect to free water! Thus, if you were to compare the gray/white/CSF anatomical contrast with and without fat suppression enabled, you should expect to see differences (leaving aside the N/2 ghost differences) because CSF exhibits no MTC while white matter, possessing a lot of bound water spins (because of myelin) exhibits stronger MTC than gray matter. Is this MTC of consequence for fMRI? No, not really. I just wanted to be complete! And talking of being complete, there's another source of MTC, too: other slice excitation RF pulses than the slice presently being considered. When an RF pulse is on resonance for one slab of water spins, it is off resonance for the "unexcited" water spins. I've used quotation marks because, strictly speaking, only the mobile, free water protons are off resonance outside of the excited slice. The broader resonances of bound water protons can still be partially excited by these other slice excitation pulses. Thus, if you do a single slice excitation with a TR of, say, 2 seconds and compare the gray/white/CSF contrast to that same slice when multiple slices are being excited in the same TR, you can expect to see a subtle contrast difference. MTC at work again! But again, it's of no practical consequence for fMRI.

5.  I happen to know that there are limitations in the crusher gradient scheme as shown in this sequence, but these limitations don't, as far as I know, show up in the conventional ways that this EPI sequence is applied for fMRI. The limitations can show up if one is using a 32-channel RF coil, and there may be circumstances when they become a concern in some phantom studies, where the overall signal level can be much higher than is typically seen in a brain. I will cover these limitations in detail in a dedicated post if it ever becomes necessary, but right now it's not an issue that's high on my priority list.

6.  Eddy currents are residual magnetic fields induced in the metallic components of the scanner, such as the steel cryostat that holds the superconducting magnet, and even the copper components of the receive RF coil. These spurious time-dependent magnetic fields are also spatial gradients, and they are created by induction when the main imaging gradients are switched on or off. A lot of engineering goes into a modern scanner to eliminate eddy currents, but it's physically impossible to remove all of the effects. And, as a general rule, the larger the pulsed imaging gradient amplitude the larger the eddy current it leaves in its wake. I don't presently have plans to do a post on eddy currents, but I may well do one eventually.

7.  There are other ways to correct the phase errors across the phase encoding dimension of EPI k-space, some of which use similar echo schemes and some that attempt more involved estimates of the odd/even offsets. It's a big subject that may become the focus of a separate blog post at some point. For now, however, it suffices to point out one of the experimental limitations of the three-echo scheme as presented. Note that the three correction echoes occur earlier in the sequence - that is, closer to the slice excitation - than the 2D readout period. Magnetic susceptibility gradients will therefore affect the correction echoes and the imaging readout train echoes differently; T2* effects will differ between the two periods. Furthermore, the assumption in this scheme is that any errors that are present during the 2D readout train are also present (with the same properties, such as magnitude) during the three correction echoes. This assumption may be invalidated by subject motion, eddy curents, the effects of RF interference and other noise sources, and these differing contaminants limit the practical benefits to the N/2 ghost correction. Some error sources simply cannot be estimated properly by the scheme, leading to residual ghosts that aren't fixed.

8.  Ramp sampling is often used to accelerate the total 2D readout, but I won't go into details here. I have another post planned on ramp sampling because there are performance issues. All that matters here is that the small red triangles happen in between data readout periods, whether or not ramp sampling is being used.

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