Common persistent EPI artifacts: Gibbs artifact, or ringing

 
Don't ask me why there's no apostrophe, it looks possessive to me. Perhaps it's (the) Gibbs artifact rather than Gibbs (his) artifact. Most people simply refer to the effect as ringing anyway, so let's move on. This post concerns a phenomenon that, like aliasing last time, isn't unique to EPI but is a feature of all MRIs that are obtained via Fourier transformation.

In short, ringing is a consequence of using a period of analog-to-digital conversion in order to apply a (discrete) FT to the signals and produce a digital image. Or, to put it another way, we are using a digital approximation to an analog process and thus we can never properly attain the infinite resolution that's required to fully represent every single feature of a real (analog) object. Ringing is an artifact that results from this imperfect approximation.

We had already encountered one consequence of digitization in the Nyquist criterion in PFUFA Part Six. However, for our practical purposes, ringing isn't a direct consequence of digitization like the Nyquist criterion, but instead results from the duration of the digitization (or ADC) period relative to the persistence of the signals being measured. In principle, a signal decaying exponentially decays forever, which is rather a long time to wait for the next acquisition in a time series, so we instead enable the ADC for a window of time that coincides with the bulk - say 99% - of the signal, then we turn it off. This square window imposed over the exponentially decaying signal causes some degree of truncation, and it's this truncation that leads to ringing. (See Note 1.)


An example of ringing in EPI of a phantom

Let's start with an unambiguous example of ringing by looking at the artifact in a homogeneous, regular phantom. Below is a 64x64 matrix EPI acquired from a spherical gel-filled phantom. You're looking for the wave-like patterns set up inside and outside the edges of the main signal region:

In the left image, which is contrasted to highlight ringing artifacts within the signal region itself, the primary ringing artifact appears as a series of concentric circles, each with progressively smaller diameter and lower intensity as you move in from the edge of the phantom. One section of the bright bands is indicated with a red arrow, but you should be able to trace these circles all the way around the image. Also visible is a strong interference pattern (blue arrows) that arises between the aforementioned ringing artifact and the overlapping N/2 ghosts. This is because the ghosts maintain the contrast properties of the main image; they are, after all, simply weak (misplaced) clones of the main image.

Another brief explanation of decoding

Here's another short video produced by UC's media people in which Jack Gallant explains in broad terms how his group's recent decoding experiment was conducted:

A good place to go next for more details is the Gallant Lab website. Read the FAQ on that page to gain a basic understanding of what the experiment was, and what it wasn't. Then go read the paper, it's written very accessibly!

Common persistent EPI artifacts: Aliasing, or wraparound

 
In Part Eleven of the series Physics for understanding fMRI artifacts (hereafter referred to as PFUFA) you saw how setting parameters in k-space determined the image field-of-view (FOV) and resolution. In that introduction I kept everything simple, and the Fourier transform from the k-space domain to the image domain worked perfectly. For instance, in one of the examples the k-space step size was doubled in one dimension, thereby neatly chopping the corresponding image domain in half with no apparent problems. At the time, perhaps you wondered where the cropped portions of sky and grass had gone from around the remaining, untouched Hawker Hurricane aeroplane. Or perhaps you didn't.

In any event, you can assume from the fact that this is a post dedicated to something called 'aliasing' that in real world MRI things aren't quite as neat and tidy. Changing the k-space step size - thereby changing the FOV - has consequences depending on the extent of the object being imaged relative to the extent of the image FOV. It's possible to set the FOV too small for the object. Alternatively, it's possible to have the FOV set to an appropriate span but position it incorrectly. (The position of the FOV relative to signal-generating regions of the sample is a settable parameter on the scanner.) Overall, what matters is where signals reside relative to the edges of the FOV.

Now, on a modern MRI scanner with fancy electronics, aliasing is a problem in one dimension only: the phase encoding dimension. (Yeah, the one with all the distortion and the N/2 ghosts. Sucks to be that dimension!) The frequency encoding dimension manages to escape the aliasing phenomenon by virtue of inline analog and digital filtering, processes that don't have a direct counterpart in the phase encoding dimension. Instead, signal that falls outside the readout dimension FOV, either because the FOV is too small or because the FOV is displaced relative to the object, is eliminated. It's therefore important to know what happens where and when as far as both image dimensions are concerned. One dimension gets chopped, the other gets aliased.

I will first cover the signal filtering in the frequency encoding dimension and then deal with aliasing in the phase encoding dimension. Finally, I'll give one example of what can happen when the FOV is set inappropriately for both dimensions simultaneously. At the end of the process you should be able to differentiate the effects with ease. (See Note 1.)


Effects in the frequency encoding dimension

Below are two sets of EPIs of the same object - a spherical phantom - that differ only in the position of the readout FOV relative to the phantom. In the top image the readout FOV is centered on the phantom, whereas in the bottom image the FOV is displaced to the left, causing the left portions of the phantom signal in each slice to be neatly, almost surgically, removed:

Readout FOV centered relative to the phantom.

Readout FOV displaced to the left of the phantom, resulting in attenuation of the signal from the left edge of each slice.