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eddy -- a tool for correcting eddy currents and movements in diffusion data

This is a new tool to correct for eddy current-induced distortions and subject movements. It simultaneously models the effects of diffusion eddy currents and movements on the image, allowing it to work with higher b-value data than has been possible with for example eddy_correct (FSL's earlier tool for eddy current correction). As of FSL 5.0.10 (and a 5.0.9 patch) it also, optionally, performs outlier detection to identify slices where signal has been lost as a consequence of subject movement during the diffusion encoding. These slices are replaced by non-parametric predictions by the Gaussian Process that is at the heart of eddy.

Selected slice in 300 volumes of a data set from the HCP project

before_after_hcp_v4.gif

On the left before correction and on the right after correction for susceptibility, eddy
currents and subject movement using a combination of topup and eddy.

The diffusion signal is modelled using a Gaussian Process, which means that it makes very few assumptions about the diffusion signal (unlike parametric models such as for example the diffusion tensor). The only two assumptions are

From these two assumptions it also follows that:

Because of the way the diffusion signal is modelled, and because eddy needs to be able to distinguish between signal variation caused by diffusion and that caused by eddy currents/movements it is beneficial if the data is acquired with either

or with both. Note that "sampling on the whole sphere" does not imply twice as many directions. From a diffusion perspective sampling along v and -v is exactly equivalent whereas from the perspective of eddy current distortions they are different. One can therefore have two sampling schemes that both sample the diffusion evenly and equally well (and with the same total acquisition time), but where one is on the half sphere and the other on the whole sphere. To make this concrete look at the two sampling schemes below. In these plots the end of each vector is marked with an x-marker. They sample the diffusion in exactly the same way but the one on the left facilitates correcting for eddy currents while the one on the right does not. Note also that either of these schemes can easily be created from the other. To for example transform the half sphere scheme to the whole sphere scheme one just need to replace half the vectors by their negations.

whole_sphere_final.gif

half_sphere.gif

Diffusion sampled on the whole sphere

Diffusion sampled on the half sphere

In order to check your own diffusion directions you can use the following Matlab commands

bvecs = load('bvecs'); % Assuming your filename is bvecs
figure('position',[100 100 500 500]);
plot3(bvecs(1,:),bvecs(2,:),bvecs(3,:),'*r');
axis([-1 1 -1 1 -1 1]);
axis vis3d;
rotate3d

The final command (rotate3d) will allow you to use the pointer to rotate the plot which is essential as from some angles a half sphere looks just like a whole sphere.

If data has neither been acquired on the whole sphere or with reversed PE-directions there is a good chance that it will still work well. In that case it can be beneficial to use the --slm=linear parameter as described in the manual.

For eddy to work well there also needs to be a minimum number of diffusion directions. The reason for this is that the concept of "close" and "distant" vectors becomes a little pointless when there are only a handful of vectors. The "minimum number" will depend on the b-value (with a larger number of directions needed for higher b-values), but it appears that the minimum is ~10-15 directions for a b-value of 1500 and ~30-40 directions for a b-value of 5000.

If it sounds like your data might be a good candidate for eddy I suggest you go on to read the manual.

If you haven't already acquired your data

If you have taken the very sensible, and unusual, step to read this documentation before acquiring your data, here are some advice.

First of all let us assume you have some maximum scan time that you cannot exceed and that this allows you to acquire N volumes. Secondly, to keep things simple, let us assume that you plan to acquire data in a single (non-zero) shell. Thirdly, you intend to run tractography on your data.

If N < 80 we recommend you acquire all your diffusion weighted images with a single PE-direction, that you acquire N unique diffusion gradients/directions optimised on the whole sphere (see above). Please note that the gradients g and -g are not unique, and that you should not acquire both. We further recommend that you acquire 2-3 b=0 volumes with an opposing PE-direction for use with topup, and that you acquire these immediately prior to the full diffusion data set. An example acquisition would be something like
PE-dir : A->P  A->P  P->A  P->A  P->A  P->A  P->A ...
b-value:    0     0     0     0  1500  1500  1500 ...
It can also be a good idea to intersperse additional b=0 volumes in the main data set. One in sixteen for example.

If N > 120 we suggest you consider acquiring N/2 unique diffusion gradients/directions, each acquired twice with opposing PE-directions. In this case N/2 is still > 60, which is sufficient angular sampling for most applications. The opposing PE-directions offers the option to use a different type of "interpolation" that we call "least-squares reconstruction". It works by combining the data acquired with the two PE-directions to solve the inverse problem "what might the truth look like that produce these two distorted data sets?". The method is described in detail in Andersson et al., 2003 in the reference list below. It is able to recover some of the lost resolution in areas that have been compressed by susceptibility-induced distortions.

If N is between 80 and 120 it will depend on what model you will use for your tractography, how many fibres you will model per voxel etc.

What is new in 5.0.11?

The most important new feature of eddy 5.0.11 is the ability to perform slice-to-volume motion correction. The movie below demonstrates what it can do with a problematic data set with extensive movement.

Different levels of correction of a problematic data set

before_after_s2v.gif

Before any correction

After correction for susceptibility, eddy currents and gross subject movement

After correction for susceptibility, eddy currents, gross subject movement and signal dropout

After correction for susceptibility, eddy currents, inter- and intra-volume subject movement and signal dropout

That feature, and how to use it, is described in detail in the users guide and in the FAQ so we will not describe it here.

Instead I will mention some of the changes made to the functionality associated with the --dont_sep_offs_move and --don_peas flags. These both guide the behaviour of eddy with respect to aligning the b=0 volumes with the dwi volumes. The Gaussian Process prediction maker inside eddy helps when aligning different diffusion weighted images to each other, but it is of no help when aligning dwi volumes to b=0 volumes. Hence there is need for some "post-processing" within eddy to make sure that these are aligned to each other.

There are two ways in which the b=0 and dwi volumes may end up out of alignment with each other:

The former of these situations is likely to affect most data, whereas the second case is most likely to occur when there is a long gap between the first b=0 and the first dwi volume (for example when acquiring all b=0 volumes at the start) and/or the subject is uncooperative.

The first of these cases is solved by eddy by "separating the offset (constant EC field) from movement". It does so by default and only if --dont_sep_offs_move is set will eddy not do that. In previous versions this was done by attempting to work out the "offset part" using a model for gradient->EC-field. As of 5.0.11 it will also do a Mutual Information-based alignment along the PE-directon. Our tests indicate that this yields better accuracy (than the previous method) and we strongly advice against using the --dont_sep_offs_move flag.

The second of these cases is solved by performing a Mutual Information-based rigid-body registration between the mean b=0 volume and one mean volume for each dwi shell. For 5.0.11 we have changed the details of how this is done and our tests indicate that we have approximately halved the uncertainty associated with this registration. The registration is always run (even if you use the --dont_peas flag (Post Eddy Alignment of Shells)) and the rigid body parameters reported in a text file, but if the --dont_peas flag is set they will not be applied to the data.

As you will have realised by now the PEAS solution will "solve" both problems, so should one always use PEAS? I don't really have a definite answer to that question, but here are the considerations you need to make. I estimate the uncertainty of the Mutual Information-based registrations to be ~0.15 mm and ~0.15 degrees for the translations and rotations respectively.

If the first dwi volume was acquired a few seconds after the first b=0 volume and your subject was reasonably cooperative, then chances are that the actual movement between them was smaller than this uncertainty. If you do PEAS in that case you will have introduced some error (stemming from the uncertainty of PEAS) unnecessarily.

On the other hand, if you have a large number of subjects and you are not sure if maybe some of those subjects moved between the first b=0 and the first dwi volumes, then using PEAS on your entire cohort ensures that you are at least never "more wrong" than the uncertainty of the Mutual Information registration (~0.15 mm and ~0.15 degrees).

If I was tasked with analysing a data set like for example the HCP, where the first dwi volume is acquired a few seconds after the first b=0 volume and were the subjects are cooperative healthy adult, I would assume that the subject had lied still and use the --dont_peas flag. But I would also inspect the file with the PEAS parameters to ensure that there were no subjects that moved excessively in that period.


Referencing

The main reference that should be cited when using eddy is
Jesper L. R. Andersson and Stamatios N. Sotiropoulos. An integrated approach to correction for off-resonance effects and subject movement in diffusion MR imaging. NeuroImage, 125:1063-1078, 2016.

If you use the --repol (replace outliers) option, please also reference
Jesper L. R. Andersson, Mark S. Graham, Eniko Zsoldos and Stamatios N. Sotiropoulos. Incorporating outlier detection and replacement into a non-parametric framework for movement and distortion correction of diffusion MR images. NeuroImage, 141:556-572, 2016.

If you use the slice-to-volume motion model (accessed by the --mporder option) please also reference
Jesper L. R. Andersson, Mark S. Graham, Ivana Drobnjak, Hui Zhang, Nicola Filippini and Matteo Bastiani. Towards a comprehensive framework for movement and distortion correction of diffusion MR images: Within volume movement. NeuroImage, 152:450-466 2017.

You are welcome to integrate eddy in scripts or pipelines that are subsequently made publicly available. In that case, please make it clear that users of that script should reference the paper/papers above.

Other papers of interest

For those interested in understanding the inner workings of eddy the following paper describes how it makes model-free predictions of what a diffusion weighted image should look like
Jesper L.R. Andersson and Stamatios N. Sotiropoulos. Non-parametric representation and prediction of single- and multi-shell diffusion-weighted MRI data using Gaussian processes. NeuroImage, 122:166-176, 2015.

The "least-squares reconstruction" referred to above is described in
Jesper L. R. Andersson, Stefan Skare and John Ashburner. How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging. NeuroImage, 20:870-888, 2003.

The following paper compares the performance of eddy to the previous FSL tool eddy_correct
Mark S. Graham, Ivana Drobnjak and Hui Zhang. Realistic simulation of artefacts in diffusion MRI for validating post-processing correction techniques. NeuroImage, 125:1079-1094, 2015.

eddy (last edited 12:56:21 31-08-2017 by JesperAndersson)