In this case one should use this option to specify to MRtrix that a set of b=0 images will be provided where each one has the opposite PE direction.
More precise would be: a set of b=0 images where the first half have exactly the same phase encoding as the input DWIs, and the second half have exactly the opposite phase encoding.
how wrong am I?
what would happen if one uses GRE rather than SE data?
The fundamental requirement underlying the operation of
topup (and any other tool based on the same premise) is that:
There is a single underlying undistorted image;
Each of the input images are distorted versions of such;
These distortions manifest as spatial displacements of signals along the phase encoding direction (potentially with resulting increases or decreases in image intensity if the undistorted image is compressed or expanded in space as a result of those distortions).
For gradient echo data, the final point is not satisfied. Because the spins are not rephased for k-space readout, the spins contributing to the signal in a given voxel will not strictly be in phase, resulting in a decrease in signal magnitude relative to the spin-echo case. For a distorted image, this applies to the magnetic spins contributing to the signal in that voxel, whether they actually reside in the volume corresponding to that voxel or not. If these distortions differ between images (e.g. reversed phase-encoding pairs), the magnitude of signal decrease due to dephasing will differ between these images. As a result, even if your estimation of the magnetic field inhomogeneity was perfect, correction of your input images based on that field would not lead to identical output images.
From the perspective of the algorithm trying to estimate that inhomogeneity field, such irreconcilable differences are going to lead to biases in estimation of that field. These biases are going to be largest wherever the derivative of the field along the phase encoding direction is largest, as this is what drives the differential phase coherence effect (visible as signal dropouts in the raw gradient echo images that are over and above that of just distribution of the signal across a larger space than that from which it originated).
One way this problem is sometimes thought of in the context of such algorithms is that if you draw a ray along the phase encoding direction, the integral of the image intensity along that ray should be fixed, regardless of phase encoding signedness or readout bandwidth; the intensities are simply displaced along that ray by the EPI distortions, and therefore appropriate correction of such should yield the undistorted signal distribution.
Note this also means that other acquisition parameters such as TE, TR, flip angles etc. should also not vary between these reversed phase encode images.
any idea where I got my initial impression from?
It’s possible to use gradient echo data to estimate the magnetic field inhomogeneity; but by using differences in phase in a multi-echo acquisition, not phase encoding reversal. It’s a completely different acquisition and processing pipeline, but it is nevertheless “EPI distortion correction using gradient echo data”.