Eddy is a tool from FSL for correcting eddy currents and movements in diffusion data. It makes use of a Gaussian process that predicts the signal between different diffusion encoding directions, which helps the registration. However, this Gaussian process is not yet generalized for methods using free waveforms, such as b-tensor encoding. Thus, some care is required to make it work.
Michiel Cottar (PhD) used eddy for postprocessing in a project on estimation of fiber dispersion [1]. Below is a summary of his experience.
Currently, eddy can only process data which varies with gradient orientation and b-value, not anything else. This is because the Gaussian processes inside eddy only support varying along these dimensions. While generalising the gaussian processes to allow the data to vary across more axes (e.g., shape of the B-tensor or TE), I don't think anyone is actively working on that at this point.
With that limitation in mind, I've found that eddy does quite a good job of registering either linear, planar, or spherical encoded data (please not that this assessment is mainly based on eyeballing the output, not a detailed quantitative analysis). So, for my project which contained linear and spherical tensor encoded data, I ran eddy twice: once on the linear encoded dataset and once on the spherical tensor encoded dataset. Afterwards, you can either register the datasets to each other (using the b0's) or to some common space (I registered them to the T1-weighted image). Note that eddy registers the data to the first b0, so if you make sure that the first b0 is the same for the linear and spherical tensor encoded data, the output of the two eddy runs should already be in alignment (I did not actually test this).
Nicolas Geades at Philips Clinical Science used TOPUP and EDDY on data acquired with linear and spherical b-tensor encoding. He encountered the "inconsistent b-values detected"-error, and submitted the following fix.
For running EDDY on Linear and Spherical diffusion encoded data: FSL EDDY expects a minimum number of measurements for each b-value (for low b-value images I think the minimum number of measurements is 6), even for the b0. If the dwi data has only a single b0 image then EDDY will not run and will give the error “Inconsistent b-values detected”.
To avoid this, one can remove the b0 image from the dwi data (by using fslroi for example) and then run EDDY on the remaining images. In order for this to work, the bval and bvec text files also need to be updated to remove the values corresponding to the b0 image in the dwi data. After EDDY has been performed, the eddy-corrected dwi images can be merged back with the TOPUP-corrected b0 images (TOPUP-corrected b0 images can be extracted during the TOPUP step using the -iout option). The TOPUP-corrected b0 images will not benefit much from EDDY correction anyway, since there were no diffusion encoding gradients to induce eddy current-related distortions.
[1] Improved fibre dispersion estimation using b-tensor encoding. Michiel Cottaar, Filip Szczepankiewicz, Matteo Bastiani, Moises Hernandez-Fernandez, Stamatios N. Sotiropoulos, Markus Nilsson, Saad Jbabdi. NeuroImage 215, 2020. https://www.sciencedirect.com/science/article/pii/S1053811920303190.