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Hi again Pablo and Eduardo,

> 
> Assuming the B0 field doesn't change from acquisition to acquisition, what I would expect is that the B0 distortions do not depend on your TE, just on your EPI readout train (echo spacing, and number of EPI lobes).  Therefore, the distortions in the images collected with different TEs should be the same.  (You could test that by collecting data on a phantom --to make sure there is no motion-- with different TEs (and b-value=0, so there are no eddie current distortions), and see if the images themselves, not the topup estimates, are the same).
> 
> So, if topup gave different estimates of the field, it must be because the different intensities in the images (due to different TEs) confuses it, and it assumes there signal intensity increase/decrease comes from piling up/stretching the signal.  (Again, a way to test this would be to take your phantom data and scale all the images collected with different TEs so that all have the same intensity.  In that case, the distortions found by topup should be the same.  Then, you could applytopup to the un-scaled data).

estimating the B0 field from pairs of b0-volumes where different pairs have different echo time should give the same estimated field. The images are re-scaled internally to a grand mean of 100, so the intensity scaling should not matter. Things that matter are, for example, subject movement and shimming. If the subject moves between the acquisitions with different echo times that field will change. As a first approximation it will “move with the subject”, but in the case of rotations around an axis non-parallel to the magnetic flux is will undergo additional changes. If you get different fields from your b0:s without re-shimming and without subject movement, I cannot quite explain that. 

> 
> Now, for applying "eddy": in principle, the eddy currents would be different when you apply different diffusion-encoding gradients.  In the case of data collected with the same TE, normally the scanner would just apply stronger gradients to obtain higher b-values, but the timing would be the same.  Therefore, the eddy currents (and, hence, the distortions) would just scale up or down.  In the case of data collected with different TEs, supposing you selected the smallest TE possible for each b-value shell, the amplitude of the gradients would the the same (maximum), and the timing would be different.  If the principal component of the eddy currents decays fast, it could be that the short-TE and long-TE shells have identical eddy current distortions: those produced by turning off the diffusion-encoding gradient before the EPI readout).  So that might explain why eddy works fine with data collected with different TEs.  However, I would not assume this will be the case for every system (every scanner might have different eddy current characteristics).

As long as you don’t specify a 2nd level model in eddy (the --slm option, which is off by default) eddy makes no assumptions about how the eddy currents in one volume relates to the eddy currents in another. Therefore it doesn’t matter if the different shells have different echo times. If ones specifies for a example a linear 2nd level model (which one would have to do explicitly) eddy would assume that volume acquired with the same b-vec would have the same eddy currents (scaled by b-value) and then the echo time might potentially matter.

Jesper


> 
> Finally, as Jesper mentioned, combining diffusion data collected with different TEs is quite problematic, since the diffusion time will be different, and you will be probing the microstructure at different spatial scales.
> 
> Best,
> 
> -Pablo