OK, assuming we’re looking at axial diffusivity maps, everything matches with what I’d expect here. DTI has historically been performed using single-shell *b*=1000s/mm² acquisitions, so it’s reassuring that everything matches in that case.

The issue at high b-values is that the CSF signal will effectively be pure noise - and with magnitude reconstruction, it’ll have a non-zero value on average (the Rician bias). So the ADC values in that regime are going to be very dependent on how these are handled. Using a single-shell at *b*=2500s/mm², I’d expect the CSF axial diffusivity to be essentially meaningless (noise-driven). For the WM, the differences will relate to the differential weighting given to the signal based on their actual (`dtiftit`

with WLS) or predicted (`dwi2tensor`

) signals, to compensate for the increase in the variance of the low signals due to the log transform. So the fact that the OLS perform differently here matches with that expectation.

The handling of multi-shell data is however a more recent problem. The fact that `dwi2tensor`

provides similar results to the single-shell *b*=1000s/mm² case is reassuring to some extent - although it’s not clear that there is a ‘right’ answer here. The problem is that the single tensor model breaks down when looking at multiple *b*-values (in fact, this is the entire premise behind diffusion *kurtosis* imaging), so these fits will never be perfect. With `dwi2tensor`

and `dtifit`

with WLS, the fit is inherently weighted towards the lower *b*-values, so it’s not surprising these look most like the *b*=1000s/mm² case. Moreover, `dwi2tensor`

updates the weights iteratively based on the predicted signal from the current fit, which will tend to reduce the weights for the high *b*-values further since these will have lower predictions than their actual measurements (as expected from the Rician bias, but also because the signal decay is not actually mono-exponential), so its fit will be even closer to the *b*=1000s/mm² case.

So to address your specific questions:

Yes - see my previous comments.

Ahem… I generally don’t recommend to estimate *any* tensor values… Pretty much my whole career has been focused on highlighting the deficiencies of that model and coming up with better methods. I’m just the wrong person to ask here.

It very much depends what you want to do. In general, it only exposes the limitations of the method, as you’ve yourself witnessed. If you are going to do tensor-based analyses, it’s much more important to ensure *reproducibility* of the measures, and therefore enforce consistency of the acquisition. Besides the fact that the values will be dependent on the details of the acquisition and the particular reconstruction method used, the values themselves are very difficult to interpret reliably from a biological point of view (too many issues to go into here, but maybe I can promote one of my review articles here ).

Maybe, if only for consistency with the literature (which is overwhelmingly single-shell *b*=1000s/mm²). But again, I’m probably the wrong person to ask, so I recommend you seek someone else’s opinion if you really want to do diffusion *tensor* imaging. More than happy to advise on higher-order analyses though.

Yes, `dwi2tensor`

does not enforce any constraints on the positivity of the eigenvalues, while other fitting algorithms might. These FA>1 voxels will result from negative eigenvalues. And these tend to occur where the *b*=0 signal is *lower* than the highest DW signal, which in turns tends to be caused by Gibbs ringing in the *b*=0 image in the areas bordering on CSF - exactly the regions you’re highlighting. I’m not sure there’s necessarily any need to worry about this, but it will depend on what you plan on using these values for - it will certainly have no noticeable impact on tractography (but then hopefully you’re not using the tensor model for tractography ). There are methods out there for removal of Gibbs ringing artefacts (I think there are plans to include one of these in *MRtrix3* in the near future - @bjeurissen may be able to provide details here), but otherwise we certainly have no plans to introduce a positive-definite constraint to `dwi2tensor`

.