Since I cannot use eddy for data preprocessing (āhalf-sphereā diffusion encoding)

Although this may not permit complete correction of eddy current distortions in `eddy`

, it wouldnāt surprise me if it still performs better than a linear registration approach, as it will generate appropriate target volumes for realigning each diffusion direction independently. Iād suggest at least giving it a test.

In my previous post I was indeed using older version of dwi2response.

Given the new results, I think your gradient table is OK; Iād suggest that it is indeed the nature of the Tax algorithm combined with your low *b*-value thatās causing the highly isotropic responses.

This approach initially treats *every voxel* as a single-fibre voxel; crossing fibre voxels are iteratively removed from the mask as the response function is progressively sharpened and multiple FOD peaks are identified. However, the lower angular contrast in low *b*-value data makes these crossings harder to identify. Consequently, many genuine crossing-fibre voxels will not be removed from the single-fibre mask. When the signal profiles within this mask are then averaged to produce the response function, the profile is not as sharp as it should be: maximal sharpness arises from selection of pure single-fibre voxels and alignment of their fibre orientations, so the presence of signal from crossing fibres inevitably broadens this shape.

- I was wondering, why optically the amplitudes of FOD lobes were higher in old dwi2response in comparison to new dwi2response

Yes, this is expected given the difference in mechanisms between the `tax`

and `tournier`

algorithms. In the `tax`

method, all voxels that are *not* removed from the single-fibre mask contribute to the response function estimation; so the overall response function amplitude will be an average of that in all single-fibre voxels. In the `tournier`

method, a cost function is defined to quantify the āsingle-fibre-nessā of each voxel, and only the top 300 voxels are averaged to produce the response function. Since the cost function includes the amplitude of the primary fibre peak, the algorithm preferentially uses voxels where the single-fibre FOD amplitude is largest (typically the splenium). Therefore the response function from this method will have a larger overall amplitude. Since the amplitude of the FOD reflects the magnitude of the diffusion signal *relative to the response function*, and the response function resulting from this method is greater, the resulting FOD amplitudes will be smaller.

2.Is here any objective evaluation criterion of response function quality? I suppose the more higher value of lmax, the better. But what in case of 2 responses with identical lmax? The higher value of SH lmax coefficient, the better?

Iām not sure if thereās a black-and-white answer to any of these; @jdtournier might pitch in at some point and has more experience than I do. But as an example: if you have a lower *b*-value, the signal power in the higher harmonic degrees is smaller; when deconvolution is then applied (at least in the linear case), thereās a reciprocal relationship between the power in the response function and the power in the resulting FOD; so thereās a risk of introducing large noisy coefficients into the higher harmonic degrees of the FOD compared to if you had truncated the response function at a lower harmonic degree. But the presence of the non-negativity constraint complicates this relationship.

*In general*, sharper is considered better, *as long as* that sharpness is derived from the data itself. For instance, itās possible to define the thinnest possible āpancakeā response function and use that; but the resulting FODs tend to be very noisy.

3.Does the āhalf-sphereā diffusion scheme make any problems/consequences for response function determination / FOD determination by constrained spherical deconvolution?

4.Does automatic selection of lmax for my āhalf-sphereā data works OK?

No and yes. All of the mathematical transformations between amplitudes on the sphere and spherical harmonics in *MRtrix3* assume antipodal symmetry, and so will work with direction schemes defined either on the sphere or the half-sphere.

However, to be clear:

From your CSD papers I understood that your acquisition schemes are āfull-sphereā acquisitions. But as the diffusion process is symmetric, the āhalf-sphereā acquisitions could be theoretically of benefit for having better angular resolution (not speaking now about the disadvantage that āhalf-sphereā data could not be corrected by fsl-eddy). Could you comment on?

A full-sphere acquisition does *not* imply acquisition of volumes where the diffusion directions are perfectly opposite to one another, and in fact this is usually explicitly avoided. A full-sphere acquisition is simply one where the directions of diffusion sensitisation are *not* constrained to the half-sphere. Typical derivation of such a scheme would involve optimising a set of directions on the half-sphere (assuming e.g. a unipolar electrostatic repulsion model; e.g. `dirgen`

), and subsequently reversing the polarity of around half of those directions so that they are spread relatively homogeneously over the full sphere (e.g. `dirflip`

). So there is no loss in angular resolution in using a full-scheme acquisition; the benefit is better modelling of eddy currents, and in fact long-term eddy currents may be reduced.

5.In case of more averages, do you recommend to average data, or prefer to stack them together?

Though it probably doesnāt make much difference in practise currently, conceptually (and for better compatibility with future developments) stacking volumes with equal diffusion sensitisation directions is preferable. Averaging magnitude-transformed volumes alters the noise distribution from Rician to non-stationary non-central chi, and so would not perform optimally in any technique that assumes a Rician distribution. However itās even more preferable to acquire more unique directions.

In the past, having multiple image volumes with equivalent diffusion sensitisation directions could cause issues as the automatic selection of *lmax* was based on the number of diffusion volumes only; however we now have a more robust heuristic in place that should deal with such data more appropriately.

6ā¦ But indeed I think it could be useful to have the option to use BEDPOSTX for ACT, to be able to compare both FOD determination methods in terms of performance and usability in different raw data acquisition setups.

Iāve added an entry to the GitHub issue tracker regarding this feature. Itās at a relatively low state of priority right now given the other issues we need to address in order to properly release the software, but I am intending on implementing a few different tracking algorithms at some point for my own evaluation purposes, so thereās a chance I might be able to implement this during my own research, and later add to *MRtrix3*.

Cheers

Rob