[Mrtrix-discussion] Fwd: csd equivalent of FA

[Alessandro Calamuneri]

Hi Donald,
I want to thank you again for immediate replies. Regarding your answer,
please see below

*From my point of view, the interpretation of AFD is straightforward
whether you have one or more fibre populations - it relates explicitly to
each individual fibre population. I guess the issue you're having is that
it's no longer a simple scalar per voxel - but then that is a clearer
reflection of the reality than a simple scalar could give you.*

sure..


*However, one option that you have available to you is to use the total AFD
- i.e. the sum of the AFDs for all fibre populations. It is clearly less
informative than the AFD per fibre population (i.e. the fixel-wise AFD),
but if you must have a scalar per voxel, it would definitely be better than
the average AFD (if you have 2 fibre populations in a voxel, their average
AFD will be half that of the voxel next door that contains only one of the
fibre populations, which is a very artificial difference). *
1) FA is "son" of tensor model depending on its eigendecomposition.
2) As far as I know FA is a measure of anisotropic water motion within a
voxel.
3) It has been widely reported FA is correlated with WM integrity.
4) The whole story should in principle work fine when a single fiber
population is present within a voxel.

If you perform tractography with your wonderful technique, usage of FA
becomes questionable when attempting to make comparisons between healthy
populations and pathological ones.

Now, I am not familiar with harmonics, hence my considerations might be
inadequate. Please correct me.

1) AFD is peak2peak amplitude of fod lobe.
2) If two fibers have been estimated in a voxel, you two fod lobes hence
two AFDs
3) In a comparison perspective between your implementation and DTI, a
direct interpretation of lobe amplitude would something more related to
highest eigenvalue lambda1. If you would compare a two tensor fitting with
CSD, two lobe peaks would roughly correspond to respective highest
eigenvalues.

If considerations 3) has somehow a sense, AFD is not exaclty CSD equivalent
to what FA is for DT.

4) An anisotropic measure of water diffusion in CSD perspective should be
something more "dixel" than "fixel", am I wrong?
5) I was thinking a plausible measure of anisotrpy for CSD should be
something more similar to generalized fractional anisotropy (GFA) Tuch
wrote in his paper on Qball. It was just a natural extension of what FA
means, i.e. th ratio between standard deviation of eigenvalues to their
rms. Could it be possible to obtain a similar measure with output provided
by csdeconv command?



*The total AFD is trivial to compute since it's the l=0 term of the CSD
output - the first volume in the file (all other harmonics have zero
integral over the sphere).*
Would values of first volume of CSD correspond to what I am looking for?
After visualizing some examples, it seems such maps be higher in regions
with low water diffusion, hence I was thinking it was something related to
mean diffusivity (MD) more than FA.
In mathematical terms, does not first volume contain level of "correlation"
between DW signal and first harmonic basis (a sphere)?



*This measure is actually a pretty good surrogate for neurite density -
with the caveat that the CSD output is not very well normalised, so care
would be needed to ensure data are comparable across subjects, as for the
AFD itself. *
Is lack of normalization across subjects due to the fact that single
response functions have been estimated for each subject? An overall
demeaning of each volume would not be sufficient to render extracted
volumes comparable between different subjects?

Thanks in advance and sorry for posing you so many questions, but I would
really like to more deeply understand CSD outcome.

Best Regards,

Alessandro
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://www.nitrc.org/pipermail/mrtrix-discussion/attachments/20150530/3c0c5ce9/attachment.html>