[Mrtrix-discussion] csd equivalent of FA

Tue Jun 16 02:24:26 PDT 2015

HI Donald,
thank you for your detailed answer!
I'll think about it

Best Regards,
Alessandro

2015-05-30 16:49 GMT+02:00 J-Donald Tournier <jdtournier at gmail.com>:

> Hi Alessandro,
>
> Wow, that's enough questions for a whole review article... which we're
> currently trying to write, incidentally. I'll try to answer your questions,
> but I'll keep it brief - still preparing for ISMRM next week...
>
> *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.
>>
>
> Well, even then it's not that clear-cut. FA is *defined *as the
> anisotropy of water diffusion - but based on a model that we know isn't
> adequate in crossing fibre voxels. We also know it's not adequate in
> single-fibre regions since it's based on a model of free diffusion - and
> the whole reason we see anisotropy in the first place is due to
> *restricted* diffusion... This is the reason why we can measure diffusion
> kurtosis, for instance, and why the decay of the signal as a function of
> b-value isn't mono-exponential.
>
> Then there's the whole question of what 'white matter integrity' even
> means - it's such a non-specific term, I personally find it very
> unsatisfactory...
>
>
>> If you perform tractography with your wonderful technique, usage of FA
>> becomes questionable when attempting to make comparisons between healthy
>> populations and pathological ones.
>>
>
> Well, I don't see that it's related to tractography at all. As Ben showed
> in his paper <http://www.ncbi.nlm.nih.gov/pubmed/22611035>, the WM is
> full of crossing fibres, and these will influence the FA measured in the
> vast majority of the WM. It's an issue whether you use tractography, or an
> ROI-based approach, or a voxel-based analysis... And this isn't because we
> happen to be looking at the data with a particular analysis technique:
> these effects are intrinsic to the brain, they'll be present whichever
> method you chose to analyse your data. Just because you've never come
> across crossing fibres using DTI in the past doesn't mean crossing fibre
> effects weren't present...
>
>
>> Now, I am not familiar with harmonics, hence my considerations might be
>> inadequate. Please correct me.
>>
>> 1) AFD is peak2peak amplitude of fod lobe.
>>
>
> Almost. Really it's the *integral *of the FOD peak of interest. The
> amplitude is easily confounded by dispersion effects.
>
>
>> 2) If two fibers have been estimated in a voxel, you two fod lobes hence
>> two AFDs
>>
>
> Yep.
>
>
>> 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.
>>
>
> Nope. I don't think it's useful to draw comparisons with the tensor model.
> They are fundamentally different. Even in single fibre voxels, it doesn't
> work that way: lambda1 is essentially the log-ratio of the b=0 signal to
> the DW signal along the corresponding direction. In CSD, the FOD amplitude
> along that direction is proportional to the amount of raw DW signal in the
> plane *transverse *to that direction. It really is not going to help to
> try to relate the two...
>
>
>> If considerations 3) has somehow a sense, AFD is not exaclty CSD
>> equivalent to what FA is for DT.
>>
>
> No, they're not equivalent at all - not even a little bit...
>
>
>>
>> 4) An anisotropic measure of water diffusion in CSD perspective should be
>> something more "dixel" than "fixel", am I wrong?
>>
>
> I'm not sure I get your question. The coined the term 'dixel' to refer to
> an arbitrary direction with a voxel, and 'fixel' to refer to the direction
> of a peak in the FOD within a voxel. I don't see what you're trying to
> say...
>
> The way you phrase your question however suggests you're still looking for
> a measure of 'anisotropy' that will extend to crossing fibre voxels. I
> think this is the wrong way to look at it. I don't think we'll ever get a
> measure of per-fibre anisotropy, it's just too unstable. Besides, all the
> current white matter models in use today assume restricted diffusion in
> thin cylinders (CHARMED, bedpostx, NODDI, AFD, AxCaliber, ...).The concept
> of anisotropy simply doesn't make sense when one of the direction is fully
> restricted - the answer will always be 1 if the transverse diffusivities
> are zero.
>
> The way things are heading at the moment is one of two directions:
> measures of fibre / neurite density or partial volume (AFD, CHARMED, NODDI,
> CSD, bedpostx), or measures of microstructure such as axonal diameters
> (AxCaliber, activeAx, etc), with the latter requiring very tailored and
> demanding acquisitions, and currently being only valid in single-fibre
> regions. I don't think anyone is still trying to get a measure of per-fibre
> anisotropy... and if they did somehow manage to identify differences in
> anisotropy between different fibre bundbles, I'd be very reluctant to
> interpret that in any way other than simply a difference in the amount of
> fibre dispersion.
>
>
>> 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 problem with GFA is that it's just as non-specific and confounded by
> crossing fibre effects as FA. It is nothing more than the normalised
> standard deviation of your ODF. It's inherently very dependent on the
> properties of your ODF - for instance, if I use different lmax values in a
> CSD fit, and compute the GFA for each, I'll get different images, since the
> smoothness will be different between the two. If I use different parameters
> in my acquisition, I'll get different values. If I derive my ODF using QBI,
> CSA-QBI, CSD, or MT-CSD, I'll get different images in each case. And it's
> very hard to see what possible useful interpretation you could put to your
> GFA values - even if they were to some extent sensitive to microstructure
> effects, they will definitely be influenced by crossing fibre effects.
>
>
>>
>>
>>
>> *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.
>>
>
> It is related to MD, in that areas of low signal in higher shells tend to
> have high diffusivity (they tend to correspond to CSF). But again, I think
> that thinking in terms of diffusivities is not helpful. The reality is that
> you have *restricted *diffusion occurring in multiple compartments in
> slow exchange - you cannot ever obtain a pure meaningful measure of
> diffusivity in any physical sense. This is why it's always been labelled
> the *apparent *diffusion coefficient - the reality is much more complex
> than that.
>
>
>> In mathematical terms, does not first volume contain level of
>> "correlation" between DW signal and first harmonic basis (a sphere)?
>>
>
> Well, it's much more simple than that. Spherical deconvolution is a linear
> model. The first volume corresponds to the mean value of the FOD, which is
> directly proportional to the mean DW signal...
>
>
>>
>>
>> *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?
>>
>
> Not quite. The lack of normalisation is due to the fact that CSD operates
> on the raw DW signal, and that signal will be scaled differently on
> different days, different coils, different scanners, different subjects,
> etc. It's dependent on coil loading, transmitter and receiver gains, and
> all manner of other scale factors in the image reconstruction.
>
> The reason it's *almost *normalised is because the response function is
> also estimated from the same data, so that these large scaling effects are
> inherently factored out. But it's not perfect, since it'll depend on
> exactly which voxels get included in the single-fibre mask.
>
> To get around that, yes you can use something like a de-meaning approach,
> but the question then becomes: the mean of what signal? Where do you
> measure it? In which image do you measure it? We often use the median b=0
> signal in a conservative WM mask, but we're always mindful of the fact that
> this signal might itself be correlated with the effect of interest. It's
> not as simple as it sounds...
>
> Thanks in advance and sorry for posing you so many questions, but I would
>> really like to more deeply understand CSD outcome.
>>
>
> Yes, there's a lot more to it than meets the eye... At least you're asking
> the right questions!
> Cheers,
>
> Donald.
>
>
>
>>
>> Best Regards,
>>
>> Alessandro
>>
>
>
>
> --
> *Dr J-Donald Tournier (PhD)*
>
> *Senior Lecturer, **Biomedical Engineering*
>
> *Division of Imaging Sciences & Biomedical EngineeringKing's College
> London*
>
>
> *A: Department of Perinatal Imaging & Health, 1st Floor South Wing, St
> Thomas' Hospital, London. SE1 7EH*
> *T: +44 (0)20 7188 7118 ext 53613
> <%2B44%20%280%2920%207188%207118%20ext%2053613>*
> *W: http://www.kcl.ac.uk/medicine/research/divisions/imaging/departments/biomedengineering
> <http://www.kcl.ac.uk/medicine/research/divisions/imaging/departments/biomedengineering>*
>
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