<div dir="ltr"><div><div><div><div>HI Donald,<br></div>thank you for your detailed answer! <br></div>I'll think about it<br><br></div>Best Regards,<br></div>Alessandro<br><br><div class="gmail_extra"><br><div class="gmail_quote">2015-05-30 16:49 GMT+02:00 J-Donald Tournier <span dir="ltr"><<a href="mailto:jdtournier@gmail.com" target="_blank">jdtournier@gmail.com</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Hi Alessandro,<div><br></div><div>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...</div><div><br></div><div class="gmail_extra"><div class="gmail_quote"><span class=""><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><span><div><i>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). </i><br></div></span><span><span><div><br></div></span></span><div>1) FA is "son" of tensor model depending on its eigendecomposition.<br></div><div>2) As far as I know FA is a measure of anisotropic water motion within a voxel. <br></div><div>3) It has been widely reported FA is correlated with WM integrity.<br></div><div>4) The whole story should in principle work fine when a single fiber population is present within a voxel. <br></div></div></div></div></blockquote><div><br></div></span><div>Well, even then it's not that clear-cut. FA is <i>defined </i>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 <i>restricted</i> 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. </div><div><br></div><div>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...</div><span class=""><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div>If you perform tractography with your wonderful technique, usage of FA becomes questionable when attempting to make comparisons between healthy populations and pathological ones. <br></div></div></div></div></blockquote><div><br></div></span><div>Well, I don't see that it's related to tractography at all. <a href="http://www.ncbi.nlm.nih.gov/pubmed/22611035" target="_blank">As Ben showed in his paper</a>, 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...</div><span class=""><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div>Now, I am not familiar with harmonics, hence my considerations might be inadequate. Please correct me.<br></div><div><br></div><div>1) AFD is peak2peak amplitude of fod lobe.<br></div></div></div></div></blockquote><div><br></div></span><div>Almost. Really it's the <i>integral </i>of the FOD peak of interest. The amplitude is easily confounded by dispersion effects. </div><span class=""><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div></div><div>2) If two fibers have been estimated in a voxel, you two fod lobes hence two AFDs<br></div><div></div></div></div></div></blockquote><div><br></div></span><div>Yep.</div><span class=""><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div>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.<br></div></div></div></div></blockquote><div><br></div></span><div>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 <i>transverse </i>to that direction. It really is not going to help to try to relate the two...</div><span class=""><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div></div><div>If considerations 3) has somehow a sense, AFD is not exaclty CSD equivalent to what FA is for DT.<br></div></div></div></div></blockquote><div><br></div></span><div>No, they're not equivalent at all - not even a little bit...</div><span class=""><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div></div><div><br>4) An anisotropic measure of water diffusion in CSD perspective should be something more "dixel" than "fixel", am I wrong?<br></div></div></div></div></blockquote><div><br></div></span><div>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...</div><div><br></div><div>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.</div><div><br></div><div>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. </div><span class=""><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div>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?<br></div></div></div></div></blockquote><div><br></div></span><div>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. </div><span class=""><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div><br></div><span><span><div><i>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).<br><br></i></div></span></span><div>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. <br></div></div></div></div></blockquote><div><br></div></span><div>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 <i>restricted </i>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 <i>apparent </i>diffusion coefficient - the reality is much more complex than that. </div><span class=""><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div></div><div>In mathematical terms, does not first volume contain level of "correlation" between DW signal and first harmonic basis (a sphere)?<br></div></div></div></div></blockquote><div><br></div></span><div>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... </div><span class=""><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div></div><span><span><div></div><div><i>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. <br><br></i></div></span></span><div>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?</div></div></div></div></blockquote><div><br></div></span><div>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. </div><div> </div><div>The reason it's <i>almost </i>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. </div><div><br></div><div>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...</div><span class=""><div><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div>Thanks in advance and sorry for posing you so many questions, but I would really like to more deeply understand CSD<i> </i>outcome.<br></div></div></div></div></blockquote><div><br></div></span><div>Yes, there's a lot more to it than meets the eye... At least you're asking the right questions!</div><div>Cheers,</div><div><br></div><div>Donald.</div><div><br></div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div></div><div><br></div><div>Best Regards,<br><br></div><div>Alessandro<i><br></i></div></div></div></div>
</blockquote></div><span class=""><br><br clear="all"><div><br></div>-- <br><div><div dir="ltr"><b><font color="#990000">Dr J-Donald Tournier (PhD)</font></b><br><div><font color="#990000"><br></font></div><i><font color="#990000">Senior Lecturer, </font></i><i><font color="#990000">Biomedical Engineering</font></i><div><i><font color="#990000">Division of Imaging Sciences & Biomedical Engineering<br>King's College London</font></i><div><i><font color="#990000"><br></font></i></div><div><i><font color="#990000"><b style="font-family:Calibri,sans-serif;font-size:15px"><span style="font-size:10pt">A:</span></b><span style="font-family:Calibri,sans-serif;font-size:10pt"> Department of Perinatal Imaging & Health, 1<sup>st</sup> Floor South Wing, St Thomas' Hospital, London. SE1 7EH</span><br></font></i></div><div><i><font color="#990000"><b>T:</b> <a href="tel:%2B44%20%280%2920%207188%207118%20ext%2053613" value="+442071887118" target="_blank">+44 (0)20 7188 7118 ext 53613</a></font></i></div></div><div><i><font color="#990000"><b>W:</b> <a href="http://www.kcl.ac.uk/medicine/research/divisions/imaging/departments/biomedengineering" target="_blank">http://www.kcl.ac.uk/medicine/research/divisions/imaging/departments/biomedengineering</a></font></i><br></div></div></div>
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