<div dir="ltr"><br><div class="gmail_quote"><div dir="ltr"><div>Hi Donald,<br></div>I want to thank you again for immediate replies. Regarding your answer,<span><div>please see below<br><br></div></span><span class=""><div><i>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.</i><br><br></div></span><div>sure..<br></div><span class=""><div><br></div><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). <br></i><br></div></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><br></div><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><br></div><div>Now, I am not familiar with harmonics, hence my considerations might be inadequate. Please correct me.<br><br></div><div>1) AFD is peak2peak amplitude of fod lobe.<br></div><div>2) If two fibers have been estimated in a voxel, you two fod lobes hence two AFDs<br></div><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><br>If considerations 3) has somehow a sense, AFD is not exaclty CSD equivalent to what FA is for DT.<br></div><div><br>4) An anisotropic measure of water diffusion in CSD perspective should be something more "dixel" than "fixel", am I wrong?<br>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><br></div><span class=""><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><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>In mathematical terms, does not first volume contain level of "correlation" between DW signal and first harmonic basis (a sphere)?<br></div><span class=""><div></div><div><i><br>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><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?<i><br><br></i></div><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.<i><br></i><br></div><div>Best Regards,<br><br></div><div>Alessandro<i><br></i></div></div></div></div>