[Mrtrix-discussion] FOD amplitude

Fri Mar 15 05:20:15 PDT 2013

Hi Dave,
Thanks very much for the detailed response, that's really very useful. 
I've responded to your points (with a few more questions) inline:

On 15/03/13 03:59, David Raffelt wrote:
> Hi James,
> Just to clarify, do you mean you extract a single peak with the 
> largest amplitude within each voxel? Then normalise by the max 
> amplitude across all voxels and subjects? If so, one potential issue 
> is that the largest peak in corresponding voxels across subjects is 
> not guaranteed to belong to the same fibre bundle. Also, during 
> pathology you might see a decrease in the FOD peaks of one fibre, such 
> that they are no longer the dominant peak in that region (and 
> therefore are excluded from your analysis).
Yes, that's exactly what I did. I agree that the largest peaks in 
corresponding voxels between individuals may well not belong to the same 
fibre bundle, but I think you could argue that this is no worse than the 
'averaging' of different fibre bundles inherent in the tensor model. At 
least this way you can claim to be actually measuring a discrete fibre 
bundle, rather than something potentially not aligned to any tracts, as 
may happen with the primary eigenvector in DTI.
As I understand it the full AFD approach might help rectify this tract 
correspondence problem, as could some other methods for determining 
common orientations (e.g. FSL bedpostX). These are things I definitely 
would like to explore in the long term.
>
> Simulations suggest the AFD along a given direction is proportional to 
> the intra-axonal volume of axons aligned with that direction (at least 
> with high b-values and long gradient pulse durations). Using lower 
> b-values means that the AFD is also dependent on the signal from 
> hindered extra-axonal water. And therefore the interpretation of any 
> AFD group differences is not as clear cut.
Interesting to know. I'm generally a bit concerned about the low bvalue 
in my data, but keen to try and use some multi-fibre/non-tensor methods 
nonetheless, even if it's somewhat exploratory. One advantage with the 
sample I'm using (Huntington's Disease) is that there's strong 
post-mortem evidence that shows demyelination, loss of axonal density 
and number of axons - so even if the interpretation isn't 
straightforward, then group differences are still likely to be 
pathological.
>
> The peak AFD amplitude is probably not a bad estimate of the total 
> intra-axonal volume of axons belonging to the respective FOD lobe. 
> However, inter-subject differences in fibre curvature (in subject 
> space) will influence the peak (due to a difference in the spread of 
> the FOD lobe).  A better measure would be to use the integral of each 
> FOD lobe. Rob uses the integral for his SIFT method, and I'm 
> presenting a new tractography-based statistical method that uses the 
> AFD integral at ISMRM next month.
Sounds great. I've had a read of the appendix and Algorithm 1 in Rob's 
SIFT paper and can definitely see the justification for using the 
integral, rather than the peak. As mention later, you're planning to 
implement this in MRtrix in the future, but in the meantime, do you have 
a script that runs the density sampling and calculates the integral that 
you can make available?
>
> One other issue is related to transforming the AFD peak amplitudes 
> into template space. Modulation needs to be applied when spatially 
> normalising any DWI measure representative of the restricted 
> intra-axonal water fraction of a specific fibre population  (whether 
> it is the AFD peak, integral, or partial volume fractions computed 
> using other methods, e.g. Behren's Ball and Stick model or Assaf's 
> CHARMED). As discussed in the AFD paper, non-linear transformations 
> may alter the width of a fibre bundle, and therefore modulation is 
> needed to preserve the total intra-axonal volume of axons passing 
> through any given cross-section of a fibre bundle.
Again, modulation looks very sensible, I can see the problems that may 
arise if it's not done. Would you also happen to have a script available 
to do this in using the mrtrix framework?
>
> Are you computing FODs using a single group-average response function 
> for all subjects? To do AFD analysis you also must account for 
> intensity variation across scans. Due to patient- and scan-specific 
> scanner calibrations, the magnitude of the MR signal across different 
> scans is not comparable. One way to account for this is to intensity 
> normalise the DW images using some reference point. Ideally, the 
> median CSF b=0 signal would be a good reference since it is unlikely 
> to vary during pathology. However, at the current DWI resolution it is 
> often hard to get a clean partial-volume-free estimate of the CSF, 
> particularly in young patient groups. Alternatively you could use the 
> median b=0 signal from brain parenchyma, however this is not ideal 
> since it might be affected by the pathology being investigated.
> The other way to account for scan intensity variation is to perform 
> CSD using a subject-specific response function, however this is less 
> robust and you might reduce your power to detect AFD differences due 
> to larger group variation, or the possibility of pathology affecting 
> voxels used to estimate the response function.
I used a subject-specific response function. Interestingly, the voxels 
that showed group differences were not those that were generally 
included in the single fibre mask used to estimate the response 
function. Not sure if this has any bearing the robustness of the 
calculation. I think I'll try and calculate the median CSF signal to 
intensity normalise the subjects, then use one response function across all.
>
> Just to clarify, the max_amp metric represents the amount of diffusion 
> in the peak direction only for diffusion orientation distributions 
> dOFDs (i.e those computed by Q-ball and DSI). Whereas FODs model the 
> intra-axonal volume of fibres as a function of orientation. The 
> amplitude of so-called "model free" diffusion ODFs is less 
> informative, since it is impossible to tease out the contribution from 
> multiple underlying fibre populations without some type of model 
> (which in the case of spherical deconvolution is the response function).
OK, so hopefully that by using the FODs in my case, I'll be able to see 
something more biologically meaningful - even if I can't directly claim 
to be measuring diffusion.
>
> Also, the peak FOD amplitude is more akin to the apparent/radial/ 
> diffusivity of the respective fibre population (and not the axial 
> diffusivity as you suggest). Pathology-induced changes to restriction 
> are more likely to influence the DW signal along radial orientations 
> (especially at high b-values where the axial DW signal is 
> non-existent). A decrease in the radial DW signal will present as a 
> decrease in AFD along the fibre direction, and an increase in the 
> radial diffusivity. Although I should warn against thinking of AFD in 
> terms of radial diffusivity, since thinking in terms of diffusivity is 
> clearly not a good way of looking at the DW signal arising from a 
> /restricted/ diffusion environment.
Very interesting, thanks for the clarification. On reflection, I can see 
that this definitely makes more sense. In my experience, RD is more 
sensitive to pathology than AD, so if I can explain this metric to 
people as approximately analogous to RD, that might be more 
comprehensible. However, as you say, I'll be careful not to make any 
claims about diffusivity per se, given the restricted environment that 
the metric is derived from.

>
> Since I'm on a roll, I might as well mention that TBSS is not ideal 
> for doing 'whole brain' voxel-based analysis. Aside from the fact that 
> it does not really analyse all brain voxels, projecting your measure 
> of interest onto a skeleton based on the highest FA is problematic in 
> crossing-fibre regions.
I quite agree. I didn't actually use a TBSS skeleton for that very 
reason. I just used the randomise tool to run the GLM stats, and thought 
I'd mention TBSS as that's the context that most people are familiar 
with randomise from.
>
> In terms of doing AFD analysis in the future, we are hoping to release 
> the tools as part of the next major MRtrix release, however this will 
> depend on how much free time I have in the coming months.
>
Quite understandable! Thanks again for all the advice.
James
> Cheers,
> Dave
>
>
>
>
>
>
>
>
> ---------- Forwarded message ----------
> From: *James Cole* <james.cole at ucl.ac.uk <mailto:james.cole at ucl.ac.uk>>
> Date: 15 March 2013 04:28
> Subject: [Mrtrix-discussion] FOD amplitude
> To: mrtrix-discussion at www.nitrc.org 
> <mailto:mrtrix-discussion at www.nitrc.org>
>
>
> Dear MRtrixers,
> I've been using mrtrix for various things and came up with an approach 
> that I wanted to run by the experts. It might be that I'm barking up 
> entirely the wrong tree, so could use some guidance. Regarding 
> voxelwise metrics derived from the spherical deconvolution (I saw the 
> apparent fibre density (AFD) paper and this is something I'd be 
> interested in trying in the long run), I wondered whether the largest 
> FOD lobe might be sensitive to pathology. Here's my analysis:
>
> Having run CSD (Lmax = 6, the b-value is only 1000, 42 directions) on 
> my data, I used find_SH_peaks, dir2amp and FSL's fslroi to extract the 
> FOD of the largest amplitude (I called this max_amp) and thus was able 
> to generate voxelwise max_amp maps per subject, in native space.
>
> I then normalised the max_amp maps (by dividing by 3.5, to give a 
> scalar in the 0-1 range), having assessed the maximum amplitude in any 
> voxel across all subjects (which was 3.51ish). The idea being that the 
> the scalar now represents a score based on the amplitude of the FOD 
> lobe relative to the highest possible amplitude in vivo tissue; thus 0 
> = absence of FOD and 1 = maximum possible FOD amplitude.
>
> These normalised max_amp maps were then warped into group space using 
> the warps calculated from generating a groupwise template from FA 
> maps. I then created a mask using a threshold of FA>0.2 (to limit 
> analysis to white matter) and finally ran some stats (using FSL 
> randomise as per TBSS). In a group of 10 controls and 15 patients 
> there were a number of significant clusters of increased max_amp in 
> controls, roughly corresponding to the corticospinal tract and corona 
> radiata. There were no increases in patients.
>
> The rationale behind this comes from the idea that the max_amp metric 
> represents the amount of diffusion in the principle direction, but 
> uncontaminated by crossing fibre effects (so perhaps a 'better' 
> version of axial diffusivity, I suppose). I'm not assuming this idea 
> is original by any means, perhaps just the implementation of it in mrtrix.
>
> Apologies for the long post, but I'd be really appreciative of some 
> expert opinions. Any ideas for theoretical / practical improvements, 
> or reasons why this might not be representing what I think it is would 
> be most helpful.
>
> Many thanks,
> James
>
> -- 
> *James Cole PhD | Research Associate | Huntington's Disease Research 
> Group | UCL Institute of Neurology*
>
> _______________________________________________
> Mrtrix-discussion mailing list
> Mrtrix-discussion at www.nitrc.org <mailto:Mrtrix-discussion at www.nitrc.org>
> http://www.nitrc.org/mailman/listinfo/mrtrix-discussion
>
>
>
>
> -- 
> *David Raffelt (PhD)*
> Post Doctoral Fellow
>
> The Florey Institute of Neuroscience and Mental Health
> Melbourne Brain Centre - Austin Campus
> 245 Burgundy Street
> Heidelberg Vic 3084
> Ph: +61 3 9035 7024
> www.florey.edu.au

-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://www.nitrc.org/pipermail/mrtrix-discussion/attachments/20130315/1a4cf984/attachment-0001.html