[Mrtrix-discussion] FOD amplitude

[David Raffelt]

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).

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.

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.

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.

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.

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).

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.

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.

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.

Cheers,
Dave








---------- Forwarded message ----------
From: James Cole <james.cole at ucl.ac.uk>
Date: 15 March 2013 04:28
Subject: [Mrtrix-discussion] FOD amplitude
To: 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*

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-- 
*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
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