[Mrtrix-discussion] tck2connectome -invnodevolume metric

[Robert Smith]

Hi Timo (and all),

So there's two separate 'corrections' for streamline count applied in
Patric Hagmann's 2008 paper:

   1. Weighting according to the inverse of the streamline length, in order
   to 'compensate' for the increased WM seeding volume of longer pathways.
   2. Weighting according to the inverse of the surface areas of the nodes
   of interest, to 'compensate' for the fact that a larger node is likely to
   have a larger number of streamlines terminating within it than a smaller
   one.

In the case of 1., you're absolutely right: as soon as you use
interface-based seeding and/or SIFT, the mechanism leading to the bias that
the heuristic is trying to correct for is no longer present, so that
correction is not 'not needed' so much as erroneous. Note however that this
is the 'invlength' metric in the tck2connectome command.

2. is the 'invnodevolume' metric. It calculates the volume of each
parcellated node simply by counting voxels and dividing by the voxel
volume, with the underlying assumption that the grey matter - white matter
interface surface area of a node is directly proportional to this volume (I
believe the same assumption was made in Hagmann's manuscript). The
contribution of each streamline to the connectome is then modulated by the
reciprocal of the mean of the two node volumes.
Personally, I would expect that a physically larger parcel of grey matter
*should* have a greater number of axons entering/exiting it, and a larger
number of streamlines is therefore reflective of this, with or without
SIFT. (In fact, there's evidence to suggest that the physical size of
cortical regions is largely driven by the density of white matter
connections necessary for their function). By applying this heuristic, the
values in your connectome matrix become more akin to 'the proportion of all
connections to/from node A that connect to node B', rather than an absolute
connection count between A and B (not a precise analogy, but close enough).
So it really depends on what you're trying to achieve with a connectome
analysis, and will affect the interpretation of any network metrics you
derive.

Bear in mind that these heuristics were derived to try to compensate for
biases in streamline counts relative to biological fibre counts, but they
do so in a relatively naive way, i.e. there is no feedback regarding
whether or not these biases have actually been corrected. In the case of
1., we can prove that the reconstruction errors are *not* adequately
corrected. SIFT directly corrects the mismatch between streamline count and
underlying fibre density, without making any assumptions about how the
mismatch arises mechanistically. And of course: if the local streamlines
densities are proportional to the underlying fibre densities, and the
streamline trajectories are correct, then the streamline connection counts
should be proportional to the underlying fibre connection counts (insert
many asterisks here); so the streamline count is the most likely
connectivity metric of interest.

Happy ... connectomics-ing?  :-P
Rob


--

*Robert Smith, Ph.D*
Research Officer, Imaging Division

The Florey Institute of Neuroscience and Mental Health
Melbourne Brain Centre - Austin Campus
245 Burgundy Street
Heidelberg Vic 3084
Ph: +61 3 9035 7128
Fax: +61 3 9035 7301
www.florey.edu.au

On Tue, Nov 18, 2014 at 10:28 PM, Roine Timo <timo.roine at uantwerpen.be>
wrote:

> Hello everyone,
>
> Another question regarding tck2connectome:
> How is the invnodevolume metric calculated and could it be used to
> calculate the density-weighted connectivity?
>
> In Hagmann et al. 2008 this kind of weighting is calculated with respect
> to average cortical surface area of the end point nodes (number of
> connections per unit surface). When using WM-GM interface seeding and/or
> SIFT, I believe the correction term 1/l(f) (in Hagmann et al., 2008) for
> the bias in tractography towards longer fibers is not needed anymore.
>
> Thanks in advance!
>
> Cheers,
> Timo
>
> PhD candidate,
> iMinds-Vision Lab, University of Antwerp, Belgium
> timo.roine at uantwerpen.be
> _______________________________________________
> Mrtrix-discussion mailing list
> Mrtrix-discussion at www.nitrc.org
> http://www.nitrc.org/mailman/listinfo/mrtrix-discussion
>
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