Inconsistent results of connection density

Hello everyone,

I am facing a puzzling issue and hope to get some ideas on it. My ultimate goal is to get connection density-behavior correlation for some specific bundles across subjects within the group. Thus, the pipeline is as follows: group response function estimation followed by mtnormalize. whole-brain tractogram(500k), pathways reconstruction with considering -number (e.g., 10k) and -seeds 0 (four pathways with varying ROIs seeds), outliers removal, merging pathways and WB, sift2 (with -term-mu), extract pathway of interest with associated weights. finally, FBC is calculated as summed weights multiplied by mu. Following the recommended method (shoutout to @rsmith for publishing such an informative paper) for FBC considering inter-subject comparison, this metric is calculated by multiplying mu and summed weights. Just to mention that after refining pathways, the streamline counts do not remain identical among subjects.
I expected to see a decline in connection density with age. however, it is not achieved. I looked closer to data and noticed there are subjects with smaller brain volume ( and wm) having more streamlines in the bundle, and young subjects with a larger brain and fewer streamlines. For instance, I write down these two subjects as a sample, however, this can be seen to some extent to others as well.

I assume that FBC should not be influenced by the number of streamlines, but it also doesn’t biologically make sense that someone with less brain volume is getting more fiber density because of having more streamlines.
Do you have any recommendations? One way might be to keep streamline numbers identical when extracting pathways after sift2, although it has its drawbacks. But since streamlines vary among the group (2300-3500), then dropping ~ 1k streamlines for some subjects might bias the results.


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Hi @NeuroSh,

Ah yes, another case of SIFT2-derived connection density estimates having the opposite direction of effect to that expected… I seem to be collecting these! Maybe I accidentally left a negative sign somewhere in the code… :clown_face:

sift2 (with -term-mu)

tcksift2 doesn’t have a -term_mu option; indeed the value of mu does not change at all within the SIFT2 algorithm. tcksift has a -term_mu option (the original intent of which was actually to obviate the need for explicit multiplication by mu); but if you’re using that, you’d need more than 500k streamlines, and you wouldn’t be dealing with weights. Maybe you meant -out_mu?

Just to mention that after refining pathways, the streamline counts do not remain identical among subjects.

This would also be the case without refining pathways: the number of streamlines within the original whole-brain tractogram that are appropriately ascribed to the pathway of interest and hence also contribute to that count would also vary between subjects.

I assume that FBC should not be influenced by the number of streamlines, but it also doesn’t biologically make sense that someone with less brain volume is getting more fiber density because of having more streamlines.

It’s not quite correct to say that FBC is elevated “because of having more streamlines”, since that excludes the possibility of differential streamline weights. If an elevated streamline count (for whatever causative bias) was not supported by the image data, then those streamlines should be down-weighted in that subject, and hence the sum of streamline weights would not change. What makes the situation more complex is considering:

  • The effect of regularisation within the SIFT2 solver;

  • The prospect that that elevated streamline count within the pathway of interest may not be just because there’s an isolated elevation of streamline count within that pathway, but because streamlines are traversing that pathway instead of adjacent pathways. So the total fibre density encoded within the image data is comparable across subjects, the total number of streamlines in that general region of the brain is comparable between subjects, it’s just that more streamlines within that general region are being ascribed to the pathway of interest rather than not.

I would also contemplate the effect of intracranial volume carefully. For instance, if you include ICV as a nuisance regressor in a GLM, does that gobble up the negative association between your behavioural measure and FBC? I would not think that minor differences in ICV would drive T2 differences of sufficient magnitude to influence FBC (since it does rely on AFD, which in turn is sensitive to T2).

One way might be to keep streamline numbers identical when extracting pathways after sift2, although it has its drawbacks.

If you wanted to attempt that path, I think what you would actually want is an equivalent number of streamlines within the pathway of interest in the concatenated whole-brain tractogram, which is more difficult again :-/

  1. The first thing I would suggest is using a more dense whole-brain tractogram and abandon the targeted tracking. While I’ve presented the combined-whole-brain-targeted-tracking as a hypothetical solution to the problem of streamline discretisation effects in very small bundles, it does act in tension with the SIFT2 regularisation. If you can get enough streamlines within your pathway of interest without using targeted tracking, that would be preferable in that respect, and reduce the complexity of the machine you’re trying to debug.

  2. What’s not shown here is the magnitude of the counter-intuitive effect relative to the variance in the data. While I’ve not interrogated it super-extensively, I do know that the variance in connection density estimates is a lot larger than would be desired for experiments such as these, and for minor bundles it can be very large indeed. So it’s possible that observation of the opposite of the expected effect is just by chance because you’re down within the noise.

  3. Running FBA on your cohort would certainly be interesting. While FBC may physically be the measure that most appropriately captures your property of interest, being endpoint-to-endpoint connection density, I do believe that FBA has considerably less intrinsic variance, since it doesn’t rely on subject-specific tractography (I’ve just never gotten around to testing that hypothesis).

  4. If continuing with the combination of targeted tracking & whole-brain tracking, you could try decreasing the strength of the regularisation. This will give streamlines greater flexibility to obtain small / large weights relative to their neighbours, and improve the fit to the model data; but be wary of individual streamlines obtaining huge weights, which has a comparable effect to using too few streamlines.

  5. If you really want to get neck-deep in trying to understand this stuff, consider this.
    Imagine that for those with the behaviour expected to correlate with increased FBC, the AFD along that pathway is elevated compared to others. Now in the iFOD2 algorithm, there is a minimum FOD amplitude threshold applied, such that directions for which the amplitude is lower than that threshold are not considered. If the AFD of a lobe is larger, then a larger portion of that “lobe” is above that threshold; whereas for a subject with a very small AFD, e.g. with a peak amplitude only just above the threshold, the FOD amplitude exceeds the threshold only for a tiny range of angles. These are the samples that are used for determining streamlines trajectories. So a set of streamlines within a dominant WM bundle with large AFD may exhibit orientation dispersion greater than that of a non-dominant WM bundle with small AFD.
    So if an AFD elevation w.r.t. your behavioural measure were present within that pathway, but constrained to just your pathway of interest and not the surrounding WM, this could result in more streamlines straying outside of the pathway of interest during propagation, intersecting some other structure, and not being attributed to your pathway of interest, hence leading to a negative correlation with FBC.
    See?! It was @jdtournier’s fault all along. :rofl:

There’s a bunch of experiments that could be done here to try to diagnose; things that I’ve been thinking about for the last ~ 8 years but never committed to doing. So try a couple of things if you can, and see how invested you are in interrogating further.


Hi there,

I have a related question. I extracted the FBC measure (summed weights x mu) per individual after extracting certain pathways of interest from a whole-brain tractogram obtained using iFOD2 followed by SIFT2. From the preprint I understood that this measure “does not scale with the number of streamlines generated”. However, the correlation between the FBC measure and the number of streamlines in the extracted pathway is 0.9 for my data. I am wondering whether I did something wrong or whether I maybe misunderstood?

Thank you for all of your help!

Best wishes,

Hi Klara,

I think this is perhaps too strong an interpretation of that specific quote outside of its intended context. A better phrase in the context of the particular evidence being presented at that point in the manuscript would be something like: “When using streamline count as a quantitative metric, if you were to generate twice as many streamlines in one subject compared to another, you would erroneously conclude that the pathway possesses twice as much connectivity in that subject; whereas if you appropriately scale by mu, you would not make this mistake”.

When not artificially modulating parameters between subjects as is done in that particular experiment, yes, I would expect there to be a pretty strong correlation between streamline count and FBC. You need only look at the nature of the regularisation, seeing that streamline weights are driven to be close to 1: for FBC to not be strongly correlated with streamline count would require streamline weights that are drastically greater than or smaller than 1, and for that to occur across a large proportion of streamlines belonging to a particular bundle. While it can happen if there is adequate evidence provided by the combination of tractogram & image data, in reality the reconstruction biases that introduce imperfections into the streamline count metric are somewhat comparable across subjects, and so the way in which FBC modulates itself relative to streamline count will also be comparable across subjects, hence the high correlation.

The main motivation for SIFT(2) was moreso the modulation of connection densities of different pathways within the same subject. As per the preprint, the mathematics does extend to comparison of connection densities of the same pathway across different individuals, but given it’s based on the same tractogram reconstruction as is streamline count, and the manifestation of streamline count biases are somewhat consistent across individuals, the high correlation isn’t surprising to me. The harder question is whether it is more or less sensitive to genuine biological differences; I’d certainly argue it’s more interpretable.


Thank you so much for the explanation, Rob!