Interpreting Fixel-based Metrics at b=2000

I imagine this may have been answered previously, but I could not find the answer.

I have multi-shell data (b=0, 1000, 2000, 64 dirs), and I’d like to estimate fibre-density and cross-section as described in the relevant portion of the documention. The documentation notes that b should be greater than 2000 for correct interpretation of AFD and previous work has used higher b-values. I understand that this is because, at higher b-values, intra-axonal diffusion is targeted because sensitivity is maximal for short diffusion distances. But, I still had a few questions to guide interpretation

  1. At b=2000, about how “broken” are the AFD assumptions? My sense is that the intra-axonal signal would still be detectable, but corrupted to some degree by the inclusion of some extra-axonal signal. I’m just trying to get a sense of how large this degree is.
  2. Does this matter less/more if I’m interested in correlations between tract-level metrics and individual differences in behavioral scores? It seems like individual differences in FOD amplitude would still mean something valuable about the tracts even if it partially reflects extra-axonal anisotrophy.
  3. Is there a better term/interpretation to use if the AFD assumptions are (slightly) broken?
  4. Does any of this effect the interpretation of fibre cross-section measures?

As always, thank you for your help!



Interesting questions you raise here…

This is true, but applies primarily to single-shell CSD, since in this case there is no mechanism for handling contamination with CSF. Using high b-values attenuates the free water / extracellular signal to a sufficient extent that it can to all intents and purposes be ignored.

However, given that you have multi-shell data, you’d be using multi-tissue CSD. In this framework, the free water signal and GM signals are explicitly assigned to different outputs, so there is much less contamination of the white matter signal. I’m not sure whether the use of multi-tissue CSD will sidestep the free-water contamination issue completely when your raw data don’t contain sufficiently high b-values, but I reckon it’ll at least do a decent job. I’d be interested in hearing what the others have to say about this, it’s slightly unclear to me how to reason about it…

There is a mild divergence of opinion on this topic… Yes, it will mean that the signal will be affected by the extracellular signal to some extent. However, whether this therefore means that any differences in AFD cannot be meaningfully interpreted in terms of actual fibre density… Well personally I’m not sure it’s necessarily such a big issue: If you detect a 20% drop in AFD, it’s very difficult to see how that could possibly be due to the extracellular signal, given that it makes up ~20% by volume (in healthy parenchyma), and has much lower signal than the WM signal, even at lower b-values. Nonetheless, it does muddy the waters slightly in that it is no longer possible to rule out some involvement of the extracellular space - some of the change may be due to differences in there, although it’s IMO very unlikely to account for the whole difference…

Note the above applies to single-shell CSD - as I mentioned above, it’s not entirely clear to me how that translates to the multi-tissue CSD…

Yes, I’d agree with that - as per my previous comment. If you find a reduction is AFD (for example), by far the most likely explanation will be a genuine reduction in fibre density, even using lower b-values than optimal. So while the AFD measured at lower b-values might not be one-to-one with the intra-axonal space, but it’s still likely to correlate very strongly with the fibre density.

Not one that we’ve come up with, no… But you could always cover yourself by talking about changes in the FOD / fODF or something like that?

Good question. Personally, I can’t see any reasons why it would - these should be unaffected. Again, no doubt the others will have their own take on this…

1 Like

I’ll just add a few words myself. In general, I agree with most things that @jdtournier said as well as the overall take-away message you’d get from his answer. I definitely also want to stress again (like @jdtournier also did a few times) that the answer here is very different depending on whether you’re performing single-shell single-tissue CSD or some form of multi-tissue CSD. All of the “AFD assumptions” and the original papers on that have been written with single-tissue CSD in mind, since multi-tissue CSD didn’t exist yet back then, or even a bit later, wasn’t fully explored and understood yet (some people would also say it isn’t yet fully understood up to this day). So well, this is a tricky story overall, and some things are definitely not set in stone. You might even be surprised what kinds of wild theories and controversies may still pop up in the future. :wink:

So this both makes sense indeed for single-shell single-tissue CSD. This is the essence of the “AFD theory”, if you will, and it indeed only applies like this for single-shell single-tissue CSD.

That’s the big question then indeed. The answer here will always be relative. It’s clear that, when going towards lower and lower b-values, at some point more and more extra-axonal signals creep into your “AFD” (well, let’s just call it FOD amplitude then, to be safe). So when being a purist, at some point, you can’t claim it to be “AFD” any more. But to answer the question “how broken”, you’d need a measure of “brokenness” if we all want to be on the same page.

This is an objective fact, I think we can all agree on this easily.

And this is indeed the more relevant question for most applications (though not necessarily for all). Diffusion data sadly has inherent limitations, and will never give us the full “truly specific” picture. So everything becomes relative. If the signal is still dominated by intra-axonal contributions, even though there’s a little bit of extra-axonal contributions mixed in, it may still be sensible to say you’re detecting a difference caused by changes in intra-axonal volume if your effect sizes are high enough (and the difference is statistically significant of course).

This would then indeed be the safe way to proceed with interpretation. Whether this matters, probably depends on the story of your study (the subjects, the effect that your studying, the hypothesis, external evidence, …). It never hurts to have a strong story backed up by a good hypothesis and other evidence.

They surely still mean something, the problem essentially becomes a slightly reduced specificity on what they mean.

Based on single-shell single-tissue CSD, it may depend. I wouldn’t argue directly against the word “likely” in there; for many pathologies this definitely makes sense (a priori or due to other external evidence). But in the absence of a sensible hypothesis, or even in the presence of some alternative hypotheses (note: not “alternative facts” :stuck_out_tongue_winking_eye:) there’s definitely some room for an “it may depend”. Let’s not forget the so-called “AFD” is also still T2-weighted. It’s surprising to see that a lot of people overlook this (even though they may in principle know and understand this).

FOD amplitude is indeed a safe description, it doesn’t come with any interpretation in an of itself. If you really want to go back to the source, you could also say something like “diffusion-weighted T2-weighted signal”. Single-tissue CSD retains that signal entirely; “all it does” (not trying to minimise the impact of CSD here) is redistribute that signal in the angular domain. It takes what was originally sitting in a smooth disk-kind of shape and puts that along an orientation; but everything is “taken” and “put” again, so the entire FOD angular integral still reflects all the signal (entire DWI angular integral). If you simply sum (or average) all your single-shell diffusion weighted images, you’ll get the same image (contrast) as the first volume in the single-tissue FOD image (the DC term, reflecting the integral).

But of course, in most studies you wouldn’t want to stop just at such terminology. If there’s no chance at any interpretation at all, the finding quite often loses a lot of its value.

Fully agreed. The interpretation is not affected, and (as opposed to for the AFD case) no biases are introduced, since the FC only depends on the warps of your data to a common template space. The only way in which lower b-values have an effect on this, is that they reduce the angular contrast-to-noise ratio, which in turn results in a slightly messier FOD at some point (but b=2000 is still very safe on that front, in my experience). This then means that the FOD-driven registration algorithm, as well as the fixel segmentation later on, are also slightly less precise. This then results at some point in more variance of the FC across your studies population(s). This then finally results in less power in your study. But no introduced biases in principle. So the interpretation of FC is safe. Note that the FDC metric factors in the effects of both (A)FD and FC though, so there you’ll get the whole story about the (A)FD of course again factoring in as well.

So all of my answers above are all about the single-shell single-tissue CSD case. Going multi-tissue CSD, a lot of that changes. Some extra-axonal things do end up in other compartments (there’s a lot of other mess besides axons in the brain). Funny thing being that this directly challenges certain aspects of the original AFD notion itself… The effect of using good old single-tissue CSD may actually end up being that you miss certain decreases in “what should’ve been AFD” (or something like that). In a good range of white matter pathologies, it’s not uncommon that decreases in intra-axonal space (axons dying or otherwise deteriorating) are accompanied (potentially with a time delay) by increases in the presence of other (glial) cells. Some of the latter may (or may not) result in an overestimation of “AFD”. So your decrease potentially gets (partially) compensated by an increase, and your effect size decreases. That’s why multi-tissue should certainly be considered instead.

However (this really never ends, does it?), you can then ask the question of where the limitations of multi-tissue CSD lie, in terms of the maximum b-value you’ve got access to. It’s clear that e.g. having b-values of b=0,200,500 or something like that will not really give you the information (contrast) that you’re looking for. The angular contrast-to-noise ration still plays a (very) important role in getting those tissues untangled, and for that, a high b-value is preferred. The inclusion of low b-values may even hinder that significantly. It’s a complex story…

And at the end of the day, all of these techniques still assume a fixed-shape (angularly and radially) response function, at most for a few distinct tissue types. While this seems to be conveniently “ok enough” for the case of developed humans, it may be a different story in other cases. I’m sure @jdtournier can already entertain you with quite a few stories over a beer or two on how fun this becomes e.g. for neonates. :wink: I’m keeping my hands (and mind) off public insights and opinions on that topic for now… :stuck_out_tongue_winking_eye:

Thank you @jdtournier and @ThijsDhollander! This is all very helpful. I hadn’t thought about the implications of the multi-tissue framework here; great points! Fortunately, I am looking at individual differences between developed humans without any clinical pathologies, so I may be able to conveniently side-step some of the more thorny issues. I suppose my interpretations/descriptions will ultimately depend on the data and other metrics we’ve collected, with possible interpretations ranging from “individual differences in FOD amplitude (which may reflect x,y,z)” to “individual differences in AFD (with potential caveats x,y,z)”.

As always, thank you for your thoughtful responses. I definitely owe the MrTrix team a few beers whenever I’m in the area.


1 Like

:+1: That sounds perfect! Which interpretations are “reasonable” does indeed depend on the context, including all data and metrics collected as well as any prior hypothesis you may have.

I can only hope you’ll be in Paris for ISMRM then! :sunglasses: :beers: