We ran a Fixel analysis on a dataset, and had a question about the interpretation of the fiber density cross-section metric. Specifically, we see results for FD and FDC, but not FC. Does this mean that the FDC metric is not additive (derived from FD and FC) but calculated as an interaction between these two metrics?
When you say ‘see results’, I’m guessing you mean fwe_pvalue < 0.05?.
One explaination for not observing significant fixels in the FC analysis is due to variance. In general, there is larger variation across subjects in brain morphology than aFD. This is particularly true in certain structures like the CST and splenium.
No, it’s multiplicative FDC = FC x FD. So both FD and FC contribute to the effect size of FDC.
One way to get a feel for what is going on is to look at the absolute effect size with respect to the control mean. We have documentation on how to compute this in the upcoming release (see the fixel-based analysis section). If you have been using the soon-to-be-legacy *.msf format to store fixels, you can convert them to the new directory-based format using fixelconvert (also available in the tag_0.3.16 branch. If you want to install this, be sure to either do a fresh clone and install, or run ./build clean && ./configure after checking out the branch)
Finally, if you have significantly different FDC fixels, in the same region as FD, but with a reduced effect or spatial extent, then perhaps not having a significant result in FC makes sense.
Such a result makes perfect sense. We often say something like “FDC is a combined metric of FD and FC”, when we formally mean FDC = FD × FC (these are the original metrics). Of course, that doesn’t mean that the stats results (or significant fixels) are “additive”: to put it simple, the stats also bring the variance of the metrics in the populations into play. In your case, seeing a result for FD and FDC, but not for FC, can mean that there was genuinely no difference in the FC (or the variance was too high, and the study underpowered to detect it). The fact that you still see a result for FDC, must mean that the power to detect FD was high enough that it could potentially cope with the added variance of FC still… or that there was some difference in FC, yet too much variance to bring it out on its own in the FC result, but there was a clear difference in FD in similar areas; so both effects “reinforced” each other in the FDC metric.
But in any way, in your case you can only safely (statistically) say that there is a difference in FD. While there is a difference in FDC, this does not imply a difference in FC, since FDC is not specific to either FD or FC (it literally factors in both).
I`m comparing groups of healthy controls and patients with a neurodegenerative disease using a fixel analysis (SS3T-CSD). As a result, I found increased (pfwe < 0.005) logFC and FDC in the motor tracts of the patient group, but no changes in FD. Previous studies have also consistently showed increased FA and decreased MD in these areas.
My results (increased logFC and FDC) might suggest the neuroplasticity of the motor tracts. However, a histopathological study has demonstrated axonal sprouting resulting in increased axonal density (but no change in FD in my study) as a result of compensatory mechanisms.
I`m thinking about these possibilities as the causes of increased logFC and FDC and no change in FD:
Yep, that’s possible. Not finding changes in FD doesn’t per se mean they aren’t there; you might’ve just lacked the power to pull them out as statistically significant. Also, there are limitations to the specificity to separate FD from FC effects. From a certain perspective, and in particular contexts, FDC is the safer but less specific metric. FD and FC can indicate a more specific source to the difference, but while theoretically reasonable, there are practical limitations. The separation of FD and FC effects is a bit blurred, so as to say.
This sounds like a very reasonable interpretation. That interpretation itself is indeed also in line with increased FA and decreased MD from other studies.
Yep, so as mentioned the key here is: don’t interpret “not finding statistically significant effects” as “there’s no change”. Due to the aforementioned degree of blurring between FD and FC, an amount of FD effect might also slide a bit into FC.
Theoretically, all very reasonable. Briefly:
Yep, that is compatible with the result you’re getting.
This one just as well. Note that with either FD or FC, we can’t separate this scenario from the previous one (1). Both are a case of increased “total” intra-axonal volume, regardless whether that extra volume is created by (or “in”) new or existing axons.
Note also that this might happen over time differently: i.e. initially the density (“FD”) might increase because axons are added or grow in size, but maybe eventually the density gets back to “normal” by stuff spacing a bit more out again, leading to increased FC. So your result might depend on the timing of the scans. This has in fact been observed before in neurodegenerative diseases, I believe: first a decrease in density (“microscopically”) followed by (“macroscopic”) atrophy. Similar idea possibly, but then in a degenerative fashion of course.
This is again possible. If it would be “purely” this effect, and it would cause enlarged tract diameter, this probably implies axons moving further apart (not counting myelin as part of “axons” here). Again theoretically, FD would then go down.
But once more, the gist is, this is very “theoretically”.
It might even be a combination of some / all of these. And we’re not even talking about what would happen if the T2 of the tract changes. And what b-value you’re using.
Ok, I think you’re getting the picture here, but there is a reasonable way to deal with all of the above though:
Context is key! The above has limitations and at some point there’s no going beyond those purely “theoretically”. So essentially, the information is going to have to come from somewhere else to complete the picture. Here’s where previous literature on this condition is important, I think: surely there will have been (hypothesises) explanations already in the literature on this (e.g. is it possible or expected that new axons appear? e.g. is there a use to axons growing in diameter? e.g. is increased myelination not more relevant to function? …etc…). Some of your points above might be compatible with that. So there’s a discussion section to be written basically. Your results will surely contribute, but on their own, they can’t ultimately prove or provide the very specific answers to the question at hand.
That said, I think your points are very well formulated; certainly none of them are incompatible with the results. Finally, just to get you thinking maye: increased FD, or FC (or FDC) isn’t always a good thing, biologically. Indeed, certain kinds of inflammation might also cause this. Many people are naturally focused on investigating decreases in these metrics in different conditions, but increases might come with equally important information. And even more finally: because that’s the case, effects may cancel each other out just as well to certain degrees. Another limitation to specificity!