I would like to continue on this topic by asking for advice if one has a longitudinal study design that includes more than two time points.

My suspicion is that you might be the first one to do this using FBA. Hope you’re up for the challenge!

Next, combine both spatial transformations (`transformcompose`

) and apply them to the native space FOD maps (`mrregister`

)? This way all FODs are transformed to the population-based template space, right?

The key here is not so much that FODs get transformed to the population-based template space, but that this occurs with a *single interpolation step*, and intra-individual alignment is not impacted by the potential variability introduced by registering each scan from that subject to a population template rather than an individual-specific template.

For the statistical analyses, would it be possible to do a repeated-measures ANOVA or mixed model analysis? Alternatively, if that would not be possible, would it be a sound approach to, like fMRI, compute a first level (within-subject) statistical test to identify fixels that exhibit a significant main effect of time for e.g. FD? And then for a second level (group) analysis, perform e.g. a one sample t test to identify those fixels that display a consistent change over time across all subjects of the group? Or a two sample t test to compare for differences over time effect between two groups?

`fixelcfestats`

uses the General Linear Model, just like basically any other neuroimaging software, and the underlying raw fixel data can be manipulated using any arbitrary mathematical manipulations. So if you can determine what the recommended processing pipeline would be for an equivalent experiment using fMRI data, I see no reason why you shouldn’t be able to do exactly the same operations for fixel data; though the incoming software changes may be required for various aspects. I would also suggest looking at the two new commands created as part of those developments and strongly consider their use in the context of your more complex experiment.

As far as two-level analyses go, I’m most certainly not experienced with the details of fMRI data analysis, but I would have presumed that the first-level analysis is not about finding a *significant* main effect of time (and then looking for *consistency* of such binary identification of such across subjects), but simply quantifying a parameter of interest from the individual subject data (e.g. rate of change over time; equivalent to simply performing a subtraction between two time points, but generalised to more than two scans), and then taking the map of this parameter for each subject and performing a group-level analysis (e.g. to determine if the group mean is non-zero). I suppose either approach would technically be statistically sound; but the quantity being derived, and hence the hypothesis being tested, would be substantially different between the two.

If you’re looking to e.g. reduce the 6 timepoints per subject to a scalar rate of change over time, this could be done using the `-notest`

option in `fixelcfestats`

; this will provide you with the regression coefficients for your particular intra-individual design matrix, which, if constructed appropriately, one of which should correspond to the rate of change over time.

As far as “what test to do”, I’ll repeat my usual schtick when it comes to the GLM: You need to define what your hypothesis is, with sufficient accuracy that you can then build your design and contrast matrices accordingly. In my own experience it tends to be a lack of specificity in one’s hypothesis that leads to uncertainty as to how to operate the software.

Also shout-out to this document that describes the relationships between common statistical test terminology and linear models.