However, if you want to ensure longitudinal effects to stem from intrasubject differences then the only way this can be ensured is through a 2-step registration (non-linear to within-subject template + non-linear to general template.
I’m not sure I would say so definitively. Imagine that you have images of newborns, then the same subjects imaged at 18 years. You generate some template, and then independently register each time point to that template. You then quantify FC and find a huge longitudinal difference between the newborn and 18-year time points. Would it be accurate to say that one “would not be sure if that effect stemmed from intra-subject differences”? Perhaps if you literally did a group-wise comparison, completely ignoring the fact that the same subjects were included in both time-point “groups”, one could philosophically make that argument, even if absurd for this extreme example. But that’s also not what’s done in @sgenc’s paper. The within-subject difference over time is explicitly computed, and it is these values upon which statistical inference is performed.
Fundamentally what I think you’re suggesting is that, instead of:
- Non-linearly register each time point independently to template;
- Quantify FC for each fixel in template space independently for each time point;
- Calculate the difference over time per subject;
, one could instead:
- Non-linearly register the two time points per participant to one another;
- Non-linearly register the participant template to the group template;
- For each fixel in the group template, quantify FC from step 1 at the spatial location determined by step 2.
This is theoretically possible. It would depend on the trustworthiness of non-linear image registration between time points, for which the intrinsic variance will differ from that of two independent non-linear registrations to a smooth group template. You would also need to decide whether FC gets quantified based on the group-template fixel reoriented into participant template space, or based on the orientation of the “corresponding” fixel in the participant template. I would expect that @Dave probably made this decision at the time based on the existing VBA literature, but I’m not as familiar with that literature myself.
Maybe there’s a student project in here?
Note also that your proposal would be highly dependent on the registration process being perfectly symmetrical. If, for every subject, you were to asymmetrically register time point 2 to time point 1, quantify within-subject longitudinal changes from that, then warp those data to a group template and perform statistical analysis, any statistical effect observable across the group could be a manifestation of internal biases of the asymmetric registration algorithm and/or the presence of image interpolation effects at one time point only.
There, the longitudinal design originates solely from the template creation, but registration is performed in the traditional FBA pipeline way. Is this correct?
Well, the experiment overall has a longitudinal design, both in data acquisition and analysis. It’s a question of where the nature of that experimental design comes into play relative to image registration. One could I suppose indeed say that in that study “registration was performed in the traditional FBA pipeline way”, but that is only because deviation of the example pipeline to handle longitudinal data occurred primarily (i.e. ignoring details of group template creation) after registration to group template (by explicitly quantifying within-subject differences between time points) rather than before registration to group template.
I hope that clarifies rather than obfuscates 
Rob
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