What is the appropriate test?

I have a program that automatically segments a region of an image of a subject, then also splits into a number (say ~10) of subregions, calculating each of their sizes.

My statistical question that I would like to take multiple images (4) from the same set of subjects (N~30), and test the consistency of relative sizes of these subregions. More specifically, I'm not as much interested in the absolute size of each subregion, but rather normalized to the overall region volume (i.e. a proportion).

So to summarize, I'll end up with 4 sets of 10 proportions across 30 subjects, and I would like to ask whether these 4 sets are different (and secondarily, if these is a difference, some kind of post-hoc test to ask more specifically which subregions are different). I understand that obviously these 10 proportions are highly dependent on each other, and similar each of the 4 sets of 10 proportions is highly correlated with the other 3, as they are derived from very similar images of the same subject (i.e. repeated measures).

Is this a situation where GEE is appropriate? I'm at a bit of a loss as to what test is most appropriate...