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I've also had edge stuff in some ASL results - example below. One possibility is the technique is very sensitive to movement and that shows up on the edges because let's say the brain moves 0.5 mm between a label the next control scan, on the edge there will be a 0.5 mm shift, so that could go from no brain to brain which would give an extremely high difference. Now of course the voxel size is way bigger than 0.5 mm, but since the ASL depends on differences way under 1%, even if a tiny part of a voxel shifts from covering no-brain to brain the intensity will be affected enough to cause a huge "CBF" change.