You can choose an arbitrarily large vessel (e.g. you can argue that you are your body + your immediate surroundings). But the brain seems to be the smallest such vessel which still leads to an indistinguishable result.
We know from neurosurgery that some fairly large parts of the brain can be removed without apparently adversely affecting the subject's sense of self, so it seems it must be more complex than drawing a boundary around the gross anatomy of the brain.