I think it should be to allow the brain time to heal . I would read it as to allow the brain time to heal .
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tinanam0102Is 'the brain' an object, subject?"To allow the brain time to heal" is not a sentence. I am not a grammarian, and I don't play one on television, but I would call "the brain" the indirect object of the infinitive "to allow".
tinanam0102And